mil std 414.pdf - Variation.com

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MILITARY STANDARD
SAMbLING PROCEDURES AND
MIL-STD-414
11 blvs7
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~M
ORfkMOO$-10
FOR INSPECTION BY VARIABLES
FOR PERCENT DEFECTIVE
TABLES
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mL-sTD-414
11 JEW 1957
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OFFICS OF TEE ~ANT SECRETARY OF DE~
Wuhlngkm $5, D. c.
Supply and Logi.ti.. 11 JUIU lb7
Sarnpflng Procedures and Table. for fa.p. ctlo. by
Varl.bl.. for Pe=cent Ddectlva
MIL-STD-414
1. Thi. .tandard h.. ~en approved by the De Pru’ne.t of Defense
and i. mandatory for . . . by the Departm. rAtoof the Army, the Navy. and
the M. force, ●ffectivm 11 June 1957.
2. h ●ccordance rnth e.tabli.bed proc.dur., the Sfandardi.. ticm
Diwl. im k.. d-.ifp.t.d tha Chemical -Carp. Bureau of Ordnance. -d
Air For.. , r.. p.ti..ly, . . Amp N.v-Air For.. custodian. .1 thi.
.tandard.
>. Recommended correction.. sddltlenn, or deletion. .hould be
●ddr . . ..d to the Stanbrdi. atior. Divi. iom, Of fic. of the As. imta.t Sec...
aary of Def.a.e (Su@y and Logistic.), Wa.hin@an Z5. D. C.
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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SECTION A GENERAL D&9tiRIPT30N OF tibfPL3t4G PL.#JS . . . . .
Table,:
Table A-1 U3LConveraion Table . . . . . . . . . . . . . . .
Table A-2 Sample Size Code tiNers . . . . . . . . . . . . . .
Table A-3 Operating Char.cteri*tie Curve. 10. Sampfiq
Plmm of S.ctiOa# B, C, and D (Graph- for
San@. Sise tie Letters B though Q) . .
SECTION B VAR3ABIL1TY UN3U40WK-STANDARD
DEV~TION METHOD
Par: J SINGLE SPECIFICATION LIMIT . . . . . . . . . . . . . .
Ex8mpl. *:
Example B- I
Example B-2
Table.:
Treble E.- I
Table B-Z
Example of Cdcafattoiw:, Simgle
sPeciflcatiOn fAmil-Form 1 . . . . . . . . . . .
Example of Calculations: Sin~le
Sp*cificatiea Ltmit-l%rm 2 . . . . . . . . . . .
M..ter Tabie for Normal ●nd Tighteoed
3nmpecti0n (Form l-Sinnle fAmit) . . . . .
Maater Table for Redueed impection
(sOrrnl-singl. LiJnii) . . . . . . . . . . . . . .
Part H DOUBLE SPECIFICATION UhUT . . . . . . . . . . , .
Examplea:
Example B-3
Exarn@e B-4
T, blem:
Table B- 3
Table B-4
Table B-5
tiample of Cdcrdatiomm: Double Specifi.
c8tioa LAnit-Cke AQL vai.4 far Upper
and Lawe r Specification Limit Combined
Example of Calculatinna: Double Specification
Umit-DIfferem AC3L values for
Upper sud fmwer Specification Umitm .
Mmmter Table for Normal ●nd Tightened
Impecti.n (Double Limit and f%rm 2siIl#le
LiInif) . . . . . . . . . . . .. . . . . .
Mssier Table for R=duced faspectiom
(Double LImitmnd Form Z-Single Limit)
Table for 3SatimatiaEthe Lot P. rcent
De fective . . . . . . . . . . . . . . . . . . . . .
. . .
. . .
. . .
Part f3J EST1MATION OF PROCESS AVZSAGE AND
C3UTE- FOR RZDUCEL AND TIGHTENED
INSPECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table, :
Table B-6
Table B-?
Table L-8
APP=dk B . . . . . .
. . . . ..-
. . .
. . .
Value. of T for Tigbtenad k#p8!cti011 . . . . . .
~ts of Estimated k; P.rcent
Defective far Roduc=d Inspection . . . . . . . .
Value. of F for h4asimum Standard
Deviafioa.[MBD) . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
‘iii
Esu
“ii
1
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5
35
37
38
39
40
41
43
44
45
46
47
5?.
54
56
58
59

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xlL-mTb414
11 Juts 1097
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coNTmzTa-caitinmd
SECTION C VASliABILfTY ZINKNOWN-~S METHOD
Part 1 sU40LSSPECZF1CATION LZMIT . . . . . . . . . . . . . . . .
kxmlfb:
E8urlph c-l Eauanph of Ckicniatidm: Simsle
S~cificatiOa Umit-FOrm i . . . . . . . . . .
3hampie C-Z Exuriplm of Cakuiati0a9: StnSle
Specification Limit. Form 2 . . . . . . . . . .
Tsblea :
Tsbie C-1 Mast-r Tabie for Normal ●nd Tightene4
Inspection (Form I_ Siql. Limit) . . . . . . .
Tabi* c-z Msst.r Tabls for Reduced lnapecUorI
(FOrml-SiOgl. LImlt) . . . . . . . . . . . . . .
Part u DOUBLE SPEC1IVCATION L3M3T . . . . . . , . . . . . . . .
Exaf+em:
Ex.mple C-3 Example of Caleulxtioms: Doubl. Sp.eUi -
catiem LiniIt-Oae AQL value [or Upper
and tiwer Spocifieu40m Limit Ckmblaed . , . .
Example C-4 Exunple o{ Caiculaiiom: Double Specif{ -
c-ion Limit-D4ifar8st AQL vahm. for
UpPer u8d Lower SPRIcZflcacJon LImitm . . .
Table,,
Table C-3 A.hmI.r Tabl. for fdmnul .md Ti#hte.ed
~P=c~a (-ble Limit 4 Ferm z _
Sias!e Z&nit) . . . . . . . . . . . . . . . . . . . .
Table C-4 Maater Tabl@ #or Reduced lmpectiom
(Dauble L&nit - Fown&Simgle IAnIt) . . . .
T.ble C-5 Ttile for Ectinmiinsthe Lot Percent
Dekctive . . . . . . . . . . . . . . . . . . . . . . .
Part Zu ESTIWTZON OF PROCESS AVIXfAGE AND
cRZT3ZRJA PVR REDUCED AND TZOHTSNED
INSPECTION . . . . . . . . ., . . . . . . . . . . . . . . . . . . . .
Table.:
Table c-6 Vaium. of T Ior .Tigbtmmd h,pecticm .“. . . . .
Table C-7 z-bits Of Eotiated kt S%rcemt
Defective for R.duced Z.cmp.ectioa. . , . . . . .
Tablo C-8 Value. of ~ 10, M&um Awe ra~e
Rsn#e(w) . . . . . . . . . . . . . . . . . . . . .
APWIUUB C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SEC7WN D VARZASZL3TY WWN
P8rt 1 SZNOZ.E SPSCW1GATZON3A3AZT . . . . . . . . . . . . . . . .
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Exmpleo :
Exumple D-l ZZxampta of Caieubtlms: Siasis
*c4fkati0n Z.imit-rofm 1 . . . . . . . . . .
&urnpZm D-3. Example of c+IeuidzioM: Si+e
Smcification ZAtaia_FOsm Z . . . . . . . . . .
Ttbim.,
Tabic D-l Msst*r Table fof Normal d Ti#btened
Zzmpoeuom {Form 1-Sk+ Umlc) . . . . . .
Tmbb D-Z titer Table [or Reducmd tJ1.p~=tiO_
(FOrml-Slr@*LimitJ . . . .. . . . . . . . . . .
61 .
63
64
6S
66
b7
69
70
71
7Z
73
80
B2
84
85
ST
89
90
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P*T5 u DOUBLE 5PECfF1CAT10N LlhffT . . . . . . . . . . . . .
3hampfe*:
3kAmpfe D-3 Esampk af Cdctdationw Double SpecUication
L6mit-Oa* AOL vahm UpPar and
fmwer Specification. fAmit Combirmd . . . . .
Exunple D-4 Emmple of .Calculatioms: Double +pecUi -
c-tion L6mit-D3ffereut AOL value- for
UpVr d kwer Specification Limits . . . .
Tables:
Table D-3 Master T*le for Normal and Tightened
fn. pectim (Double Limit and Form Z-
Simgleumlt) . . . . . . . . . . . . . . . . . . . . .
T.bla D-4 Master T&ble for Reduced 3nop.ctiom
[Ooubk Limit..d Form Z-Single Limit) . . . .
T.ble D-5 T-ble for Estimating the fat Percentage
Defective . . . . . . . . . . . . . . . . . . . . . . . .
P*rt Ul SST1MATION OF PROCB AVESAG!C AND
CSJT&R3A FOR REDUCED AND TIGHTENED
INSPECTION . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .
Tsble#:
Table D-6 Value. of T for Tightened frt. pection . . . . . .
Table D-7 Limit- of Ectinutod IAX Percent
Defective for Reduced hmpecfiom . . . . . . . .
APP*6 D........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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98
99
101
103
104
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INTRODUCTION
mlL-8’m-414
llhfislm?
Thi. Stamdardwa. prepmred to meet ● growing IIeeo for tbe U. of standard
●u’npliq ptmm for Jampection by vari*ble. in ti~rnmatn procurement, DIIpply
and .torage, and maintenance ia.pciion opa ratiozm. Tbe variabf.. sampJ&s
plane .pply to ● ●in@e quality characteristic which can be rnea.tirmd on ● coattntm..
scale, and for which quality i. ●xpressed in term. cd percent de fectiue. The
theory unclerlying the developrne.t of the wari.bte. .aniplim~ plaua, including the
oparatiq charact=rimtic curve.. a.awne. that rnea.urem.mt. of tba quattty char.
●cteristic ●re independent, identicslfy di.tribufed normal random varisblea.
1. comparium with atfributa. ..mpfing pfmn., warlah!es umpfiag plamm
have tbe ●dvanta~e of ummfly remdtin~ & cmmide rsble .avinem in #ample ●ifor
.xmnparabl. a..uruice . . to the correctness. of decision. in judging . .in#le
quality characteristic, or for the .arne sample size. greater a.mirance is obtained
using variable, plan.. Attribute. sampling pfan. have the advantage of
greater simplicity, of being applicable to either .ingle or rnuttiple quality characteristi
c., and of requiring no knowledge about the distribution of the contlaueu.
rn. a.ur. rmenc. of any d the quality cfur. txeridc..
It 10 imporfsmt to mot. tfut variable. .amptfmp pha. ● rm mot to be um.d
i.di. crirninat.ly, ,impfy bec.u.e. it i. po..ible to obf.in vaxi.bk. tnea.urarnemt
,data. fn conmlderq appfieatlon. where the rmrmatity or irtde~nde.ce ●.smnption.
may be que.ticmcd, the user i. ●dvi.ed to cm-..ult hi. technical agency to
detci-rh in. the fe.. ibility of appfi calion.
Thi8 Srandard 1. divided into four .ectimm. Section A describe. @n. rat
procttlur. a of the .amplimg plan.. Secfic.m. B utd C de.crib. .Pcifi. procedure.
and ●pplic ation. of the .arnpIing plan. when w.=iability i. unknovr., In Section B
the .stirn.te of lot .%and. rd d.vi.tion i. used .s lh. fn. i. 10. an ● .timat. of the
unknc.w. variability, and in Section C the average rams. of the sunpf. 1* used.
Section D desc=ibes the plan. when variability is known.
Each of Sectiono B. C, and D i. divided into fbree part.: (l) SAMPJIIW PIUM
for the Single S~cifieuiom Limit Ca.e, 111)Sampfimg Plans for th. mubl. Spcific.
tion Limit Case, and (3JJ) Procedure. JorEsthnation cd Proce.. Average and
Criteria fer Tighmned ●rid Reduced Ja. pection. For tba ●ingle s~cification
limit ca. e, Lhe ●cceptability trite rio. i. giv=n im two foran.: Form 1 amd Form Z.
Either of the fonnc may be u.ed, ●ii-ici they ●rc idettticti a. to .ainple sise -d
deci ion for lot ●cceptability or rejeetabilify. III deciding whether w u.= Form 1
or FQrrn Z, the followin~ poiDt . should be bo=n. in mind. Form I provide. the lot
●ccept ability cri~. rion without ●.titn.tirtg 10I percent defective. The Form 2 101
acceptability criterion require. emtirnates of Jot percent defective. Theme e#li -
mate. at.o .r. ~quimd for e stiznatbn of tha proea ●a ●verage.
Operating Characteristic Curve. fn Table A-3 how fhe r=latioa.ftip betweem
quality and percent of lot. expected to be ●cce~able for thequality cbaractari.tic
inm~et.d. A. stated, the .e Ope rating Characfe ri ‘tic Cur-. are &sed 011tbe
..#urnpiari that meam. mment. ● re .ekctedat raadanalrom a ciorsnti distribution.
The corre spending ●unpfin~ plan. in SectiW. S, C. ~d D w. m mstcbed
● . closely ., po.. ible ~der ● .y.tem Of fixed .unpfe .Ise with re. pcct to their
Opcraling Characteristic Cu?wes. O~raUng Chsracteristjc Cum. in T.bf. A-3
h..= been computed for the .mpling p]an. b... d orj th. ..timate of lof .tudard
deviation ef unknown ..ri.bility, Thy are eqully .pplie.ble ior .arnpllns plan.
hoed on th. averaga range of the .awIpI. of unfmown variability and theme bam.d
on known variabUity.
C.rtaim cln..cmri.:ic. concerning the sunpliag phm. in S..tiom. B amd C
-d tbosa la S9ction D dwufd b, moud. Pkn. baa.d on fba ● mtima& ot umk=09m
Wariablllty require fe~r .M@e wit. for cm~ra~e . ..”ranca -baa tb ● d.
Mate of lcM .taadard tiwl.si~ i. “..d than _bg. ib .~..ae rua~. d ffn .-+
in u.ed: on fhe ottwr tid, plan. Vsbg the .W~.gG r~ge of the #AM@. r.quira
VII
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mb61v—414
11 June 19s7
●imphr compuuttmm. Plarm umlnn bm=variablltty -qutre con*l&rablT f-r
sample tmk far comwrabk amUJrMC* tbaI ●ich=r of the plans whw =TIabtuty
1s uakam: @we wer, tba roquir=mw.t of k#umII -rkbiUty Is ● ●rtnsent am.
The user 1s. dvised to co.milt MS tectalcal~uc~ bdom WPIYLW cunptiaj
piano U.tng bDOwa w8rIAbuuy.
Tath B-8 provids ● values of tbe f~ctor F to compute tfia maxfmum standard
dewiation hfsD. The hfSD se-s M ● ~uide for the magnitude of tht eatirnate of
lot standard de-scion when u-in Plazm for tbm double spcff ication limit c--e,
based on the ● intimate of lot .taa~rd deviation of un.bn- .arimtdUty. SimifArly
Table C-8 provides vmlue- of the Iactor f to com~te the maximum average range
MAR.
●rnple
The MAR ●or.ew m a g de for tbe magnitude
wk. usin# planm for “ke t do.bfe .pecific.tia.
of the average ruige
limit . . . . . ba.ed
of the
. . the
ave rage range of the cunple of unbam wariddlity. Tba edmate of lot ●tmdard
deviation or ●verage range of the ●mpk, U it is Iem thm the hfSD or MAR.re.
●t=ctively. hslps *O immure. but doe. mot guarmt.e, lot accept. bfllty.
AU ●ymbols and their definition. ● re gimn III tha a-ix to Part JU cd the
applicable #*ctim. h Ulumtratim of the com~tiom and proc.durma .~ed IIJ
the .unpling plans i. give. i. the ●nmplec uf Part- I and 11of tbe spplkable
.ection. The computathmm irwolve simple ●rithmetic operation. such am .dditina,
●ubtractio”. multiplicuion, &d dIvimion of mwnbera, or ● most, the taking of ●
.quare root of ● number. The user should become funiliarwith the g.neral procedure.
of Sectian A. and refer to she ●pplicable sectioa for detailed iawtructiom
regarding ●pccific procedure.. cornpu. ions. md tables for [he Barnpliag plan..

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Al. SCOPE
SECTION A
GENERAL DESCRIPTION OF SAMPLING PLANS
All Pur Thi 8 Sammkrd =stablimhes
mmplnng +’ P anm and procedures for inopec -
ticm by variable ● for use in Government
P*.c. reme.t. s.ppfyuad stora~., and rnAJltetts.cc
inspection op8rati0rIm. when .ppli -
cabfe this Standard #hall. be referenced in
the specification, contrzct, or in8pcctien in-
.tructic.r. m, and the provision, set forth
herein shall #ovem.
Al. ? III*PC ction. lnmpeclion i. tiw pro . . . .
of measur, ns. ●xamining. testing. gaging. 0.
othe rwise comparing the “unit of product”
(See Al .4) with the appkabfe requirememla.
AI.3 lnspccti- by Variables. Inspection by
variables i. inspection wherein r+specified
quality characte-ri. tic (See AI.5) on a unit
of proeuct i. measured on . continuous
.cale. .u. h ●. pound-. iwheo, feet per second,
etc., And ● rneamtreme. t is recurd. d.
A1.4 Unit of Product. The unit of product
i. the entity of product in.xcted in order
to dew rrnine it; measurable quality char-
●cteristic. Thim may be a single article, a
pair. a ●et. ● component of an end product,
or the end product itself. The unil of product
may or may K.t be the sune ●s the unit
of purchame, supply, production, or
thipmer.t.
A 1.5 Quality Characteristic. The quality
charact. riatic for varxablee in. pecti4n is
that characteristic ef i unit of p,oduct that
is actually m.a. uzed, to determim conformance
with ● given requirement.
A1. b Specificaticm Limit.. The ●peclflcation
Iimtt(e) is the requi rerncnt that ●
quality characleri. tic .hould meet. Thi*
req.~rement may be exprenmd ●n ●. upper
●prc~f ication limit; or 6 lower pacification
limit, called herein ● .in~le specification
limit; or bolh upper and lower .~cifieatiem
limit., called herein a double ●~cificmion
limit.
A 1.7 Sampli.~ Plans. A sampling pfan 1.
a PrOCedUr* *h*ch ●peciiies the rmxnber c.<
units of product from ● lot which ● re to h
itmpected, arid th. cril. rion Xor aecepfabil -
ity of the lot. Sampling pfazm desipated in
thi. Standard are ●pplicable to the insPctfon
of ● chgfs quality cbaracteri-fke of a
~14
11 Jmfe 14s7
unitof product. Tfm se pfwm may be used
whether pracuremrml inspection i. per.
km’rmd at the plant of ● prime coatract?r.
wbcontractor or vendor. or ●t destination,
-d -S90 may be uaod when AppTOPrU1O in
●ppfy and storage. and main fanaace fL18pection
ofm rattom.
A3. CLASSIPTCAITO?f OF DEFECTS
AZ. I Mtthodof Cia8sifring~fect@. Asf8m -
.ificat, c.n al defect- . . the ●rmine ratio. of
defect. of the unit of product claasifi. d
according to their irnporfaace. A defect 19
● deviation of the unit of product fr-am, requirement.
of the specifications; drawiags,
Purcha.e da~cripfia”., and aay cbu~c
the reto in the contract or order. Defects
normally belong to one of fhe fOllO*g
classes; however. defects may be plkced k
other ciao. cs.
AZ. 1.1 Critical Defeeto. A criticaf defect
i. .“. that iudeme. t and axmrience indicate
coule reeult ;.. hazardou. “or unssfe conditions
for individual. u.ing or m.imaining
the product; or, formajnr end it.rn9 unit~of
product, such a. ships, aircraft, or famba. ●
d.f. ct that could prevent fmrforrnaaco of
their tactic-i fumction.
A2. I.2 Major Defects. A major defect i8 a
defect. other than critical, thaf coutd result
in failure, ormateritlly reduce the usability
of the unit of product for its intended fmrpobe.
A2. I.3 Minor Defects. A minor defect is
on. that doc n not materially reduce the usability
of the unit of product for itm intem&d
Purposa. or i- ● deprfurc from ●stablislmd
atandard9 hating .0 signUi CUIt bOa CinI OrI
the effective u.e or operation of th@ unit.
A3. PERCENT DE FECTTVE
A’3.1 =.PT89.88. Of NO. CMtfO_ co. Tti
e$fcnt of nonconformance of pro dues 9fnff
be expre-scd i. terms of percent &faetive.
A3.Z Percent f%.feetiwe. Tbe percent d.fectiv-.~acterimtic
of ● Ii%.
lox of prodv;t”i. th~ number of unit. of praduct
de fectiwe for that cfuractc ri.tic divided
by the tataf number of unitm of product And
multidimd by on. hundred. Expressed ●man
.auatiorx Percen: rkfectiv8 -
Number of Aefectivea x 100
Numbs r of dtm

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lx Jlfffe 1957
Ad. ACCEPTABLE QUALITT LEVEL
A4. 1 Acce@abZc Ouaiil bwl. Tba =-
● a CBOmlnaf
value ●xpr*s.e.i in farm. of percaat d8f*c -
tive .Pcif ied for ● sbigle quUity characteriatic.
Grtain numeried vaftws o; AOL
r=~img f ram .04 to 1S.00 parce.nt am ●hO-a
i. Table A- 1. Whe. . ran- of AOL VUWi.
.pecified. it dull he treated ●s if it wore
equal to the WdUC of AQL for which ●mfa2i0c
plms ●re lu-whed and which i~ bcluded
within the AOL range. When the •~c~ted
AOL i- a particular value other tb& tivme
for which oamplhg pfanm ● re furniched, the
AOL, which i- to be used in ●pP2yihg the
yovi.ions of this Standard, .Itafl be ., .ho~
m Table A- 1.
A4.2 Specifying AOL1 c. Tin particular AOL
vafue le be used for ● ●ingle quality char-
●ctarimtic of a given product must be ●peeified.
fn the CM. of a double ●Pcifi.athm
limit. ●ith. r an AOL value it #PcUied for
the total percent defecti.. muaida of bath
up~r -d lower specification Umita, o. t-e
AOL value. are specified. om. for the upper
limit and another for the lower Ifmit.
AS. SUBJbflmAL OF PRODUCT
A5. I lat. The tsrrn ,,1ov hall nmmn ,virtcpecti~lot,
-’ i.e., a collection of unit. of
product from which ● sample is dram! ad
inopec~td to dete rm”me complhrme with fhe
acceptability criterion.
A5. 1.1 Formation of Lots. Each la; shall,
● s far ●mla practicable, con.iwt of unit. cd
product of ● .ingla type, gssde, ~Ass, size,
or cornpo. itkn manufactured under e.. enri.Ily
the same conditimit.
A5.2 Lot Sise. The lot ●im 1. tha number
of unit. d product in ● lot, and may differ
f rem the quantity de.i#r.atmd h fbs comtraet
or order a, ● lot for prod”ctlar., ●biprnellt.
or Ether Purpo..,.
A6. LOT ACCEPTABILITY
A6. I Acce Sabfiity Criferien. The ●cca@-
●bility of a lot of material ●iknitid br
imapc:kta ddf be detennh.d byum of ~
of the .ampling plait. a..oeiaf.d~tb. .pec -
ffied value of the AOL{S). Tbi. Standard
provide 8 ●ampliag plaa. baaad ombaowa 4
b- variability. fn the Iatfar can
two affa mativo met+, ●m provitid, -
bared on the e ●tfmaia of im ●fattdard dovi.
atioa and the die r on lb am rqe range of
the t-fate. These .r. r. f.rred to . . the
standard dowiatio. method and tbe rinse
method. For tha case of a single cpeeifiea -
tiatl unlit, lb acc.ptabiu~ criterion I-
8
A6.2 Choice of SarnfAim Plain. SunpUaB
~D u!d PIWCEOU-9 a:e pro-dad in d8Ction
B if Variddlity 10 uabnown amd the
.taadamf de rf.uion mathd is !mwd, h Soc -
ticm C U variability i wunbaewn a?id the range
matbod i c uced. and in Secfioa D if .ariabUity
is bnown. Urdesa otkrwi.e ●pcffied, un.
b-n variabiUty, ●-d=rd dewiafim method
●unF41rtd plans. and the ●ceef=ablfifv crl -
terbr. d Farm 2 (for the 9ic@e specification
iimit case) Aaif be used.
A7. SAMPLE SELECTION
A7. I Determination of Sample Sise. The
.Unpl. .,- h, tha mm’lfmr of unttmof product
drawn frcan ● lot. Retati~ samph aIws
●m Aesimated by cute letters. The 8ampf4
sise cod= Iette r“depcitds on the.inq=ticm
le.ve: and the lot ●1=4. There ●m fiva h-
•f=ctiOale=J~: L U. fU. IV. -d v. ff~e-~
othe rwhe ●pecffiod Ia-fmctien Ieval IV shali
k used. The ●unple .i.e cod. letter applicable
to the .pcifi.d izi.pectim l.wel arid
for lots of given sise .hdl be obtained from
Table A-2.
NOTICE-5P. c ial Reservaticm for
Critical CharackrnB1ic8. Tbe Go.errm’i.nt
re. e.vo. tbe rmhl to insmct emryunit mbmkkd
hy the ;uppfier fos critieti etir.c -
te!rimko, uad to reject the remainder of the
lot Immedlafelyafter ● defect is fouud. Tbo
GOvemirnent timo rcr:rvee tht right to ●ampfe
fo~ criticmf d. f.ctc evm ry let aubmittad
by tk ●uppUer arid to reject any I-* if A
sample dr.wm thrnrefr~ is fo-d to contain
ow or more. criticti da fects.
A7.2 Dr.wimB of Samples. A sample 10 om.
or mere unit. ol product drawn from . lot.
UnItc of ttn munfdo Aa2i be, ,al~ct,d with-
O* re#ard to t?bdr q.safity.
Proe.dure ● for ● 8tLmatfmg 22n preeomm
awrage @ criteria for ticbtaned and re -
dweed in. fmcftan bared = th Umpacthn
romiito of pmeedinc lots are provided in
Part uf of dactiorm B. C. and D.
AS. SPECIAL PVOCEOURE POR APPLI-
CATION .F MIXED VARIABLBS-
AlTT21BLfTES BA?APLJNG PLANS
--

I
I
I
I
I
i
i
● lu prwid=d for tin Miad w8*bl9D-
●ttrlbcuaa -Wunpumg phmm bon18 ad that
tbOM h ,T=tih A-S a- z-t W#idk.]
Condltlon A. Amptm wwI&mc. oximta
W tbm produ ct cubmittod for iaapctioa IS
●mhctod by Ch #Upfli, Z tO meat tfM ,IWXiZ
Ikatlan ltmit(s) by ● ●creemlng proee ●m
f rmn ● Iarae r qus.mtity of product which 1.
not being produced wltbln tba ,Pclfication
Ilmlt(al.
CodltiaQ B. Other condltiorm adst
tbt warrant tb= u , . of a .arlablacmttributem
•ara~i4is *-.
A9.2 Definition..
A9.Z. 1 in.pactlom by Attrlbut8s. fnspectioa
by ●ttribute. I* inwpectkoa wbardc. tba unit
of product is Chsdfied simply m defective
or mandcfectiwe with reapact to a given re -
qtiire.mom 07 s.t of nqutrnmentm.
A9.Z.Z Mind Variabla ●-Attrib* ● lnmP8c -
tion. tinnd varimhle ●-attributes inmp8ction
~mgpcction of ● ●arnfie by sttributa ●. in
●ddition to inspection by variable. mmlready
mad. of ● previo.a ●unple, before . dee
ki,on .ao ~o.,*: ca~qsi!iv.o r .*I- c-bili~ ~
● M ctihmtie. ‘. ‘-
A9.3 Selection of Samplirtc Plans. The
miaad *arlable.. att Yi- S -plmg plan
stall h ●elected in UCOdUICe with thn
fcdlovim~
A9.3.1 Select the vsrlableo #vnpliag plm
M ●ccorduaca with Section B, C, O, b.
a
A lot
mcdm Ui* ●ccef%abi me of
the fouo’wln’ Comtitiem. i. .*tL.fic.&.
Camdltkm A. 7bo lot com~i4s with
ttn apprsprmta variab14 ● ●cca*bllIty crl -
terlm of section B, C. or D.
Caa6itLm B. The Ist cmIPU*s +tb
tbe ●cceptabif ity crita rkm of pragrapb
11.1.2 of bAIL-sTD-!05.
A9.4. 1 U Condition A ia not ●atiefied, pro.
coed iri accordance with tk ●tttibute ● oM’l -
plirig plan to meet Condition B.
A9.4.2 lf Condition B ia not cati;lied, the
lot doe #not meet the 8ccepabilicy crlte rian.
A9.5 Se=rltY of Iaaopaetion. The procedures
for .everity ❑f m.pecti.m rel=rred to
in ~rarraph A8 are net ●ppficsbl. for
mixed Vaziable..attribum. inm~ction.
NOTICE- When Gouerrmtemt drawin#..
SPedfiCatiOmn, or othc.r data ●re u.e4 tar
UIY prmme other than In connection wltb a
definitely relamd Government procurement
opa ratloa. thm Lbit.d States Gow rrunent
tbe=aby imzur, no re. pm.ibility or my obligation
wbtcoevcr; and the fact that the
Co.ernnteztt may have form.latd. f.rnimbed.
or In uIy way ●pplied the ●aid Lrswiags,
●wcificationa, or other data (* II@ t. ‘=
rm~arded by implication or otherwime ● in
mY m-e r licerming the tilde r or any otha r
pcr*On or corporation, or conveying any
rights or p rmis. ion to m-nufbctufe, u**.
or ●ell aay patented invention thu may in
mn7 =*T h ra~-td tbreto.
—

or spd56d A03. va3u.eI
a236q WiIhin mmu r-got
— to 0.049
0.050 to 0.069
0.070 to 0.109
O.lloto 0.164
0.165 to 0.Z19
0.Z80 to 0.439
0.440 to 0.699
0.700 Ie 1.09
1.10 to 1.64
).65 to 2.79
2.80 to 4.39
4.40 to 6.99
7,00 to 10.9
11.00 to 16.4
Use thh AQl
Vazue
0.04
0,O65
0.10
0.15
0.Z5
0.40
0.65
1.0
1.5
Z.5
4.0
6.5
10.0
15.0
4
““”m6610 1JOIB35DF31
111 to 180 Be&c I
181 to 300 Et DFH_j
301 to 500 C32GIK
501 to 800 DFHJL
801 t“ 1.300I EGIKL
1.301 to 3.200 FHJLM
3.ZO1 to 8.000 Gl Lhi N
8.001 to 2z,000 HJMNO
mample .i;e code letter. given in body of
Uble ●re appli. abze when the indicated in-
●ptctim levelw are to be “med.
. - --,-

I
I
TAB- A-S
OpraCinC Clmr.ete.si.tic CtMW9. for Sun@iD* Plan.
of t%cti~m B, C, 4 D
mL-sm-414
11 Smn 1*
-.

TABLE A.3
OPERAllNG CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANOARO OEVIATIOM METHOO ii!
;f
SAMPLE SIZE COl)E LETTER
W
4:
B
ICures * m?l~s p-i bed - ml,. +ti 0“4!.- .V1.wlty “. “.o.lld* iq.k.llnl )
!!
a
I
—

.——. .—— . . . ——. .—
TABLE A.3
oPERAnNo WARAC7ERISTIC CURVES FOR SAMPLING PUJ49 SASEO ON STANOARO OEVIATION METHOO
.4
-0 10 so 30 40 w M ‘m 00 w 100

U%RATINO CW#fWTERISTIC CURVES FOR SAMPUNO PLANS BASEO ON STANOARO OEVIATION METHOO
ii~
.

----- .—.__— ._
TABLE h .3
IYERATINO CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANDARD 0EVIA710N METMOD
SAMFI-E SIZE CODE LETTER
E
I b, * t9#wq pm, bed m mm,.dti ●*9k“- ..I.W, m “.”l* +.do”t 1
w
bo
‘0
a 40 loo
!m
#
-0 10 IQ 30 40 w w
M,I., rq!lmom - Ut Is#.ul 44,1, 1“1, I., - I“tpn, ”,

t!
7ASU A.3
OPERAnNG CHARAC~RISTIC CURVES FOR SAMPLING PL;NS BASEO
ON STANOARO OWIATION METHOO
SWR_E SIZE cow LETTER
F :,
,,
[corm f“ S*, ,19.1,b,,,d m .,”,. 9A,4 9.#t“- ?wI.bm, “
* “,”(++ ,,uk,td )
1
.- .- .-
!
OUAU1’V0? W3Mt?lC0LOTS I 1.,.md 4./.,!1..)
hl-,tWllrdcfhh-lMhh
-rw. nM-#An.u.O..,o .
-94 d Iuo9 k , - m,t”b.+”,

*
TASU A.3
ON STANDAm OEVIATION ME I MOO
OPETiATINGCHARACTERISTIC CURVES FO+7 SAMPLING PIANS QASED
wu SIZE COW $lTER
F I Cenfh.edI ,

TABLE A .3
OPERATING CHARAC7ER15TfCCU17VESFOR SAMPLING PLANS 8ASEC ON STfi?!DLRD DEVIIITION METHOD
ii
SiMFLE S1ZE COOE LETTER
:~
*
G
I C.*.B IV ..v96, p!ru b.n.dw

-.
TMLE A . ;
ON STANOARO OWIATION METMOD
OPERATING CHARACTERISTIC CURVES FOR SAMPUNQ PL+W 8ASE0
SAMFLE SIZE CODE LETTER
G ( Con!lnwd)
Ii x
w
OUUllY Or SWMlllfO 10U ( h pod tihdb, I
%.- - - - k.+.bl. B-m, 1“9101. -d hv., m”,
I
l___

*
-----
TABLE A-3
WERATINQ CHARACTERISTIC CURVES FOR SAMPLING PLANS BASED ON STANDARD OEVIATION METHOO
SAMFtE SIZE CODE LETTER
“
H
Itiwl & ,@h, ,h., b.sd m ,,”,, 44 W4know,.“i,blll!, “, ,,,,d,+ wI.,IA )

.
TABLE A.3
CURVES FOR SAMPLIN6 PLANS BASEO ON STANDARD OWIATION METHOO
OPERATINO CHARACTERISTIC

TASLE A.3
OPERAllNO CIWACTERISTIC CURVES FOR SAMF1.lNO PLANS SASEO ON STANDARD DEVIATIDN METHOD
SAMP.-E S1ZE CODE LETTER
I
Ihi la st+q tlmt k.d m rm~. AA -t h- .wI*WI, u. .m..lhlb H.1..lrd )
m
e
.
-a

.,
TABLE A-3
OPERATINO CHARACTERISTIC CURVES FOR SAMPLIN13PLANS BASED
ON STANOARD OEVIATION METHOD
SAMPLE SIZE COOE LETTEfi
I ( Contllwl )
?s

TAME A-3
y
OPERATINO CNAIIACTERISTICCURVES FOR SAMPUNO PLANS BASED ON STANOARO OEVIATII?N METMOD
E!j
SAMW SIZE COOE LETTER
?&
J *
f Cnns for ‘u#l., ph. h,,d m m,, ●w O..*k-l .“lMI, “, “Al+ b+’.w I

I
.- .——
TASK A.,3
O~RATINO CHARACTERISTIC CURVES FOR SAMPLINIJ PL~NS 8ASErI ON STANDARD DEVIATION METNOD
SAMRE SIZE CODE LETTER
J (Conm.td)
lb.., k M@”, ,1.., b.).t - Is.,. AM##Lu.n,O-l.bill* Um “,-II* Iqwdmf )
I
I
I

.-
,,. 2
TABLE A. 3
y
OPERhTINQ CHARACTERISTICCURVES FOR SAMPLING PLANS BASEO ON STANOARD OEVIATION METHOD
3
Sf+@LE SIZE CODE LETTER
g“ !!
K +
{ C-w, * ,1.@q ,1,., b,,d m ,..,; 4.* “a h.- W,bdll, w, ,,,,”1;4$ qulw.1”1j
!3

.,
TABLE h .3
OPERATINO CMbRACTERISTICCURVES FOR SAMPLING PLANS BASED 0:1 STANDARD DEVIATION METHOO
SAMFLE SIZE COOE LETTER
K ( Cennn.t~)
{ -t b *I p-t h-i m lul\s - “4 i- .ul.w~ .9 ●***W+ +!”.1-1 I
ht., ~,, m - “ bm+tl. dmltt,1“,!, 1- -d ,“,,o,wz

TA9LE A-3
=!5
CHARACTERISTIC CURVES F(XI SAMPUNG PLANS BASED ON STANDARO DEVIATION METHOO
c@ERAnNo
:x
SAMFtE S1ZE CODE LETTER
L
t*8 f- Wt }1- b-d m m,, dn4 -8 in- vul,blhtjw, cud!+ WIV,lon!I
1
f

o
TASLE A.3
CMbRACTERNWICCURVES FOR SAMPLING PLANS BASED ON STANDAR5 DEVIATION METHOD
cmmo
SAMFtE SIZE COOE LETTER
L t Con!h..d )

:!E
~f
gln
TABLE A-3
OIWMTINO ChARACTERISTIC CUfWES FOR SAMPLING PLANS BASED ON ST.ANOAROOEVIATION METHOD
~y
Cm$
a
SAMPLE SIZE CO@E LETTEII
!4”
,:
I h,,, 1“ ,,q,!h, ,hns b,,,d m ,,.9, ,A,b ,,* hnwmvwl,blhl,w, ,,nwdl,ll, ,,u(v,M }
Tli+n*d mmaItofbl,npwl,* $.h
-W!* 9! - * h “01...19 ul
91UW* - - s 4 419!?IM-. ou4m of WBulmo Lois [ h ,,remtW.nil,. )
?&I,%f,~,,, m,-, “, 8.,,,!,,,, O@,, c“.,, f- w,,, ,“,,,,,,..
,

TABLE A -3’
OPERATING CHARACTERISTIC CURVES FOR SAMPLING PLANS BASEO ON STANDARD DEVIATION METHOO
SAMPLE SIZE CODE LETTER
M ( Contln..d )
I W-.sa ?0?snplhl, ,19.s b-d m ““,0 604 “d i.- ..rl.bnll, “. “m!h!lf @!mlWd)
,.
.
. . .
. .
m+dall?--dtiwr-eh il
etiti—rti-1, “
mb9md d b- * - ●lnwm Wm of WSM171C01.079 { 1.ptm! 4.1..!1.,I
m,, ~., * - ..9k+. 0“.l,t, L“.1. 4- W.*I h+.,llo...
I

TASLE A.3
CURVES FIX? SAMPLING PLANS BASEO ON STANOARD OEVIAilON METHOO
OPERATING CHARACTERISTIC
SAMFtE SIZE CODE LETTER
N
fI&w, b ,udq ,!,”, b,,.d m ,,”,, “Ihd -4 t.- .“l.b.t,l, “. ,,, ”l,tq ~.,.di,,, )
thl*. dm#w9*s!h**-t.4 bh
-=@-- nM-h.b9..9wwnl8 . I
-d 94e h , 4 4M”MI.,
aumm or woumo LOU I I. ,,,,”1 ..h.th. I
w., nw, - - “. Auvl.bl. 0“.!1!,1“,1, t. “-”, M*,*,*).”

m
TAGLE A . S
CURVES FOR SAMPUNG PLANS GASED ON STANOARO OEVIATION METHOO_..
OPERAllNQ CHARACTERISTIC

-.
. . .
TABLE A.3
ON STANDARD DEVIATION METHOD
DPERATING CHARACTERISTICCURVES FOR SAMPUNG PLANS BASED
SAMPLE SIZE COOE LETTER
o
i G“, 1“ a+, ,Im, $,,,4 m ,,.,. 44 W, t-mm.ar,.bdlt,w

-——
.— -—-—-—.
TASLE A .3
OPERAnNG CHARACTERISTIC CURVES FOR SAMPLINO PLANS BhSED ON STANDARD DEVIATION METHOO
SAMPtE SIZE CODE LETTER
O I Contln.*d)
ICnrm fw “w-q PIM1bm.d m r9ng.4M -4 k.- v“i.bill!, “. .,,,.lhl~ qll.,1-l I
r5

.i
TABLE A. 3
~15
OPERATING CHARACTERISTICCURVES FOR SAhiPLINQ PLANS BASED ON STANOARO oEVIATION METHOO
gi
:
d:
SAMFtE S! 2E COOE LETTER
!/
P
tC4WW8 t- ,qll., ,Im, b.,.d m rq. ..fbti .,, &.cu vwl.btit+,,, ,,,.”1,+ ,,.,..1”1 )
B
W +., d lb ,Wcmld It, *ml*4 1,“
-w. **ti .,-,, .
*4 d M k , - 4M”MI* 9UALIT7Of 9u9Ul~D LOTS I 1.,,,w,TId,f,,l),, I
MA) f,~,,, 0! unu “. kr@.b!. Owl,!, L,.,t, t- w.,+ b!,,.,,,o”,

.—— _ _
TABLE A .3
CURVES FOR SAMPLING PLANS BASED ON STANOARO OEVIATION METHOO
SAMPLE SIZE COOE LETTER
P I Conllnwd1
( e--m 1- -I )Iul W m Ire,, d -4 i“- .“kbllllj “, “oatId+ tq.lnl.! )
lbdat?l-wddbf,-?-abb
---**”O--*, “
Wdd-b@--dak$*Mm OUALIWOr SWUl17t0 101S I 1.,.r.m$#.1..lh.1
lb,,, nw,., - -. “. k~,.,,. 0,.1!,,L“.1, I- -..1 In,,,,,,..l.

,.$,
TASK A -3
CURVES,FOR SAMPLING PLY RA5E0 ON 5T,ANDAR0DEVIATION METHOC
opERATING CHARACTERISTIC
SAMFtE SIZE cooE LETTER
Q
ICuml fw t.wh”, 01,”,},,.4 m f.”,, ..*W .. . b.- .“i,blmy “, ,,,m,, d,, _“,.,!M! )
a
1
OUAUW OP $uBMITrCoLOTS ( h ,.,,,”9 ,.1,,1,.,)
W., flpt .I - W. k.pl.bl. IWI~ L...l, l,, f.x.,1 I,TV,,I,W
mmkuilm~tibl,~,,bb
-.woM*ubal -,,.
-04 d a k * d 41,+.MI..

., .,
TASLE A.3
OPERAllNQ CHARACTERli~lC CURVES FOR SAMPLING PIANS BASED ON STANDARO DEVIATION METHOD
SAMPLE S1ZE COOE LETTER
Q ‘( Cmfln.,d )
I h, f- ,+*, ,S.., b.,d 01 ,,.,. dti mm,bin.., .whb,hly “. ,,,4+ w@vdcd I

VARIABIIJTY
S1. SAMPIJNG PLAN FOR SINGLE
SPECIFICATION LXM!’T
Thi. pArl Of the Standard deocribe. the
procedure* for us. whh plani for ● oingle
ape .ifiution limit when variability y of fhe
lot with re.pect to the quality charae%eri. -
tic i. unknown ●nd the .tandard deviation
method ia u#ed. The acceptability criterion
i. given in two equivalent iorm9. Tbeoe are
identified as Form 1 -d Form.2.
B1.1 Use of SamPtinfl PlaJw. To determin.
whsther the lot me=t. the ●ccept -
ability criterion with respect to ● particular
quality cfuracteristic a.ud AQL. -Iue.
the applicable campling plan shafJ be uced
in ●ccordance with lb. proviaionm of S.c -
uc.n A, Generai Description of Samplmg
Plan. .-d th.. e in %hi, part Of th. Standard.
B 1.2 Drawi..qof Samplem. AfI .amplew ●hall
be drawn in accordance -’th paragraph A7. Z.
B1. 3 Determination of Sample Size Code
~. Th e .smpla ●zce cod ● letter ●ha
be selected from Table A-Z in ●ccordance
with parasraph A7. 1.
B2 SELSCTING THE SAMPLING PM
WHEN FORhf 1 IS USED
BZ. 1 Maater sampling Tables. Th= muter
●anmlmn tables for mlana based or. -riabilit~
-MI for ~ ●ingle specification
limit vben using the ctaadard deviation
method ●re Tables B-1 .nd B-Z, Table B- I
in .m=d ler norm.] and tighter.ed iriapection
art< Table B - Z for reduced imspeetioit.
B 2. Z Obtaining the Sa?nPlinK PIan. The
.mnpl.tig plan cons.st. .1 ● .unple .i.e 8d
m ●~nociafed ●Cc.eptability COtI.unt. 1 The
sampling plan i. obtained from Mater
Table B-1 -, B-.?.
B2.2.1 Sam Ie Sise. The #ample .ise - Z*
●houm m~ t e ma.,.. tabl - eo.-.. p-.fing *O
.-.1. ..cnple ●ice cute tetter.
SSCTIW B
uNKNowN-sTANDAmf DEvlAnoN
Parf I
SINGLE SPEUF3CAT10N LUA3T
BS. Z.2 Accepu bility brmant. The acc.pcdility
corutaaf k. correewmt .gtotbemunple
size mentioned ia pnagraph B2.2.1, ia
indicmed in the column of the nuster table
cor re~pmxling to tbe applicable A(2L value.
Table B-1 i. entered from the fop for normal
inopecfion ●nd from the bottom for
tightened inspection. Sampling plum for reduced
inspection are providd_ in Table B-2.
B3. LOT-BY-WT ACCEPTABILITY PRO-
CEDURES WHEN PURIM 1 LS USEI?
B3. 1 Acceptability Criterion. Tbe degree
of conformance of ● q uafit y cb8ractericti c
with respecf lo ● single specification limit
.W1 be judg.d by th~, qusntity (u-XJI* or
fl-L)/i..
B 3.2. Corn tatien. TtIt following quantity
.haff b- (“-X)/’ ., (x-L)/., d,pendiagon
whether the specification limit i,
~ qper or lower limit, +ere
U i. tk upper specification limit.
L i- tbe lower specification limit,
X i. the sample mean. and
. i. the ●.tirnate of lot ●sn&rd de.rlatioa.
B3.3 Acc ability Crite rfon. Cumpare the
abifttywmst-nt k. ff (u-x)/m or (x- f.)/a ia
equal to .ar gre8ter tlun k, the lot meets the
=cc~tiIf.fty criterion: if (U-X)1.** (X-f-)1~
ia l.mm Uu8 k or nerative, 3hrm the M &es
not meef the •=e~llity criterion.
M. t31JM3tMRY FOR OPXRATION OF
~~MNG PLAN WREN FORM s m
The foLIowfnr ‘soP* •~marise ‘he PrO -
=~u... t.. . . mllowed:
(1) Daterrnirw the sxmple .i.ecode lti -
ter from Table A-2 by uming the let sise and
in.pccfion leeel.

MIL-m-414
11 Jt333e1957
(2) Obfai. Pk. from Mamer Tab)= B-1
or B-z by .eleeting the sample size n and
the ac..ptabill$y constant k.
(3) Select at random the sampl= of n
unit. lrorn the let; inspect ●nd record the
mea. urernem of she quality characteristic
fer each utiit of the sample.
(4) Cmnp.te the s.mpIe mean ~ and
estimate of lot sts”dard dcvistic.n . . and
● ISO compute the quantity (u-X)1. for an
u per specification limit V or the q~ntity
A-L)/. for ● k.wer .peciticatio~ lids 3..
15) M the quantity (u-X)/s or (X-W.
i. equal co or greater than k, the 10I meets
the ●c.ept.bilicy criterion: it’ (u-X)/. or
(X-L)/. i. [e.. (ha--- k or negative, thes the
lot doe’ rwtmeel Iheaccepttii lily criterion.
B5. SELECTING THE SAMPL3NG P2AN
WNEN FOfUd Z 5S USED
S35.1 h4asccr Sampling Table.. Th. ma. ter
.ampJmg tables for plans based onvariabil -
ity unknown for a single specification limit
when using the m~nd-rd deriatitm method
sre Table. B-3 ●nd B-4 of Part If. Tsble
B-3 is used for normal a“dai~htened inmpec -
eion and Table B-4 .fc.r reduced.inspection.
B 5.Z Oblainin~ the Sampling Plan. The
sarnpli”~ plan co. ss.ts of . .unpl. ,Ize and
sn ●ssociated maximum alk.w=ble percent
da$eclive. The samplin~ plm i. obtained
from MaDter Table B-3 or B-4.
65.2.1 Sample Size. T)M ●mnple mice n is
●hewn m the ma. tcr table cortespendin~ 10
each sam>le .iz. code letter.
135..?.Z Maxim. mAllow8ble Percent De feet$ve.
The rrmxim.tn ●llowable p.=. ent de-
=live M for ample ●stimate. correspond.
img to the .unple size m=nt ioned in
pa:agrmph 95.2.1 is ittdicated in the column
of the nm.ter table .xxre.pondiytg to the
●Pplic=ble AOL value. Tabl. B-3 i. =nt=,.d
from tbe top for normal inspection -d from
the bottom lo, lsghter.ed in. peetion. Sam -
-li>g plan. lcIr reduced inspection
v-l d ea ,. ~a~,e ~-,.
● rm pro-
B6.1 Acceptability Criterion. The dc~ree
of conformance Of a quallty characteristic
with respect m ● ai.ngle specification limit
hall b, judged hy the percent of rmnem-, -
Iorm,ng product outsidt the upper or low+r
%. Ex_pie B. z for .a cemplete ●xample of thb. prOc*dure.
:38
cpecifteation limit. The percentage of Macoaforming
product is cstimattd by wiieria’
T~le B-5 with the quglity index and the
sample ●ize.
B6. Z GE-I utatio” of Qtufit
~-lity~-X)~rnpE~
if the specification limit i. ●a upper limit
U, or OL . (X- L)/t if it is a Io-er Jimit L.
Th* quaatitie.. X ●md s. ● re the ●arnpl.
mean ●nd e.timm e of lot standard deviation.
respectively.
W. ~e -ii-t-d P.,. em d.f=~ti- in d
lot ●bove the upper specification limit, or
by ?z.. th. estimated percent defective below
the lower .pecifi catian limit. Tbe ●stimated
Pc*.=.: defective PU or PL i. obtained by
enterina Tabk B-5 with Ou or QL and the
●ppropriate ●anple size.
336.4 Acceptability Criterion. Gmpare the
estimated lot pereent deIectivepU or pL with
the maximum allowable percent defective M.
U PU Or Pl, 1. eqUf to or leas thn U, the
lot rneets the acceptability criterion; if Pu
or p~ is greaier than M or if Qu or Q is
,negative, then the 10: does not meet \he
acceptability criterion.
B7. SIJ71SMARY FOR OPERATION OF
SAMPL3NG PL.AN WHEN PORM 2 3S
USED
The fellc.rnng step. .umrnariz.e the procedure.
to be fallc.u.ed,
(1) Determine the ●mple .i=e code let -
ter from Table A-2 byu. ing the lot size md
the inspection level.
(Z) Obtain plan from Master T=ble B-3
or B-d by .elecfi.~ the .unple .ixa n attd
the maximum allowable percent defective M.
(3) Select ●t random the #ample of n
unit. frmn the Iof; inspect UId record the
m.asurernemt of the quality charact. rimic
cm each .unh of the ●ample.
(4) Cmnpute3h= sample mean X arid the
ectimale of lot .ta”dard devfatian . .
(5) Compute the quality index Q
(U-X)/ * if ●n upp. r .pe.ific.tie,. limit Jfi:
●P.*ified. or OL = (x. L)/. if ● lctwerspec -
iiication 1;...;. L

Mu.-sm4l4
11 Juoe 19S7
fi) ff the e.timated lot percerndefective is~reatertl.an U Orif QuOr C3~ is aepti e,
PU Or PL i. ~ud to or 1... than the maxi. then the lot doe. ml meet the ●ccepmbi rIIY
mum .dlowable percent defective M. the lot criterion.
meet. the ●cc.pt~bil$ty criteriom if PU Or PL
EXAMPLS B-1
Exmnple of Calcufatio.s
Single Speci!icatlon Limit-Form I
Variability Unknown - Standard Deviation Method
ExAmple The rn.timum temperature of operation for ● cer:aindevic. i. .pecifi.d ●. .?09”F.
A lot of 40 item. i. submitted for inspection. Zn. pection Z-evel IV, normal inspection,
with AQL = 1-% i. to be u, cd. From Tables A-2 ●nd B-1 i! i. aee : that a
marnplc 01 sise 5 i. required. Suppose the measurement. obtained are ●. 1.s3
The lot rneetm the .cceptabiltty criterion. mince (U. ~)/s is ~remt=r than k.
Explanation
(975)2/5
190,435 - 190,125
310/4
-s
97515
[209 - 195)/S .81
S.. Table B-1
See Par&. B3.3
NOTE: If ● ■ingle lower spcffieat{on limit L is given. fhen compufe the q~ntilY ~-~)f~ in
Iin. 10 -d com~re il with k, the lot meet. the =ccept8bility *rii=.iQn. if (~-Ll/* is
equal to or greafer than k.

!.
M2~-414
11 June 1957
Single Specification Limit-Form ,?
Variability Unknown - Standard Detiation Method
CUmple The maximum temperature of operation for ● certain device is specified ●s 209” F.
A JOI of 40 items is ●ubmilted for inspection. 2nspection Uvel IV, normal inspection,
with AOL = 1% in 10 be u.ed. From Table- A-2 and B-1 it i. .een that a
sample of .ize 5 is required. S.ppome the measurements obtained art ●. follow.:
197., 188-, 184.,205-, and 201 ‘; and compliance with the acceptability criterion in
to be deter rnitied.
—
Lime
J
z
3
4
5
6
7
8
9
10
11
1?,
13
Sample Size: n
Inforrntiion Needed
Sum .3[ Mea. urcme.ta: XX
Sum ef Squared Measurement.: 1X2
Correction F=ctor (CFh (IX)zln
Corrected Sum of Squares (SS): lX~CF
.V.4@I

g
Sample size
code letter
B
c
D
E
F
G
34
,1
J
K
L
5.4
N
o
P
Q
-
... I
TABLE B-1 Standard Deviatiom Methc.d
MIster Table Far Normal &.d Ti~htened fn. pectlo. for PlaIJs Based on Variability Unknown
[Single Specification Limit– Form 1)
5
7
10
15
20
25
30
35
40
50
75
100
L150
zoo
Gik
,10
+ k
,15
k
Acceptable (
.25 .40
kk
-
allty
.—
.65
T
.CVCIS (normal inspection)
1.50 2.s0 4.00
m
k k k k
m
k
t
—
i
— l-k
7
$ 1.45
—
1.65 1.53
k
2.00 1.88 ).15 1,62
.?.24 2.11 1.98 1.04 1.72
1
v
1.34
1.40
1.50
1.58
—
1.12
1,17
1.24
1.33
1.41
.958
1.01
I.07
1,;l 5
1.23
.765
.814
.874
.955
1.03
2.64 2.53 2.42 2.3?. 2.2o 2.06 1.91 t.79 1,65 1.47 1.30 1.09
2.69
2.72
—
2.73
1.17
2.77
—
2.83
2.90
2.92
2.96
2.97
—
.065
2.58
2.61
2,61
.?.65
?.,66
—
2.71
2.77
2.80
Z.84
2.85
I
I
2.47 2.36
2.50 11.40
2.51 2.41
2,54 2.45 I
2.5s .3.44
2.24 ,?,11
! 3..26 2.14
12.2.9 2,15
2.31 2.18
2.31’ 2.18
—
1.96
1.98
—
2.00
2.03
2.03
2.6o 2.5o 2.35 2.22 2,08
+
2.66 2.55
2.69 2.58
2.13
--t-
2.61
2.73 2.6.?
2.41 2.27
2.43 2.29
2.47 a.33
2.47 2.33
2.12
2.14
7,1!
2,1[
1.8.?
1.85
1.86
1..99
1.89
—
1.93
1.98
2.00
2.03
2.04
1,51 1.3)
1.53 1.35
1.55 1.36
1.57 1.39
1.58 1.39
.
1.61 1.42
1.65 1.46
1.67 1.48
1,70 1.51
1,70 1.51
.10 -t.15
.25 .4o i .65 I ,0(
—
1.50
—
Z.50 4.00 6.50 ,0.00
AcceptableC alit, ,fVela lightened inspectio!
1.69
1.72
1.73
1.76
1:76
1.80
1.84
1.86
—
1.89
1.89
1.12
1.14
1.1s
1.18
1.18
I.ZI
1.Z4
i.26
1.29
1.29
T10.00 15.00
+
k k
.566 .341
. .
.617 .393
.67S .4s5
.7s5 .516
.82n .611
.886 .664
I 5.00
i
.917 .69s
.936 .71,?
.946 .723
.969 .145
.971 .746
1.00 .774
1.03 .ao4
1.05 .819
I.07 .841
1.07 .845
A21AOL wdue8 ye knpercent de-a.
[Irst tunpllq plan belcw ●rrow, that is, both sample OIZ.Sas well ao k va2ue. When nample sise equdt er e=ceedo lot ~~
1::: ,V.V ,tern hth. lot must be inspected.
I

TABLE 23-2 “Standard Deviallm Method ~E
Maater Table for Reduced lnmc.ectimfor Plana Breed On Varlabilitv Unkmwm
(Single Sp’c.ifi..tl.n Litnit-F. rm I)
I I
ISampIe size Sunple
mCode latter size
I
D 3
.04 I .06S
I
.10
-L
—
.15
k
“Ac
x.—
k
—
uality Levelo
.40
EEE
Z.50 4,00
—.
k
k k
—.
.—
J+~~
l.lz .958 .165
1.12 .958 .765
—
1.12 .958 ,76$
6.50
k
.566
.566
.564
E 3
I,lz .95.9 ,165 ,566
-i-
*
T 4
G 5
H
7
1 10
J 10
K
15
TL Zo
u Zo
N 25
0 10
P 50
Q
75
Z.53
—
i
Zoo
z Z.11
Z.4Z
IZ.Z4 Z.)z
Z.11
Lzo
Z.58 Z.47 z.16
—
2.58 Z.47 Z.36
z.61 Z.50 2.40
t-t
Z.Z4
—
.LZ4
2.Z6
I1.$8
I
.—
1,65
i.75
1,45 1.34
—. —
1.51 1.40
t
1.17
1.Z4
1.62 1.50 1.33
1.01
1.07
1.15
1.9a
—
1.84 1.7Z
.
1,58 1.41 1.23
1.9a !.84 1.72
k
1.50 1.41 1.23
2.06
Z.11
—
Z.11
1.91
:.96
1.96 -1--
1.79 1.6S 1.47 1.30
1.8Z 1.69 1.51 1.11
1.8z 1.69 1.51 1.33
2.14 1.90 1.85 I I,7Z 1.51 1.35
2.Z8 .?.!5 2.00 d1.86 1.73
— — —
—
Z.Y5 2.ZZ Z.08 1.91 1.80
*
Z.41
2.27
2.IZ
—
1.98 (.84
——
1.55
—-
1,36
.—
..914 ,617
.874 ,675
.955 .755
1:01 .828
1.03 .828
1.09 ..986
I.lz .91?
I.lz .917
1.14 .936
1.15
—
.946
I.zl 1.00
1.24 1.01
i65i
k
.141
.141
_—
.141
.341
.393
—
,455
.536
.611
II
.664
.695
—
1.61 1.4Z
,114
All AQLvm3ues ●re in percent defective.
f2rotdunplln,g plmbelowtrrow. that it, both mm-qde nize no well •~ kvalue. Whertaemple oize equal, or exceed. lot
~~;;, e,:,, ,,,m i“ the ,0, lll”,t t., ,mpetted.
1.65
1.46
.695
.712
.72J
.80$
.—
I

I
S8. SAbfPLLNG PLAN FOR DOUBLE
SPECIFICATION ~
This part of the Stan-dard describe. the
procedures for use with plain for ● double
specification limit when variability of the
lot with re.p. ct to the quality cluracteristic
i. unknown and the standard deviation method
is used.
Bfl.1 use of Sampling Phm.. TCIdetermine
whether the lot meets the ●cceptability criterion
with respect to a particular quality
characteristic a“d AQL value(.) the applicable
campli”g plan ●ha31be used in accordanc.
with the provisions of Section A, General
Description of Sampling Plans, and
those in this part of the Stamdard.
B9. SEIJ2CTI?JG THE SAMPLING PLAN
A sampling pJa. for each AOZ. value
.hall. be ●elected from Table B-3 or B-4 m
[C.;J”WS:
B9. 1 Determination of Sample .Stze Code
ktter. The .arnple i.. cone letter .hal;
be selected imm Table A-Z in ●ccordance
with paragraph A7.1.
B9. Z Maater Sampling Table.. The master
satnplmg table. for plum based on variability
.“kt-mwn for a double specification limit
when using the standard deviation mctbod
are Tables B-3 and B-4. Table B-3 i. u.ed
10. normal and tighlened ir.spection amd
T=ble B-4 for reduced impectiom
B9. 3 Obtaining Sampling Plan. A sampling
da” .— consists of a .arrml. ..ze and the assoeiated
maximum allowable perceni defective(s).
The sampling plan to be ●pplied i.
inspection shtil be ob-iaed from WSter
Table B-3 or B-4.
B9.3.1 Sample Size. The .unple #ize o is
show” in the mater tablas correape=ding
tO each sunple size cod. letter.
B9.3.2 M-.imum Allowable Percent Defec.
*. T h. maximum allowable percem
defective for #ample estinuLe. of pert.mt
de fe. civ. for the Icxmr. upper, or both .pec.
ificatiori limit. combined, corresponding to
the sample .ize mentioned ia paragraph
f39.3.10 in shown in the COhmm of the master
table corresponding to the applicable
AQL value(s). U different AOL, S ●re a.sign=d
to each .pe cification limit, de.ignmfe
Part n
DOUBLE SPEC337CATZ034 3XM3’I
the maxfzmIM tiowable percent de fecfivc by
ML for the lower limit, mad by M for fhe
upper
IiAt.
limft. If one AOL is asci~e 3 to both
contbi.ed. designate the timum
Ulowable percerd d-f% by ht. Table B -3
i. ●ntered from 3be 30p for marnul flupection
and from the bottom for tisbtaaed fLl-
Wpecffon. Samp3fng pfuu for reduced fnspect.ien
● re provided io Table B -4.
B 10. DRAwU?G OF SAMPLES
Sample# shall be elected in accordance
with paragraph A7.2.
B11. ;:&-.o;&O T ACCEPTABILITY
.
B 11.1 Acceptability Criterion. The degree
01 Conformaa Ce or a WlA3ity elaaractcria3fc
with re. pect to m doubje mpacification limit
.hafl be judged by the percent of r.onconform-
% P.tiuct. The percentage of manconforrn -
img product i. e.timated by entering Table
B-5 with the quality index and fhe’.ample
.ize.
U is the upper specification limit,
L ia the lower sp.cificacion limit,
X is the sample mea., and
s is tkm estimate of lot standard deviation.
B 11.3 Pere=nt Defective i. the Lat. The
aualitv . . of a lot shall be cx~r.a~terms
of the lot perc=nt deiecti~c. Ita estimate
+33 be de.i~ted by p~. PUO Or P. me
iadicsten cmifornunce with
:::;52ptL upper .Pe.tllctiorl limit, PF
w.ilh .e. pee: to fbe lowez .pecifiutio. lima .
-d P for both .Pecifiati.n limit- eombimed.
The emtimstea p mid p
determined by wIterins + ●ble B- Y . ‘w’ r=.pec be-
tively +f.h QL and f)” md the sample ●isc.
The eotinute p Zhmfzbe determined by ●dding
the corresponding ectinuted percent defective-
pL and p“ found in the tible.
B12. ACCEPTABILITY CRITERION AND
SUMMARY FOR OPERATION O F
SAMPLING PLANS
B 12.1 be AOL value for both Upper and
Lower s’ ecxlncatson Lwm umd.

MI L-STD-414
11 JurIe 1957
B 12.1. I Acceptability Criterion. 4 Carapare
the ●stimated lot pe.rcatt delective P = PW +
PL with the maximum ●llowable p=rcent
d. fective M. 11p in ●qual to or less tfun M,
the lot meets the accepmb{lity criterion: if
p is grcatertban Mor ii eifher Qu or QLor
both ●re n.@ive ,then the lot does not meet
the ●cceptability criterion.
B 12.1.2 Summary lor Operation of Samplin#
Plan. In cases where a ●m.glc ACfl. value is
~lished for the .tmer and lower .pccifi -
cation limit combined for ● .in81e quality
characteristic, the following mtep. ■umma -
rize the procedures to be used
(1 ) Delerminc the ample size code
letter [rem Table A-2 by “sing the let .i%e
●nd the iriap. ction level.
(2) Select plan from Master Table
B-3 or 8-4. Oblain the ample size “ ●nd
the maximum allowable percent defective M.
(3) Select ●t random the sample .af
“ unit. Imrn the lot: i.sp. ct and r-cord the
mea. ur. merit of the quality characteristic
on each unit O( the amp]=.
(4) Compute the ●mple rnesn X
and c.timltc Of lc.t .tand=rd dcviatic.n s.
(5) Compute the quality indices
QU = (u-X)/. and QL= (X. L)/,.
(6) Determine the estimated lot
p.,r.n: d. fecfiv. P = PU + PL from Table
B-5.
(7) lf the e.tirnated lot percent defective
p i. equal tc. or 1,.. than the maximum
●llowable ptzcen% defective M, the )ot
meet, the ●cceptability criterion; if p is
ur.~t=, th=n M Or if either W or QL -
bolhar. ne~.tive, then the 101doe. not met
the ●cceptability criterion.
B] 2.2 Different AOL Valueo for Upper and
Lower specification Limit.
B 12.2.1 Accernability Crit’eria.5 Gmpare
th. e.tirnated 101 fJC,C.llt dd ectives pL and
PU with the cm? c.pn.ding rntimum allow.
able p.rcem defective. M
compare p = F.L + Pu wfth tke%~#~fa?L
and Mu. If pf, i. ●qual to or Iesn than htL,
PO i. =qu*: to or le.. than MII. and P im
.@al to or 1.*s than the larger ‘of ML “and
tdu, the lot meets the ●ccepubi.fityc riteria;
otberwimm, the lot doe. not nwet the ace~.
abf3ity criteria. U .mither QL or Qv or botb
are me~tiive, then the 101does not meet the
acceptability criteria.
BIZ.Z.2 SurnmaryfOr Opertiianal Sampffrt&
Plan. 3n ca. eg where ● t erenf AOl. walue
~stablished le. the upper and lawer .pec -
ification limit for ● single quality cfuract=r -
istic, the following steps sunururi’e the
procedures to be US=CL
(1) Deterrninethe ample .izecod=
letter from Table A-2 by twin, the lot size
and fnspectimt level.
‘(.?) Select the sampling plan from
Master Table B-3 arB-4. Obtain the.ampfe
.ize . and the maximum allowable percent
defective Mu and M’. corr=apondi.g to the
AOf. va2ues for the upper and lower specification
limft., respectively.
(3) Select .1 random the ..ntple of
n unite fr.rn tie lot; ia. pe.t and =ecord the
meas”remerd of the quality cfur. cterimtic
on each unit in the .mrIple.
(4) Compute the sample mean X
and estimate . 10I .tamlard deviation s’.
,,
(5) Compute the quality ittdice.
Qff = (u-X)1. and OL = (x- L)/a.
(6) Deterrniae tbe estimsted lot
percent defective ~ and p~, correspandiag
\othe percent defective* shove fhe upper
and below the lower .peciIscaticm limit-.
A2eodetermi”e the combin.d percent delec -
tive p = pu 4 p~.
dition.:
% ●
+S.. Etimple B. 3 {or . cmnplete ●xample of ibis proc.dure.
*W Example B.4 lot a cmmpl=te exatnple of thfs procedmre.
42
‘L.
(7) 11all tbre=of the f.dlowin~ corl-
(a) ~ i. equal t. 0? 1... thll
~] PL !9 =LNJ81tO 0, h.. t3UII
(c) p is equal to orlemmthanfbe
larger of ML ●nd btU,
are sati. fied, fh= lot meet. the ●cceptabifhy
criteria; ofhe=wi. e the lot does mat meet the
acceptability criteria. ff either OL or Gff
or both ●re negatiwe, then the lot does not
tne=t tbe acceptability e=iter ia.

I
i
I
I
1’
1’
I ,..
E-de
Line
—
1
2
3
4
5
6
7
s
9
10
II
12
13
14
15
16
17
3SXAZ4PLC E-+
Example of Cdcu3ati0nm
Double spa Mlutino Ltmtt
VariabiNty ?.bbnamn . Stutdard Zkuiaticm M.thod
0.. AQ L Value far both Upper and Lower Specification. Limit Cmmbined
Z41L-STD-414
Ii June 1$S7
Tbc minimum temperature of operation for a c=rtAtn device 48 speetfied 8.180- F.
The masimwnt.mprst.re h 209” F. A lot of 40 item. i- submitted for imopection.
3nmpection Level 3V. normal in.pect(on, wtth AOL. s 1% im to be ..d. From Tablam
A-2 and B-3 it is neen that s sample of ●i=e 5 is zequird Suppo*e the rne...re.
mcntm obtained ●re 8. fof30w.: 197”, 188”, 1M., 205”, md 201-; ●nd cmnpliuw.
with the acceptability criterion i. w b. determined.
Sample Sise: n
Znforrnatian Needed Value Obtained Explanation
Sum 01 Measu.. mant.: SX
Sum of Squared Measurement: XX2
Correction Factor ICF): (2x)z/n
Corrected Sum of Squarca (SS): XX~C~
Variance (V): SS/(n- 1\
Estimate of Lot St&rd Deviation s: &
Sample Mean ~: ~1.
Upper Specification Limit: U
Lowe r Specification LitnAt: L
QtuIity Index: Qu - (U-X)/s
C3udity tid=: OL = & L)I.
Eat. of L9t Percen5 hf. Ab0V8 U: %
Est. of Lot Percent Z)ef. below L PL
Tataf E81. Pe.rcm13 hf. & La& p = pu + pL
Max. Nlowable Percent Da f.: 3.4
Acceptability Criterion: Compare P . Pu +
p~ with M
s
975
190,435
190,125
310
77.5
195
209
180
8.81
1.59
1.?0
2.1 9%
.64%
2.85%
3.32%
2.85% < 3.3.2%
‘3& lot meet. the ●cceptability criterion. Ante P s Pu + PL i. 1=. s t~ M.
43
(975)2/5
190,435-190.125
310/4
m
9?5)5
(zo9-1951/a.nl
(195-180)/8.81
.%- Table B-5
See Tablm B-5
2.19% + .66%
See Table B-3
See Para.
812.1.2 (7)
—

m&6w14
11 Jone 1957
EXAMPLE B-4
Exampl* of cazcU2Mf0m
DOnbla Spcffiuti.=n Z.imtt
Vari&i3fty Uakm - 5tsadard Deviation Method
Different AQ3. Value. ior Upper and Luwer Specification l.imitc
Example The minimum temparamre of optra3foa for ● certiin dewice i. .pecified ●- 180- F.
The rnu5mumtempQ=a3ure ii 209” F. A lot of 40 items in subrnkted for inmpm=3ion.
f.mp=ctic.n L=v=l Iv, normal imW=CCICQI.--I* ACZL = 1% foI *= upper -d ~~ =
2.5% for tha 10uer specification limit is to be used. From Tables A-Z and 23-3 it
is ●.en that . sample of sise 5 ia required. Suppcme the measurements obtained
are aa follows: 197. , 188. , 184”. 205”, and ZOI. ; and compliuce with the acccpt -
ability criteria i. 10 be determined.
~
1
z
3
4
5
b
7
k
9
10
11
lZ
13
14
is
lb
17
la
Sample Size: n
Information Needed
Sum of Mesmmements: Z X
Sum of Squared Meaour.m.mta: XXZ
Correction Factor (CF): (ZX)2/n
Corrected Sum of Squares (SSh lX~CF
Variance (V): SS/(n-1)
Estimate of Z.ot Stam&rd Deviation s: fi
Sample Me= X XXln
Upp=r Specification Limit: w
Lower Specification Limit: L
CluaIity 3ndex: Q“ . (u-X)/o
OAity index: (ZL = (X. fJ/.
Est. of z.&4Percenf DA ●hove U: ~
Eat. of f..of Percent Def. belsw k. PL
Total E.;. P. rcent &f. in Lot,: p . PU ● pL
Mu. Allowfahlc Pereent Def. •bov~ U: MU
Mu. Allowable Percent Def. below & ML
Acceptability Criteria: (s) Comp-rc PU
@) ;;;p;f pL
(c) Compare p
Wifh ML
Vat.. Obtain. d
5
975
190.435
190.125
310
71.5
195
Z09
,1s0”
8.61
1.s9
1.70
2..19%
.64%
2.85S
9.00%
2.19%. 3.3.?%
.bf+ < 9.80%
Z.esn c 9.80%
Explanation
W75)215
190.435-190,125
31OI4
m
97515
[209 -195) /6.s1
(195 -180) /n.81
See Table B-5
see Table B-S
2.19% + .6W
See Table B-3
See T*1. B-3
See Para.
Blz. z.z(7 )(a)
see Psra.
BIZ. Z.2(7)(bj
S.. Para.
BIZ..2.Z(7)IC)
~e lot meet. tbE ●cceptability criteria. ●be 18(s), (b); ad (c)are •ati~fied; i.-.. PU ~
pL

TABLE B-3 S1and*rd Devittlon Method
Minter Tsble for Norm81 and Tightened tnapcction for Plms Blsed on Variability Unknown
(Double Specification Limit and F.rm2-Single Specification Limit)
t Inorm.1 in! ●ctim
Acceptable ~
1.50
i~
~
I.00
.04 .065 .10 .15 .2s .40
Sample cite
code letter
M
ii-
M M M M M M
7.59
3
B
16.45 ZZ.8b 29.45 36.90
10.9Z
v
5.50
v
1.53
4
c
14.39 ZO.19 Zb.56 33.99
9.80
5.83
3.3Z
1.31
5
D
; - i +
0.422 1.o6
‘Zzo I““l 4 ‘0$0
10.54 15.11 ZO.14 Z1. S7
8.40
5.35
3.5s
Z.14
7
E
1.Z9
4.77
—.
4.31
Z,17
v v v 0.349 0.716 1.30
10
r
9.46 13.71 18.94 z5.61
6.56
3.26
—
3.0s
Z.11
0.099 0.186 0.31Z 0.503 0.818 1.31
15
G
8.9Z 12.99 “12..03 Z4.53
6,17
4.09
Z.95
2.o5
0.13s o.2zn 0.165 0.544 0,846 1.Z9
Zo
H
13.6311Z.571 17.511 ZL97
5.97
3.97
Z,86
Zoo
0.155 0.250 0.380 0.:51 0.017 1,29
Z5
I
’47I ‘2’61“024I“s’
8.10111.871 16.651 Z2.91
5.06
3.91
z,03
1.98
0.119 0.280 0.413 0.581 0.079 I..?9
30
J
5.57
3.70
Z,68
1.87
0.110 0,264 0.388 0.5}5 0,847 1.23
35
K
s.091 11.85[ 16.61 Iz2.86
5.5B
3.72
z.71
1.88
0.17 9 0.275 0.401 0.566 0.873 1.z6
40
L
7.61 11.Z3 15.87 ZZ.00
5.20
3.45
Z.49
1.71
0.16 3 0.Z50 0.36 3 0.503 0.789 1.17
50
M
7.15 10.63 15.13 21.11
4.87
3.ZO
2,Z9
1.60
0.14 7 O.zze 0.33 0 0.467 0.7.20 1.07
75
N
a6.91 [0.32 14.75 ZO.66
4.69
3,07
1.53
0.14 s O.zzo 0.31 7 0.447 0.68 9 I.oz
I00
o
6.57 9.86 14.ZO Zo.oz
4.43
z.#9
2..?0
—
Z.05
1.43
0.13 4 O.zo 3 0.Z9 3 0.41 3 0.63 8 0.949
150
P
6.53 9.81 14. IZ 19.9Z
4.40
Z.nl
Z.04
1.4Z
0. ;3 5 O.zo 4 0..294 0.41 4 0.63 7 0.945
zoo
Q
.06 5 .10 .15 “.25 .40 x I .00 1.50 Z.50 4.00 6.5o 10.00 15.00
—
AcceMabilitv Qualitv Levelt ( ;htem insrmcticml -.
-5
All AQLandtablcvsluet ●re inpercent defective.

,—
TABLE 23A
o Vsrlablllty thkn.awn
!clfic atim Limit)
Muter Table far Reduced fnvpecclm [m Plan. Bared
(Double SpecU{cation Limit -d Form 2- StttgteS
10
~
1.00
=2 M
=
1.50
zi-
Acceptab
7
..?5 .40
—
I }.( t.. ,
—
.— —
I
ample cite sample -j
:xI* Iettsr 81;0
3.4
-ii-
—
7.59
--
B 3
7.59
c 3
1.59
D 3
18,06 26.94
7.59
E 3
!S.50
16.45
10.9Z
t
1.53
—
14.39 I 20.19 I Z6.Sb I 33.99
4-4-4-=
9.46 I 13.11 I 18.94 ] Z5.bl
9.80
5.83
3.32
5.15
3.5s
F 4 v
—
—
G s
1.33
v
H 7 0.412 1.06 2,14
I
8.40
A a
1.Z9
4.71
3.26
7.Z9
4.77
3.z6
1. 10 0.349 0.716 1.30 Z,17
—
J 10 , 0.349 0.716 1.30 “Z.17
6,56
4.31
3.05
K 15 0. ( 2 0.s03 i. fllfl 1.11 Z.11
6.17
4.09
—
4.09
1.95
—
2.95
0.544 0.846 1.29 “~2.a5
0.365
L I Zo I 0.228
6.17
0.544 0.946 1.Z9 2.05
0.365
M. Zo 0.ZZ8
N Z5 O

—
.—— _ —. _____
TABLE B-5
TSWO for Eotkmtlq th~ &t Pe, CCIIIDefective U#lnS Standard Devl.ilon M#thedl

.- .
TABLE B-5-Conthed EZ
k!’
Thblofor E!tim.tlng the tit Percent D*(ectlve U#lng S;mdard Devlaiion MQ~hod
1

-.
.,,
TABLE B-5-Conllm.wd
Table for Eotlmatlag tbo bt Percent Deltctive Usln@ S1-d~?d Deviation Mathod
. ,.-
. .
,.

J
TABLE B-5-ContlnueU E
Tmblcfor Eotlmatln[tho lmt PcrcerIt D6fecllve Uc@Stmdard Deflation Method
k F
s
.
i.
I

.—. . .—
TABLE B-5-Cadimed
Tatdo for Eattnutlq tho kt Poreant Def*ctlwe UOlag Standard Derlatien ,Mothod
a
“
E
“.
-“

ML-rm-414
11 J5fffa 1957
Pmrt m
C5TZMATZON Or PBOC= AV~E AND ~TER3A
REDUCED A35D TIONTU4CD =PECTION
B13. ESITbfATfON OF PR~ AVBR-
AGE
The ●verage percent defectiwa. b-cd
up. = group of let- submitted for origfnd
inspection. i. cafled the proceo- ●voragc.
Originaf imspectimi i. the firm im*pecfiOn Of
~ -~cb? ety of p~ ●bmttted
for ●cceptability a. dfotiaguf.kd from f3M
immpec;ie. of product wbfch ti. been remtbmifted
after prior re&cftcm. 3%. pro-..
average .fuU be ..timated from flm r..uft.
of in. peetic.. of samples dr.wmfmrn a .peeified
number of precedfq lot. for the pur-
~.= Of d=~=rdaiag ●.v9rity of iacp.cfian
d.rin~ the c..r.e of . cmdr.cf in accordance
with ~rag,.ph B14.3. AD, 1- sM1 b- iucIuded
only once in ●stinuffag lb pxocem.
.verqe. The ..ti_t. ef Uw prw.. ●wr-
=K= i. d=. i~t=d by PU -be. eompufed wifh
re. pect to an upper ●pee fficatier. lisnit, by
PL w.h=. c,.mpyte,d w+fh rc.pecf to ● lower
.P=c,f,.~t*- I.mtt. md by p when computed
with re. peet to a double .pecfficatio. fimit.
.-.
B 1~.1 Ahn.rmA R.muft.. l%. r.. ult. of
inspection ef product _ufaetured under
. ..”diti... mot” typfcd of ..IuI p.odmeficm
.3u15 be exeluded frmn the ●.tinnted prece..
avera~e.
FOR
and the ~rremmondtnsedmtid 1c4 +rcud
&fOcfiw ~ & p=,-respectively. iw mad
from tfm fable. Tbe ectinuted proceco ●vcrage
~ i* * ~ifhnwfic meaaef fbe fad3vtdual
e.ttrnmted tot perce.t defective- pu’ c.
6tmitarly. the etiimated procem ● ●=rage
$L it tbe arithmetic mean of the individual
●ctfaut9d 30t pareemt &facUwa pL’8.
B 13.L2 Uoubl. SpecW. UtImI Limtc. The
. ●timated Iof percent defecfive ● c &-
.termIned from Table B-5 for the pfaim ba.ed
on the standard deviation method. The qtuf -
It,imdf... Qu d 0= sti ba e-vu-f.
Tabfe B-5 i- enzered ●epar.tely wlfh ~ and
QL d the -unP5e ●iae, d the eor--mpmdfag
~ and PL us read fmm the t8ble. Th.
eatitrmt.d lot percent defecfive t. p = p .+
PL. The eatimuted proc. ●S a=rage p is se
●rifbm.fic mea. of the individtuf c..tinuted
lot ~rcenf defective- p’..
D 13.Z.3 S cfal Cam. It the qtulity index
OIJ or C3L< a negative ‘numb=.. the. Table
B-5 i. entered bvdimrenardins the negative
.ip. f-i---- , ‘i. tbi.- a., ‘h. c..fi&ated
lc.t percent de fecfive above ftm uppa r limit
or below fbe lo=. Zimit i. obtafned br mzbtractiq
the PCrcenuge found i m the” table
from 100%.7
B 13.2 (hnputmtion of the Est5nuted %0.
. estimated procem- ●=ratm
‘~ t. t e ●r thmetic ‘h mean of fhe .atfmafed
l~t percent defective. computed from b
.amptia~ iit.p. ction *..uft. d the pxecedtms
ten (10) lcIt. .M a. may be othetwf. e decig.
.BIL. NORMAL TIGHTENED, AND m-
DUCED IkBP33CTfON
Thts S-*rd esti5fah*d campfiag
pfam for normal, tightened, and reduced
iMpactiOn.
nated. b order to e.tirnate tbe lot percent
dal.etive, tba quality Ucea QU tiler QL
shaff be cmn~ted for ●ub lot. Tbom ~e:
C3U = (u-X)/c md QL= (X. L)/a. @em pus.
Sr*pb 3511.2.)
B 14.2 -as 31WWetfon D9rtm, tba c0ur9*
Of hmcuon. Mrnuz tirncttan ●haff be
fisbtmnd er ‘r.duc8d LrJsp.cficm 1. ~ mrquir9d
b •ccor~ wttb pr.sr.~ B 14.3
d n14.4.
B14.3 Tishtaa8d 311spectioa. TI~btarnd h.
●poetfon ●balf b- fmtitmad whn tha c cti -
matid pro- ●a .nragm wmpidmd from tfm
When Form I -Sfngl. Spectff~tfon ~ 1. rm.d for tba acmptabfflty criterion. tbe “octl -
mafe of 101percextl &feetfve pu.or pL 10 mot obta.lmed;fmordertoewtimate the proc.am ●v8r -
~s=. it i* n=c=a~=rr to complete paragrapba B6.2 uuf B6.3 of Form L
7FOraXUnP18. U ~ . -.50-0 = 1.60. us~ ●SMPZO SCM SO,PU = 100% - 30.93% = 69.071b,
P1. 9 ~-n -P* 69.07s + S.sk . 74*.
. ..-
52

I:
I
II
I
I
..
preceding ten (101 108. (Ot ..& 04h*r rlwn -
bar of lat. de. i~ted) 1. =crnrduue with
Kr=zr&pb BIXZ i- srestcr than the AQL,
-d when more than A c=rta~ number T of
them lots have e.timafes of flx percent defective
sxceediq the AQL. The T vdttbs
●re given in Table B-6 far the procea. .verage
computed from 5. 10. Or 15 Iots.e
NormmI inspection shall he reinstated if the
..tinut.d preces. ●ver-ge of lots und=r
tightened i..prction is cqud to or 1..8 tkmn
the AQL.
B 14.4 Reduced Im.pectiom. Reduced ilI-
.pection may be inmitumd prc.vid. d that ●ll
of the following condition- are ●atiofied:
Condition A. The preceding ten [10)
lot. (or .uch other mmnber cdlm. de. igruted)
have been under nornul ia.peclio. and nom
has been rejected.
Condition B. The e ctimated percent
defective for each of theme preceding lot. io
1=.. U- the appUcable lower limit shown
in Table B-7; or km =ertak .arnplirIg plan. ,
XIL-STD414
11 June 19S7
b estimated lot percent defective is eqtnt
to =ero for a ●pedfied number of conmeeutiwe
tot, (gee Table B-?).
Cad6tfon c. PrOdnctiM is ●t a
●teady rata.
Normal impaction ●hall he r.in.tated if any
oaac of the following condition. occ. ra undcr
reduced inspection.
Condition D. A lot i. rejected.
Condition E. TM emtimated prc.cem●
●.eragc is greater tham tbe AQL.
Condition F. Production become.
irreguI~r or delayed.
Condition G. Qther condition. .. .
~? ~brrmt that normal inspection .hould
be reinstated.
B 14.5 Sampling P18m. 1.. Tightened Or Reduced
lmpecthm. Sunplu-ig plan. ior tightene
d and reduced in.pecticm .re provibd in
Section B, Part. 1 and U.

I
,
I
..
MIfA3TD-414
11 Jwm 1SS7
4 4
L 6 6.
a 999910
4 44
M 6 7
9 :
I 10 I
/
Cuve] t49mbar
Z.5 10.0 15.0 Of bta
4 4 5
6 :
8 9 1: ‘0 i5
4 4 4 5
1 1 10
9 10 1: 15
4 4 4 5
10
1: 1: 1; 15
4 4 4 5
1: 1! 1:
10
.
15
4 4 5
.: 10
11 1: 1: 1s
4 4 4 5
a a a 10
11 11 11 15
4 4 5
: a a 10
11 11 11 15
4 4 4 5
8 8 10
11 11 1: 15
4 4 4 5
a e 8 10
11 11 11 15
4 4 5
8 : 8 10
11 11 11 15
4 4 4 5
8 io
11 1: 1: 15
4 4 4 5
8 8 a 10
11 11 11 15
4 4 4 5
s 8 8 10
11 11 11 15
4- — 4-- -4 5
“8 a a 10
11 11 11 15
mm ●re m 9mp31a# pluu prwuad la thio Staa&rd far Unse code lctirs dAO1.wshm9.
M
..-. —-

-.
unmlTP514
11 Jrmd 19s7
TAB= B-6

—
—.
TABLE B-7 Slmdtrd DevIa440n M!thod I“
::
Llmlt# 01 &#tim~ttd Lut Percent Defective for Reduced Za.pection
T5-
Acceptable Ouili!y Level.
.40 I .65 [ 1.0 [ 1,5 I 2,5
sample tll*
code letter .04 .063 1 .10 I .15 I .25
[IO]** [lZ]** ( 9]**
I
$
[IO]** [ 7]0.
0.00 .74
4.40 9.96
6.S0 10.00
1.38 4.24
5.96 10.00
6.50 i
=
tool 5.19
6.50 10.00
& I i
-1-
),s0 6,06
6.50 I0.00
& A
4.29 7.40
6.5o 10.00
1 A
4.59 7.74
6.50 10.00
1 A
.
.77 5
15.00 10
& 15
6.06 5
15.00 10
& 15
—
9.09 5
15.00 10
& 15
iO.47 5
15,00 10
4 Is
11.51 5
15.00 10
L 15
112.07 5
15,00 10
A 15
lZ.4> s
15.00 10
& 15
[ZB]**
I
23 * ● * ● *
[15]**
● ● [45]** [II]** [22]**
c ● ● ● ● *
[ 9]**
* [31]** [25]** [18]*. [13]*O
D ● ● ● * ●
.11
z.65
4.00
.00 .00
[18]** [14]** [11].. ,10 .88
.es 2.49
E ● ● * ● [25]**
1.05
3.56
4.00
.000 .000 .003 .044 .>06
.016 .101 .317 .74 1.80
.123 .369 .81 1.50 2.50
? .000
F ● ● ● ,000 .001
.002 .029
1.64
3.94
4.00
.011 .041 .136 .123 .84
.143 .310 ,643 1.14 2,23
.315 .6.?6 1.00 1.s0 2.50
v .000 .000 .000 .002
G ,000 .003. .006 .018 .057
.003 ,010 .02s .062 .151
Z.24
4.00
,&
.04.s ,121 .266 .521 1,14
,2.3s .445 .78s 1.31 2.40
.396 .65 too 1.50 2,50
.000 .000 .002 .005 .017
H .004 .010 .03.3 ,040 .111
.013 .029 ,0s0 .10!! .?.1s
Z.49
4.00
A
.083 .185 .36o .653 1.33
.214 .509 ..963 1.39 2.48
.40 .65 I .00 1.50 2,50
.001 .002 .006 .014 ,037
1 .009 ,020 .039 ,071 .146
,03.1 .043 .077 .133 .248
lz.69 5
15.00 10
-+- A 15
1
4,81 1.98
6.50 10.00
,A h
Z.66
4.00
A
.113 .231 .431 .750 1.47
.306 .550 .909 1.44 Z.50
.40 .65 1.00 1.50 A
-..
,002 .005 .012 .023 .054
J ,011 .021 .050 .087 .169
.027 .0s2 .089 .146 .2s
+
●Th=i* mrcno mmpliag plain provided Anth!o Standard for these code Ieltero and AOL vduei.

.—— ,. —.- -—___—_ ,._
TABLE B-’f-ConUnued Standard DevlaIkIn M,t~d
Limlto of Cctimalcd Lx P~rcetN Delectl}e for Reduced hwpectim
Sunple OIZR Acceptable @di}y Levels Numha r
code letter .04 .065 .10 .1s .25 .40 .65 1,0 ! 1,5 2.5 4.0 6.5 10.0 15.0 of &to
.004 .008 .017 .03.? .069 .137 .210 ,483 .8.?1 1.57 2.19 4,96 8.1s 12.08 5
K .017 .033 .059 ,099 .186 .3Z.9 .577 .940 1.47 2.50 4.00 6.5b 10.00 15,00 10
.012 .058 .091 .15 .25 .40 ..65 1.00 1.50 L h a 1 & 15
.005 .011 .022 .040 .082 .157 .300 .5, ?5 .876 1.64 2.88 5.08 a.z9 13.03 5
L .020 .038 .065 .108 .199 .343 .596 .961 1.49 2.50 4.00 6,50 I0.00 15.00 10
.035 .ObJ .10 .15 .25 ,40 .65 1.00 1.50 6 A 4 h A Is
.008 .016 .030 .05?. .102 .187 .345 ,507 .959 1.76 3.01 5.21 8.50 13.2s 5
M .025 .045 .075 .120 .215 .36{ .621 .989 1.50 2.50 4.00 6,50 10.00 1S.oo 10
.04 .065 .10 .15 .25 .40 .65 1.00 b 1 A & & & 15
.014 .026 .044 .0?2 .134 .235 .414 .6.91 1.082 1.92 3.24 S.!iz 8.01 13.60 5
N .0)1 .054 .081 .136 .2)6 .389 .65 1.00 1.50 2.50 4.00 6.50 10.00 15.00 10
.04 ,065 .10 .1s .25 .40 A A 1 k A A & & 15
.01s .032 .0s3 .085 .153 .261 .453 .733 1.[49 ,?.01 3.36 5.67 8.98 11.00 5
.014 .058 .091 .14J .245 .40 .65 ‘ 1.00 1.50 ,?.50 4.00 6.50 10.00 15.00 10
.04 ,065 .10 .15 .25 b A k , , , , & L 1$
0
.023 .039 .064 .101 .177 .296 .501 .799 1.Z31 2.13 3.52 5.87 9:22 14.07 5
P .038 .064 .10 .1$ .25 .40 .65 1.00 1.50 2.50 4.00 6.50 Io.oo 1s.00 10
.04 .065 b A 1 A A A b & A a & A 15
.025 .044 .069 .108 .1!38 .312 .525 .830 1,276 2.19 ~.59 5.96 9. N. 14.19 5
Q .04 .065 .10 .15 .25 .40 .65 I .00 1.50 2.50 4.00 6,50 10.00 15.00 10
& A & i A b A & 8 i 1 i 1 A 15
Ml AQL sad t~blo values, ●xe*pt three in the brackets, 8re in percent defectlvo.
VAf3methe flrot figura In dlraetZom o{ ●rrow and corresponding number of Iotm. fa ●ach block tha top (Igure rofcrc to the
prccedlos 5,10ts, the m5dd2* figure to tho preceding 10”lott, snd the bottom figure to the prteedlng 15 loto.
“
Reduced 6nspectlea IIWY ba Sr@itoted when wary ●ttlrmtd lot P rcsnt defcctivc!from the preccdins S, 10, or 1S leto it ~
F
bdow tha flpr* civm tn the tabl*; rcducod inspection for sampling PIMC mmk.d (**) la fho tlblc raquireo that tha ●atlmtiod
lot po?cent dcfoctlvo 10eqttafto saro for the number of conteeulive lots Indicated In bracketo. la sddltlon, ●ll other cendltlont r?
for roduead Inspection, in Pmt 223of Section B. mutt be ostitfi.d.
s
~g
N1 ●aih’natem of the lot parcent defectIv* are Obtained from Table B-5.
,:

ercec
—
1.50
leOudity L.cvelo(in
T
-.
.65 I .00
tepll
z
—
.04 .0b5 .Io .15
sample tiaa ‘ Sample
code Imttr Oise
34 3
,399 .4JZ .47Z .S28
,)53
.319
c 4
—
.)73. .408 .45Z .s11
.374
.
.346
.Jz)
,Z94 .108
D 5
.345 ,M31 .4Z5 .489
.318
.Z9S
,Z53 .Zb6 .Z80
.24z
E 7
I
.5Z4 .359 .403 .4b0
.Zlb
.23s .248 .Zbl
.2Z4
.214
F 10
.309 .344 ,386 .442
.Z98
—
,Z84
.262
,Zzz .,215 .248
.211
.18?. .I.521 .19s .202
G 15
.302 .3)6 .371 .43Z
.Z17
.255
.z16 .ZZ9 .Z42
.z06
.177 .18J .190 .197
H Zo
,291 .331 .372 .4z6
,27)
.251
,Zlz .Zzs .238
.203
.114 .180 .181 .193
I Z5
.Z95 .320 .369. .4Z3
.?70
..?49
.Zlo ,22J .236
.201
.173 .119 ,185 .192
J 30
m
.Z91 .323 .364 .416
.?bb
“,245
.Z08 .Zzo .ZJZ
.198
.170 .176 .183 .189
K J5
.290 .3Z3 .363 .416
.Z66
.245
.207 ‘.Z19 ,232
—.
,ZOJ .Z14 ,ZZ7
.190
—
.194
.169 .Ilb .182 .IE.5
L 40
.408
.156
.317
.Z84
,Zbl
.241
.166 .112 .178 .184
M 50
.399
.348
.310
.Z79
.Z5S
.Z35
.199 .Zll .ZZJ
.189
,lb2 .1613 .174 ,181
N 75
.393
.345
.307
.Z7b
.2S3
—
.Z49
.Z31
—
.Z30
,197 .208 .Z20
.la7
.160 .lb6 .172 .179
0 100
)81
.341
.30Z
.z71
,191 Z06 .21b
.185
.1s0 .Ibl ,170 .175
P 150
.386
.338
30Z
.Zb9
.Z48
..?Z8
.191 ;,Z03 .215
.183
—
.151 .163 .lb8 .175
Q 200
L
The MSD msy b, obtalmdby muh’iplylmg the factor F by the diNereace balwoen the uppr spaclflc~tlcm Ilmil U and lower
spee5fictiian limit L Tha formula lt MSD = F{ U-L). The MSD s+met m I gulda for the magnitud- of the ●oiimatc of let
otaad~rd deviation whtnu81a[ plmc for th* double specification Ilmh came, bm.td en the eatlmat. of 108ctandard davlatlea of
umbown v~riability. The estimua of lot otaadard deviation, if it Ic IF-o Ihm the MSD, helps 10 imure, but doe- not uuarMIee,
Ipt acceptability.
NOTE: Therm Is s corr*opondlng acccptablllty constud In Tikle 6.1 for ●achvdue of F. For reduced lnopectlen. find
tbmaccc~tabil!ty commnt of Table B-Z In Table B-1 and u,e the corresponding vahe of ~.

I
I
,,
1’
i
I
I
,
t
I
I
!
5!!!!9!
m
x
.
u
L
k
Qu
QL
%
‘L
%
P
M
ML
%
P
Pf,
T
F
>
<
.x
Red
X bsr
Q ●ub U
Q ●ub L
p sub U
p s“b L
M sub U
M sub L
p bar
p bar sub U
p b-r ●ub L
APP@Du B
~efinitkons
Sample ●ix. for ● .i=~le lot.
Definition
Mx~14
11 Juno 10S7
~P1. M==. Arithmetic mean Of .mup3m me.surememm i~~m
● .Ixl.qlc lot.
E.tinute cd lot ctandmrd deviation- Standard deviation of ●un -
ple measurement [mm a ●insle lot. (See &xmpIe* iaSect40n
33.)
Upp=r ●pecffic~tiOm limit.
Lower ●pecificalfiOn limit.
The ●cceptability eon. tant @ven i~ Table. B- 1 and B-2.
Quality index for u.. with Table B-5.
Ouality index for u.. with Treble B-5.
Sample ●.tirnale of the lot percent defece . . above U from
Table B- 1..
Sampl. estimate of the 101 percent defective below L from
Table B-S.
Total .ampl. e.timate of the lot percent defective P = PU + P~
Maximum ●llowable percent defective for .-pie eatinutea
~iven in Table. B-3 and B-4.
Mtimum allowmblc Pcrceat defective ●bove U given i. Table.
B-3 and B-4. (For uoe when differeot AOL valuea for U and
L are specified. ]
Maximum Alowable percexaf dcfecfive below L given in Table-
B-3 and B-4. (For we when differenl AQL vtiuea for U &
L ●re #pacified. )
Bamp3e ●intimate of the proceem percemf defectivw i.e., the
estinuted procea ● ●ve rage.
Tbe estimated proce. m8varage far u upper specification limit.
The eslimatad procenm sv.rqe for ● 10W* r ●pacification Mmft.
The maximum number of eattnnted prece. s sveragam wbkb
may ●xceed tb#AQL BlverI in Table B-6. (For u.e in determining
●pplication O! ti~hteaed inspection. )
A lactez ua.d in d.te rmim.i~ the ~um Standard Deviation
(hLSD). The F valu=s are given In Table B-8.
Greater than
ham than
sum of
Ml

Cl. SASIPLUJG PLAN FOR SINGLE
SPECIP3CATZON LDdIT
‘This part d the SUmZ. rd describes the
prO.y@ur=~ fOr. u*e wilh PlaM for s Si=ule
rep..c1ficati0n knit whcri variability O{ cbe
lot with rempecl 10 the qtmlily cbarseteri. -
tic M u.knowm and the ZWC nmtlmd i. used.
The -cceptability criteric.ti i# give= in lwo
equivalent form.. Th. mc arc identified as
Fo,rm 1 d Form Z.
the .“pplic~ble ●amplih~ PI- ●hall be treed
in .ccordance with the provisions of Section
A, General Demcripciou of Sampling
pl.m.. b the... in thi. part of the Sc.ndard.
SEC’ITON c
VARIABILITY UNSNOW7J-3LMJGE METBOD
Part 1
sZNG LE SPECIFICATION UT
MZL-STD-414
11 JufM2 19s9
CZ.2.2 Accep-ility Comstit. The acceptability
COa.t-t k. correspo~w tithe sunple
mi. e mentioned in paragraph CZ. Z. 1. is
indicated in the column of the master t.ble
corre. poading m the applicable AQL value.
Table C-1 i. enmred lrom the 10P lo. nc.r -
rn.1 impection ●md from th. bottom for
tightened inspection. Sampling plans for reduced
inspection a*e provided in Treble C-Z.
C3. WT-BY-L&fT ACCEPTA=ITY PROZ
CEDURES WffEN FORM 1 IS USED
C1.1 use of SUnpliag Plan.. To determine
whether the. 10C meet, tbe ACCCpt- C3. 1 AccepUbiZity Criterion. The degree
ability criterion wJth respect to a particu. of coaormance of a quazmy characteristic
lar quality characteristic •~d AQL vaZue. with re8pect to ● #ingle specification :imit
Cl.2 Drawing of Sarnp3e.. AN .armples sbdl
be draw. m accordance wltb paragr@iA7.2.
Cl.3 Determination of Sample Size Code
Letter. T he sample sme cod e letter •hd~
=ected from Table A-2 in ●ccordance
with par~raph A7. 1.
CZ SELECT3NG THE SAMPLINO PLAN
wHEN FORM 1 ls USED
CZ.1 Master Samplin~ Tmblec. The matter
●mplmfi tal C* cor DlaM b- ed on varia -
blIity u---n for ~ single ●peef.fieation
limit wbenuakg & raag. unfkodaro Tables
C-1 ●nd C-Z. Tabia C-1 b .u..d for normal
●nd ti~htened inspecfi.m uuf Table C-2
for reduced izupoction.
CZ.Z Obtining the SunptinS P3an. The
.unp3im~ plain ccmsastmO{ . .unple ●X ● -d
●m ●sociated accepIAbUiv C- taut. f The
.unplimg plain ia obtain.d from Maater
Table C-1 or C-Z.
CZ. Z.1 Sam le Si=e. Tbe sample size a it
.homa ,n ~ 1 e nla’ter table CC4rrm#p0~
each ●mple .1== e-de Iater.
tO
●haZl be judged by the quantity (u-X)/R or
{X- f.)lsi.
:/::1 -i: ‘iw%”%(ilwz
depending on whether the specification Iimi!
is = upper or ● lower lirnis. where
U im the upper specification limit.
L is fhe lower specification IimIt.
X is the sample mean, and
~ i. the ●verage range of the #ample.
3n this Standaqd. K ia the average range of
,.bKrmip ranges. 32ach d die subSro.p.
consists of 5 mea*u*emenl.. except for tbOa*
plans with ●unple ●ke 3, 4, or 7 in which
u** fbe ●kgroup ●im 19 fh sum as i.h
sanw3e sise. Zm wanpufiq K 338= Ord=r Of
Ihc sample meam=rem=iits u .-de c=u*t b=
rer.-iimd. Smkgrwpa af cnumcrmive nn.. -
urements must ba formed d the range of
.xh .ubgroup obtalwd. X is the ●weraae of
tbe individnaZ ●bgroup nngea.
C3. 3 AeceptsbIlltY Crite Finn. compare the
q.mtity (u - m (X- L1 ‘Kwithtbe “C’%%
●bilitv cor.8cant LOrZf (u-XI/X or (X- L)
equal “to or Creater than k. the lot meats tbe
●.ccptab13icy c rito rloix u (u-X)/R or
(X- 2.)1X ia less tbm k or m.’afiva. tbea the
lot deem not met the .c..ptability e ritoricm.
1Se. Appendix C for definitions of afl cymbolo us id b tbe ●ampllng pl~o bac.d on varIablltty
uak90wm- raaga mmbod.
%we f+ample C-1 f.r ● cmIIp3eto ●xunple of tbi. procedure.
al
._ . ..-

I
3A1L-m-414
11 June 1957
CL f3uMM~Y
SNAP LANG
USED
FOR OP3IRATION OF
PLAN WHEN FORM 1 LS
Th$ following 8tepm umun.riz. the procedure.
fn be followed:
(1) Determine the ●ample .i, c cede letter
from Table A-Z byu. iq the 101.ize and
the in. pecti.an level.
(2) Obtain plan from Mater Table C-1
or C-Z by .elecfin~ the sample ●ize n and
the acceptability ccm.taat k.
(3) select *1 random the .;rnpl. of m
“nit. from the lot: in. pect .nd record the
meamurernenx of the quality charactari. tic
for ●=ch uait of the sample.
(4) Compute the .;rnple mean X and the
●vera~e range of the .arnple ~, .md ●l.o
compute the quantity (u- X)IR for am upper
●pe. ificatiomlirnit V or thequamtity (X- L)/R
for . lower specification limit L.
(5) ff th= quantity (u-X)/R c.r (X. L)/R
i. equal to or greater thas k, the lot meet.
the ●cceptability criteriow if (u. X)/11 or
(X- L)llf i. I.*9 than k or negative, then the
lot doe. not meet the ●cceptability criterion.
C5. SELECTING THE SAMPLING PLAN
WHEN FOR64 2 3S USED
C5.1 Ma#ler Samplinj? Table.. The ma. ter
●amplmx table. for plana ba. ed o= varisbil -
ity unka&n for a single specification litit
when u.iq the rang. method ar= Taidec C- 3
●nd C-4 of Part IL Table C-3 is used for
nc.n’nal and tightened inspection ●nd Table
C-4 for reduced inmpectimi.
C5. Z Obtaininz the Sampltng Pllrl. Th ●
sampling ptan con. i.t~ of m .UIWI]e .ize and
an aooo~ik.d maximum a310w&le percent
def ●ctive . The ●amplfq ptam ic obtdncd
from Ma.t=r Table C-3 or c-4.
C5. Z.Z Maxd8mtmAIIc.wable Pereent Defective.
The madrnwn allowable percemt de-
=ive M for s-pie eotim.tes corres~nding
10 tbe sample ●iz= me~tie tied in
paragraph C5.Z.1 i. indicated tn tbe COIUMII
Of the rnmms.r tabte correa pending to the
applicable AfZL value. Table C-3 ii entered
from lb. top f-r ~orrnal iaapectian mad from
the botfom for ti~htened in. pecticm. Sun-
P~ Plaru for reduced inspecticm are pr.avided
in Table C-4.
3See 3cxAmple c-z tar a complete example of thim pru..dur..
62
CO. f.CfT-BY-LOT ACCEPTABI w P%
CEDU3432S WNEN FOR3A 2 3S USED
c6. 1 AcceptabUity Criteric.n. The degree
of conformance of ● qutilty characteristic
with respeet CC.● ●imgle .pecificstimi limit
.hafl be judged by tbc p.r. mit of notlccmfomnirt~
p.od. ct out. ide the upper er lower
specific aticm limit. The percentage of rmnconforming
product i. estimated by emtering
Table C-5 with the quality iadex and the
#ample ●i*e.
c6. ?. Computation c.f Quality Index. The
quality izidex Or, . (U- ZC)CIR hall be com -
puted “if the sp%cificaticm limit i. an IIppcr
limit U, O= QL = (X- L)c/K if it is a lower
limit L. Tbe q“amitie., X ●nd R, ●re the
sample mean and ●verage ran~e of tbe sample,
respectively. The compmatioa of K i.
●xplairted in paragraph C3.2. The facbar c
is provided in Master Tabl=s C- 3 an& C-4
corresponding to the .unple size code letter.
C6.3 fhtimate of Percent Defective in bt.
The quditv of a 1.s1 hall be expre.. ed by
PU. the =.timated percent de fe~tive in the
lot ●bov= the upper specification limit, or
by PL. the ●.ti-@d p.r. =ntd=fectiv= belothc
lower ●pccificatiort lirnii. The ●.tima~ed
Percent de f=cti~. PU O, PL i. mbt~im=d by
.mteri+j Table C-5 with Qu or QL .nd the
●pp. Opri~t= ●AMPlt ●i*e.
C6.4 Acceptability Criterion. Compare the
e.timated 1m percent defective PU or pL with
the m~imutn aZlew.hle perceM defective
M. U .pU or pL is equml to or le.. Uun M.
the lot meet. the’ ●cceptmbitity criterion, if
pu or pL is grekter than M or U QU Or QL
i~ negative. then the lot does not meet the
acceptability criterion.
Cl. SUMMARY OF OPERATTON OF SAM-
PLING PLAN WHEN FOR3d 2 IS USED
Tha fellowinK ,tep~ ●un’unar 3s9 the
ptwedures to be fallowed:
(1) Demwime ihe -ample .ise code lel -
ter from Table A-S ~u~inn the lot dae and
the iriapecttosi Iov@l.
(Z) Obtmi. plan from t.mater Iable C-3
or C-4 by .electirg the -ample sk= n. the
factor c, and tbe maximum ●llowable pw. -
ceat defective M.
(3) Select ●t random the sample of n
unit. {ram the 10C inopect and record the
meamm.mem al the quazity characteristic
on each nut; of the 8sMple.

.
MI L-sin-414
11 June 1057
(4) timpute the ●unple me-m X 4
av.ra~c raaSe of the ●ample K.
the (7) Uthe ●.timaled lot pcrcentdelective
PU or PL i. eqtml to or Ie*. thaa the md-
(5) Comp@= the q.=lity “ index QU =
(U-X)c/K M the upper speckfieation limit U
iripecified, or QL = (X- L)CIK i3 the lower
.pccificatirm limit L ia .pecif ied.
mum azlowable percent defective M. 3he lot
meets the acceptability criterion; it PU or
pL img.eater than M or U Ou or O’i.%=_~
-i”.. them the lot doe. W1 meet the ●ccept-
●biliw criterion.
161Decermirie .-, ——— the ●.limaled 10s m.rc.r..
defective PU or pi. from Table C- 5.-
~PLJl c-1
Example of Ca3culati0n*
Single Specification Limit-Form 1
Variability Unknown - Range Method
EXarnple The lower .pecifie.tion limit for electrical r.miataace of ● certtim ●lectricti component
is 620 ohm.. A lot of 100 item. is submitted for inspection. Inspection
Level IV, normal inspection, tith AOL = .4% i. to be used. From Tablet A-2 ud
C- 1 it i. ..en that a sample of size 10 i. required. Suppose that value. of the’
sample resistances in the order reading from left to right ●re . . follow-:
Line
—
1
.?
3
4
5
6
7
8
643. 651, 619, 627. 650, (R, = 658 - 619 = 39)
67o, 673, 641, 538, 650, (Rz = 673 - 638 = 15)
and compliance with the ●ccept ability criterion i. to be determined.
Sample Site: n
3nf. rrn.ti.. Needed
Sum 01 Measurements: I X
Sample Mean X: XXI.
Speckfieatio. Limit (LOwer~ L
The qu~tl~ (X- L)/It
Accep3AZZity Camsmt: k
Acceptability Criterion Compmm (X- L)/l!
with k
Value Obtained EXP1anatiom
10
647o
647 6470/10
37 (39+35)/2
620
.7s0 (647-620)/37
.811 &- Tabla’ C-1
.710< .811 ●&e ParaLc3.3
The lot doe. not meet tbe ●cceptability criterion. .irIce (X- k.)f~ is 1c99 than k.
= U ● .imK1e .PP=r .Pecificati.. limit U im give., then compute tb. quantity (u-Xl/X kn
line 6 ●ad cmmpar= it with k the lot meet. the acceptabUitY criteriom, if (U- rnf~ iequal
10 Or greater [ham k.
.-—
I

MIL-ST13-414
11 June 1957
EXAMPLS c-2
12xample 01 Calculation.
Single Specification Limit-Form Z
Variability U.knowmi - Rang. Method
Ex. mple A lo.ver specification limit for electrical re. i.tan.e of ● certain electrical component
i. 620 duns. A 10I of 100 item. i. submitl.d for inspection. Zaspection
Level lV. normal in. Dection. wish AQL - .4% i. m be used. From Table. A-2 mad
C- 1 is is seen thal ; sunple of ●izc 10 i. required. Suppo. e lh. v*Iu=. Of the
sample reaiatance. in the order readimg from left m. right are as follows:
Line
—
I
z
3
4
5
6
7
8
9
10
643. 651, 619. 627. 6S8. (R, = 658 - 619 = 39)
670. 673. 641. 638, 650. (R2 = 673 - 638 = 35)
●nd compliance with the acceptability criterioo i. 10 be determined.
Sample Size: m
Inlorrnati.n Needed
Sum of Measurememtm: IX
sample M,.. x: ZXJ.
Average Range ~: XRlne. of subgroup.
Factor c
Sp=. ific*tiO. Limit (~we. ): L
Q.a2ity Zndex C3L = IX- L)CIX
‘ct. ‘f bt ‘ercent “f.’ PL
Max. Allowable PerceIIt De f.: M
Acceptability Criterion: Compare pL with M
Value Obtained
10
6470
647
37
620
2.405
1.76
2.54S
1.14%
2.54%> 1.14%
The jot doe. mat meet the acceptability criterion. ■ince pL is gr=ate. than M.
6470110
(39.3S)12
See Table C-?
(647-620)2.405/37
See Table C-5
See Table C-3
See Para. C6.4
-E: U . .ingl. upper specification limit u i. Rive., th=. compute the quaii3y frufax QU ~
fU-X)c/3! in line 7 d obtain the eotimate of lot percent defe.tive PU. -mpr= PU
with M: the let meet. the ●cceptability criterion, U p“ ia ●qu~ io or i’z*. ~hn M.
M

. .. ——. _ .
TABLE C-1 RmIrn Method
unknown
Master Ttble far Normat and Tightened Zn$ptctlonfor Plans Based an V~riabIllty
(Single Specification Llmlt - rarm I I
1
15,00
ml in pectiml
-
K 2.50
sample t 1se
code letter
T
Y-
-
.587
k
.178
.296
. 50?, .401
B
.116
.Z?b
—
,2?2
.450 .364
.!325
—
v
.s’38
—
c
.184
.431 .)52
.498
.565
D
.189
.266
.405 .336
.465
.SZ5
E
..?5?.
.~41
.307 .424
.519
.65o
F
.216
.360
.516 .452
.610
.684
G
.105
.398
.371 .484
.647
.7,?3
H
,310
.403
—
.577 .490
1
.~lj
.406
.581 .494
.654
—
.658
.730
—
,734
J
.321
.s15
.591 .s03
.668
.746
K
.327
.421
—
.43Z
.598 .510
.336
+ .610 .!21
.616
—
.689
.754
—
.1b8
L
M
#2
i$!
24
.780 .701 ,621 .530 .441 .34s
0’
.791 .111 ,631 ,539 .449 .3SB
— —
—
P
.807 .7z6 .644 .552 .460 x
--1--
Q
230 1.21 1,21 1,16
.309 .728 4.364
.46z
I — —
—
2.90 4.00
15.00
,“:: tir,t &amplln$ plan below ●rrew, that {s, both sample -lie S* well as k value. When sunplt #its equa.loor ●xceed@ let
a ●, 9wory Item 2atha lot mnmtbn ln#pected.
1.)2 1,,06 .996 .932 .87o
.646 .5s3
I
.063
I
.10 .15 .25 ,40 .65 1.00 1.50
I
+ 6.50 10,0[
I
Accepmble Oualify Levels (tlgl med Impec m)
[
—
AU AC2Lv~ueo ●re in gercent defeciivo.
4s
‘i

-— .—
:6
TABLE C-2 Raa[e Mtthod
Mantar Table for Reduced Tnnpeclion for Plan~ Based on VariabLllty Unknown
(Siogle SpeciflcalIon Llmi!-Form i }
6,S0 10.00
1.50 2.50 4.00
:ept&l
J
.15
k k
k k k
7
.
-i-
.196 .178
.581 ,502 ,401
*
.296 .178
,296 ,178
*
.296 .178
Sample iiaa ISarnpls
EEE
code latter ●{SC
--1--
B
3
c
3
D
3
E 1
.216 .176
4
;
.27?. .184
.498 I .43, 1,.3s2
.565
.614
.663
G 5
.61J .569 .s2s
.266 .189
.75s ,703 .650
.141. .252
-u--
,7s5 .703 ,650 .579 I ,50? I .424 .341 .2s2
.192 .738 .684 ,610 5J6 ,452 .360 .276
.B35 .179 .723 ,647 .s71 .404 .398 .30$
—
.815 .179 .723 .647 ,s11 .484 .398 .10s
.E43 .707 .130 M.654 .371 .490 .40~ .Jlo
.E4e .791 .734 ,658 .5s1 .494 .406 .JIJ
— —
.E85 .826 .768 .6.99 .610 .521 .4J2 . JJ6
.899 .8J9 .7E0 .701 .621 .5)0 .441 ,34s
— —
7
33
.8[[
—
.811
.861
I
10
1
..963
T.916
J 10
.850
.90J
9 .958
K 15
.896
—
.896
.951
E1.10 1.0s 1.01
L. 25
.951
1.10 1.05 ;.01
23
M
.904
,959
1.10 1.o6 1.02
N JO
+
.900
.
.94.9
.964
1.11 1,07 I,0.?
1.00
1.16 1.11 1.06
60
P
,962
I.oz
1.17 I.IJ 1.08
8s
I
Q
i

C8. SAAfPLDfG PLAN POR DOUBLE
SPECIFICATION LtMIT
Parf 1I
DOUBLE SPECIFKATION
This part Of the Sf-rd describes the
procedures for tue with plain [or ● double
cpecificafioa Iimft when variabttify Of the
let with respect to tbe quality characteristic
ia u.knc. wm ●nd the range method is umed.
cA. 1 u.. a{ S-.11.. Plan.. Tc, determine
------- -. ——..- .. —”. .—— .—-—
~hethe r the 8.x meet. tbc .C eept.bility c rite
rion *ith rcapeet to a partiastar quality
char.eteristic .~d AQL. vtiue(. ), the .ppli -
cabl. ●ampliag F.lao ●U be used in accordatxe
with the pre. i.imm of Section A, General
De.eription d SunplinS PIMa, ●wJ
the. e in thi. part of the Staadard.
C9. SE LECITNG THE SAMPLING PLAN
A ●unplhg plaa for ●ach AQI. .tiue
.N1 be .clectcd from Table C- 3 or C-4 ●m
10UOU.. ,
. . ...- . . . . . . .
C9. 1 Determination of Sunple Size Code
~. Th ● .unple .s. code letter =hfi
b. ●elected from Table A-Z in accord-ee
with paragra~ A7.1.
C9. Z hta-tor SamIIlimX Tabla-. The master
munnlinn tablem [or mlam hmed Onvariabil -
ity ~fca~wu for a d~ble specification limit
wbeo uming the range rn.tbod ●re Tablea C-3
●nd C-4. Tsble C-3 is used for norrnaf and
tightened im.pectiom and Table C-4 for ra -
duced Lrup.ccfion.
C9. 3 Obtaintng Sampling Plan. A ●sM@in4
plm Comai,ts of ● ●ampfe sise - the sl -
●octatad maximum attowablo percent dafac -
tiw-e(. ). The cunplin3 plan to be ●pplied in
kn#pect&a stmfl be ~btied from Maater
Table c-3 or c-4.
C9.3. I Sun 10 Si=e. The ●antple sise m Is
.bownbiitdl,.. .Orr..pmdiag to
each ●unple ●ice code letfer.
C9. 3.2 Maximum Allowable Percent DeIe cfive.
The maximum-t allowable PCrcrnnt de-
~tive for cunple e.tirnatec of percent
def ●etiv. for the lower, qpsr, or botb ●p.c -
.
-..
67
Lf3d3T
xf~14
11 Jfffw 19s?
mmtimum ●llowable ~rcemt defectively ML
for the lower Iindt. ad by MU for the upper
limit. If ~ AOL i8 88sinmd to bofh limits
c.mbiaed. designate tbc -urn aflo.able
percemtdelecfiveby M. Table C-3 is entered
tram fhe cop for aornul inspection and from
tbe bottma for tAIhtamd inspection. Samplim8
P1W9
— .
Sor
.
roduce!ttmpaction
vialed iii Table G-4.
●re pr. -
C1O. DRAW7NG OF SAMPLES
sample. .fmfl be ●lected in ●ccord -
aace with ~raarapb A7. Z.
C1l. ;~~OT-~;~O T ACCEPTAB1_
Cl 1.1 Acceptability Criterion. The degree
of c.nfo~aracteristi.
with re. peel to . doub_fe .~cific. tion limit
hall be Judg.d by tbc percent ei wnco. -
ICr.rni.g producL The per.enta~e of no.-
Cwderming product is estimated by entering
Table C-5 with the quafity imd=x ●nd the
‘ample :Ue.
Cf 1.2
qualify
timputatioa
inchcea Q
of Ouality
{u .C xl
bdicei. The
[R and QL=
(X- L)c/R cbdl be !o&uted. -here
u
L
c
x
u
im the upper specification limit,
ia the lower .peeificalion limit,
is ● iacfor provided in Tables C-3 and
C-4,
i. fbe ●mple mean, and
i- the ●verage range of the sample.
b tbh Standard. R is the >verage rmge of
tba ●bsroup rauKc& ~cb of tie sti#*0Up9
consimt. of 5 meuurement$. ex’c=pt for those
pduu dtb ●rnple ●is. 3, 4, or 7 in which
case flu ●ubaro.p ●is. h th= ●ame ●e the
s-pfa ●~e. 3a computing R, the Order Of
fbe .unple meamtrernemm ●s nude mat be
ratahad. subgroup of co-ecutive meu -
urementi mnot be formed and tbe range of
etch ●ubgreup obtahed. K ia the ●-erase
of the individud ●ubgroup ranges.
Cf 1.3 Percent Defective In the Lint. The
qualify of ● lot ●hall be exprew~ed SrImrmof
the lot ~rc.nt dof=cfi.=. Its •c~~** W~
be dosipawed bY P L, PUO 0? P. The ●gtiwta
PU iadic*eD contmrmca ~tb respect to tbe
UPPGr spockfieatien Mnait. p with resp.ef to
the lower .peckfi.atim lAU. - P fOr
b o t h spaekfieation limlta combined. TIM

=.cirnatc. p.Laad pU ●baJl be determined by
entering Table C-5. r.mpacti..l~ ‘iJb Qt.
●nd Qu ●nd the ●ampl* ●i=.. The =~tim~te
p shall he dew rmined by ●ddin~ the co rres -
pcmdimg estimated percent defective. PL
amd PU found iii the table.
C12. ACCEPTAB1~ CRZTER20N AND
SUMMARY FOR 0PE2tAlTUN OF
SAMPLING PLANS
Cl 2.1 O!ie AQt- value for both Upper ●nd
b-e r + Cit,catmm Limit Cmnbmed.
Cl 2.1.1 Acceptability Criterion. 4 Compare
che eetimamd lot percent delectlve P . p“ +
PL -ilh the maximum ●l10-abl* Prc=nt
dcfcc:ive M. U p is equal to or less than M.
$h. lot meets the ●cceptability criterion, if
P i. e,e*t=, th*n MOr if either QU ‘r ‘Lor
both .re negative, Ihenthe Jotdoes not meet
the ●cceptability criterion.
C12.1.2 Summary for Operation of Sampliag
Plain In came. where ● .ingle AQL value 1.
=blished forth. um~er and lower s~ecifi -
C~t;ori limit cornbin;~ for a ●i=gle quality
.haracleristic. the following steps summa-
=i.. lh. procedure. to be used:
.
ll)”Dctcrminc the sample si. ecode
letter from T.ble A-2 by using ‘the Jot sic
and the in, pe. tie. level.
(2} Select plan from Maater Table
C-3 or C-4. Obtain the sample ttie n. th=
factor c, and the maximum mfloumble percent
defective M.
13) Select m random, the ●ample of
n unit. from the lot; respect and record tbe
mea. urem.. t of the quality characteristic
or. ●.ch unit of the sample.
(4) Compute the sample mean X ●nd
average rmge of tbe ●ample R.
IS) -mpt tbe quality indite. OU
F
. IU. X)c/K arid QL, = (X. L)C/R.
(6) Determim the emtimtiad lot
y-fi=nt d= f=ctiv= P * PU + pL frOm T~bl=
(7) 2f the eotinuted lot percent defective
pi. equal to erlem. thui the maximum
d20wable percent defective M. fbe 10Jmeets
the acceptability criterion, if p ia graatar
lIIM M or U either Ou or QL Or both am
negative, then the lot doe. awt meet tbe acceptability
trite rion.
C#w.~r Different AOL va.luet for Upper a~d
p8cuLcmU0m LamIL.
CIZ. Z.1 A.c=ptabitity Critdria. 5 timp8re
the estimated lot Per.cenc de fcctive~ Pt. ~
P with the corresponding
8eIe percent defective
maximum aTiow-
M ●nd Mu ●lso
compar. p . pL + Pu with tk e larcer Of ML
●nd Mu. 2f pL ia equal to or 1=6s ~h~ Mb
PU is equal to or lees than b4u. d P is
equal to or 1=0s than the larger of btL ~
Mu. Ihc lot meet8 the *cceplability critcri=,
otheruase.7be lot does not meet the scce Pl -
ability criteria. 33●ither QL or OU or both
●re negative, then the lot does not meet the
aeceptabitity c riteri&
Cl 2.2.2 “Summary far O~~atic.n -f ~mPliWf
PJan. & ~.ses m.h.re ● cliffere.t AQL value
~tmblished (or the upper ●nd k.wcr .Pec -
ificatio” limit fc.r a sim~ie quality characteristic,
the fol Jmnimg steps ●m-.mari=e the
procedures to be used:
(1 I Dcternai~e the sample ai.e &d.
letter from Table A-2 by using the lot ●i=c
and inspection Jewel.
(2) Select the sampJitig plan from
Master Table C-3 or C-4. Oblain the ample
size K.. the factor c. -d the m~mum
●llowabJe percent defective. MU and ML.
corre. pondi=g to AOL VaIUeS fo, the uPP=r
●nd lower Specific atiec. limit., respectively.
(3) Select ●t random lhe ●ample of
a utit. from the 10C inspect and record the
measurement or the quality characteristic
on each unil in the .UTIPIC.
{4) Ckmpute the ●ample mea. X ●.d
●.er.~e rams-kof tbe ●unpJe R.
(5) Compute the qualiJy imdicec QfJ
. (u- X)c/R. and OL =(X-L)CfU.
(6) Determine the ●.timm~ed lot
percent defective. pU amdpL. corresponding
to the p.r. em defective. above the upper
and below the lower specificticw limitt.
AJSO determine lbe combined percent detectiV=
p - ~ + pL.
dbt~ons:
4tie ~pk C-3 for . campl,ete ●xample d tbi. proc.dure.
SW *PI= c.4 for . =om**t* exunpZe of Ma PrO=~ur*.
-. -—.. . .
~u.
(7) 32atl three of the lollowlris cos-
(a) PU is =q-~ tO Or lEM tbu
(b) P,. ia aqtml co or I=*w th*m
ML-
{c) p is equal toor Jesmtin the
l.rger of ML and Mu.
●re ●aticfied. fh lot m.mtmtbe accepfAbi21ty
criteria; otherdse the lot hew not meet the
scc=ptability criteria. If either Oz.,or QU or
both ● re =gative. fba. *h. lot dw* tit UI**C
the acceptability criteria.
—

I
*.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
EXAUPIX C-3
Example of Calculations
Double Specification Ltrnit
Variability Unknown - Aver age Rsnge Method
One AQL Value for Both Upper and Lower Specification. Limit Combined
MIL-STD4M
llJunelDS7
The ●peclficstioni [or elec:riea2 recisfaace -f a certaiu electrical cOrnponeu5 *
65o.o ● 30 ohm.. A lot of 100 item. is ●ibmitt.d for In*petiiar& fmspecfi.. Uwe2
IV, normal intpectiea, wftb AOL . .4% ii to be used. From Tuble. A-2 and C-3 it
is ●eer. that ● samfle of size 10 1. required. Suppose the vafuea of the ●mnp2e
resistance in the order reading frm-n left to ri~ht are ●s follows:
643, 651, 619, 627, 65B. (Rl . 658 - 619. = 39)
67o. 673. 64). 630, 65o. (R2 s 673 - 638 c 35)
and compliance with the acceptability criterion i. m be determined.
Znf.armatiom Ne.ded V.lu. Obtti~md Zcxpla.atien
Sunpl. Sise: . 10
sum of Mea. u,. m.clt.: xx
.%mpl. U... X: XXI.
fawer Specification Ltmit: L
Ctudity Index Cfu . (U-X) c/R
Ouality Zndex: C3L = IX- L)e/11
~-t. of Lut p--t D=f. ●b- u: w
Est. of 3A Percent Def. baleu L pL
Tota2 Est. Parcant Def. h fak P = Pu + PL
Max. A210wable Percent Def.: M
Acceptab12ify Crtterloa: Carnpare p -
Pff + PL titb 64
6470
647
37
680
620
.?.405
2.15
1.76
.35s
..2.54%
: 2.89%
1.14%
2.e98 >1.14s
6470/10
(39 + 35)/2
See Table C-3
(680 -64Y)z.405/37
(647-620)2.405/37
See Table C-5
see Tsble C-5
.s5s + 2.54s
SOe Table C-S
See P*ra.
CIZ.1.Z(7)
Tbe lot dtm. nut meet tbe ●cceptabifify crilerlOn. since p = p“ + pL 1~ greater ~ M.
de
—

xm.-sTD-4l4
11 Jute 1957
I EXAMPLE c+
I
~ph of Cakuhuom
Doub3e Specfficatlom LimI1
I V.riab33ity Unknown - ~we ra~e Range Method
Different AQL Values for Upper and Lwer Specification Limit-
I ZZ.unple The ●pecifi.aticm. f.r electrical reaiscance of ● certain electrical cmnpone~t i-
650.0 ● 30 darns. A J*1 of 100 items im ●ubmitted for inspection Zn.pectimi 3AV.1
IV, rmrmmz impecziou, vifb AQ3. . 2.5$ far the upper and AQL E 1% far tbc lower
specification limit i. Ie be used. From Tablet A-z and C-3 it i. ●ce= that ● .am -
P1. of size 10 is reauired. SuPrmse the values of the sample resistances in the
irder reading fmm left to right “a-re a. follows:
I
I
I
3
4
5
6
7
8
9
10
11
lZ
13
14
15
643. 651. 619, 627, 658. (R, = 6S8 - 619 = 39)
670, 673, 641, 638. 650, (Rz = 673 - 638 = 35)
and compliance with the ●cceptability c*iteria i. co be determined.
Sample Six.: n
Intc.rrnation Needed
Sum of Me.. urcment.: 1X
.%rnplc Mean X: IXf.
Average Z4.nge ~: X3tlno. of .ubgroups
Factor c
Wp=r specificatio~ Limit: U
kwer Specification Limit: L
0ua2ity index Qu = (u-X) c/R
OuaIity fndex: QL = fX-L). /R
~s~. Of ~t Perce=: Dcf. =bOv= u: FU
~.t. ‘=f kt p=c.mt D=f. belOw fA PL
Tad Ems. Per.emt Del. in tit: p = PU + PL
MAX. A130wab1= Percent Def. ●bove U: Mu
- A330wabla Percent Def. below 3A M’
Acceptability Criteria: (a) CDmpmre PU
with Mu
(b) Compare PL
with ML
(c) ~t~p~ue p
Value Obtained
10
647o
647
37
680
620
2.405
Z.15
1.76
.35%
2.s4%
2.89%
1.42s
3.23%
.3s%

———— . .. —_. —
Rtrme Mcihc.d
T10.00 1s.00
M M
31.6q 40,47
29.43 3b,90
26.S9 33.95
I
2).s0 30.66
21.06 2?.90
19.36’ 2%92
TABLE C-3
Mamer Tbbl. fer Nermal .nd Tlthtencd fnsmctionf.r Plan. B.nedmv..i.hlltt.. lIA.,w.
(Double Speclficatlon ~lmlt ●ndf;r Form Z-Single ~peciflc”~fion Limit; ‘“””’---”
4cceptable C mlity Levels (normal in#pectlon]
Sumplc *IS* Ssmple
iiir!t
.04 .06S .10 m-
cede Icller *11*
.25 .40 B.65 1.00 1.50 Z.50
fa:to?
4.00 1 ZE-1
MMM T M M
MM M M M
B 3— G
.7.59 lfI.86 Z6.94
~vv
c 4 z.a34
t.sl 5.50 10.91 \b.45 ‘ 22.S6
D 5 2.474
1.42 ‘3.44 5.93 9.90 14.47 ZO.Z7
v
E 7 2.8)0
.28 .89 I .9q 3.46 5.JZ 8.47 12,]s 11,s4
I.ZJ
r 10 2.405
.58 1.14 Z.05 3.Z3 4.77 7.42 10.79 I 5.4q
It
—
G 15 LJ79 .061 .136 .2s3 .430 .786 1.]0 Z.lo 3.11 4.44 6.76 9.76 14.09
34 2s Z.358 .125 .214 ,>36 .5o6 .827 1.27 (.95 Z,8Z 3.96 5.98 8.65 12. s9
1 30 2.353 .147 .240 .366 .53? .856 1.z9 1.q6 ,?.81 3.q2 5.88 s.50 12.36
17.40 23,79
4
w
17.19 23.41
17.03 z3. zi
12,24
5.85 8,42
1.98 2.82 3.90
.883 1.31
.564
J 35
16.55 22.38
5.61 0.11
1,B8 2.69 3.73
.842 1.Z5
.lbS .261 .391
-tt-
.)60 .232 .375
2.349
11,04
.539
2.346
m 4b
+- 16.20 ?.2.26
.169 .Zbl .)81 .s42 .818 1.25 1,60 Z.b3 3.64 S.47 7.91 12.57
—
.13S .244 .356 .504 .1.51 1.16 1.74 2.41 3.44 5,17 1.s4 11.10
++-
.1561.Z4Z I .350 .493 .755 I.lz 1.61 2.37 3.30 4.q7 1.17 10,73
2.342
L 50
I $.64 ,?1.63
2.339
M 60
15.11 21.0$
2.335
N 85
t4.14 20.31
-L
14.i5 19.88
I4.1O 19.02
1$.00
.133 .230 .313 .468 .718 1.06 1.58 Z.zs 3.14 4.76 6,99 10.37
—
.z3q .210 .303 .4Z7 .65S .972 1.46 1.0s 2.93 4.47 6.60 9.89
-t-t
I
.43Z .661 .q76 1.471 2.0.5 lz.q2 4.461 6.511 9.!34
—
.23 .40 .65
—
,ceeptable (3 dlty Levelo (N:htemd Inspection)
2.333
0’ 115
2.111
P 113
z,j30
230
0.
-!Asl.& 4OOI6JOI1OJO
parcant dafactlve.

-!5
Ran[a Method ~
TABLE C-4
~$
Maamr Table #or Redueed Zmpecticmfor Plan, Baoedon VSrlabillty Umkmwn
(Doubl* Speclficalion kltand Form ?-Single SptcUicttion LlmII]
Acmptablo OuaZ{t IAVCI1
Smnpl* 81SC Samp10
.065 .10 .15 I ..?5 I ,40 I .65 I$1.50
cede letter ●IX*
2.$0 in- 10.00
L
MM M[hI’l MIM M MM
M
-ii-
*
1.99 18.06
40.47
7.59 18.86
40.47
7.59 18.86
1!59 1.s.86
10.92 16.’5
9.90 14.47
,
8.47 If?.Js
7.42 10.79
7,42 10.79
v 6.76 9.16
S.9.3 8.65
.21 1!
1.910
26.94 33.69
1.?10
26.94 33.69
1.910
Z6.94 33.69 40.47
1.910
26.94 3J069 40.47
2.234 1.53
2Z.8b 29,45 36,90
i
-
G 5 4Z.474
1.42 3.44 !.93
20.Z7 G- 33.95
H 7 2..530
1.99 3.46 5.3Z
17.S4 Z3.SO. JO.66
I.Z8
II
I 10 2.4o5
.58 l,i’ 2.05 1.23 4.77
15.49 z1.06 21.90
—
-1--
J 10” Z.405
.58 1.14 Z.05 ).Z3 4.77
G G Z7.90
K 15 z. 379 .253 .430 .786 I,JO Z.10 3.11 4.44
14.09 19,30 Z5.9Z
L“ZS $Z,MB .214 .336 .506 .S27 l.z7 1.95 Z.8Z 3.96
IZ. S9 17.48 Z3.T9
M 25 2.358 ,214 .136 .506 .827 1.21 1.95 2.82 3.96 8.65 IZ.S9 17.48 Z3,79
N I 30 Z.353 .240 .366 .537 ,S56 1,29 1.96 2.81 3.92 5.88 8.50 12.36 17.19 2>,42
z.349 .261 ,391 .564 .883 1.33 1.98 2,82 3.90 5.85 8.42 la.z4 17.03 Z3,ZI
—
Z.339 .144 .356 .504 .75.1 1.16 1.74 2.47 3.44 S.17 7.54 11.10 15.64 21.63
Q Z.J3S .242 .350 .493 ;755 l.l Z 1.67 2.37 3.30&5.98
4.97 1.Z7 10.13 15.17 21.05
I
ML bad table waluec tra in pcrcmt d. f.ctlve.
%deZ3rdt #ampNnszdmb.kw’.rrtmr, that,,, betb ccmple,l.ea~ weNa* MvsJu*. ‘ WI..SamPle S1S. OqU~C or ,xc.,do 10,
05
I
I
1,
:

... .. —.— — —-. —
TABLE C-5
Tabh for EcUmatInI lha Lot Percent Defective USIIIg Rans* Methedl
I
I
L-... . ..-
I

TABLE C-5-ConUINed
Ttbh for E#timatln# tba Let Percent Defective Ualng Rune Method
. ,. “
.“ .- ...
. ,.. . .
., ,.” ,..
. . .“ . .
. . ,.” .“
;,. . .
.. t.. ,-
.. .“ ,,*
.. ,,. ,,.
I.. ,.. ,.”
,- ,.a ml
9..,= ,-
*“ ,.. ,,.
. 6.. 0,”
. . . . ,-
. . . .. . ..
4...“ ,,.
. . ,.. .,”
.. . “
. . ...
“ ,.- **
.“ ,.9.s
4.. ,.. .*
i
. t.” ..”
a * ..
).. ,.* . .
,A ,a ,,.
l.. ,.” ,..
,.. ,.0 ,,..
1.. ,.” ,,.
i
. ,.94 *..
. . *..I
,,. ,.n *.S
“ ,. .
. ,.=D..
s.. ,.” .
,. ,- !..
,.” A. 9-
,s ,.. -
,. m “
1
I

.
TABLE C-5-ConUnursl
Tabh for Estimating tbo Let Par.ml t3ef@c11veUcla: Ilmte Method
,
I
I

— ‘-- —-
TABLE C-5-Continued
:!
Table fer Eotlmatlng the l-al Percrn! Defective Uolnc Range Method
I

_—
TABLE C-5-Contlaued
. .
T*Mo for Estimatlq ttm Lot Percm! Defective U#inS Raa[t Method
.\.
.
. ...

ESTIMATION OF PROCUS AV~GfZ AND CRfTERfA f=OR
R=UCED AN(3 T1Gf4TENE0 3NSPECTION
C 13. fig~MATION OF PROCESS AVER-
Tbe .verag. percent defective, based
~POa ● group of lot. .ubmttted for c.ri~iii.l
In. pectmn. i. called [be prc.ce. a ●verase.
OrigiM1 im.pectiert imthe fir.t inspection of
. particular quantity Of product .ubmitted
le. ●cceptability . . diati~uiah.d from the
ia. pe. tion of praducl which hambeen re. ub -
rnisted after prior rejection. The pr.acc..
●vera~e shall be e.timated from the remdtm
of im. peetion of ●mple. drawn from . .pec -
Uied numb. t of pr. ceditq lot. for the pur -
PO.. of delerminiag .everity of imapection
durimg the .our. e cd ● co=t?.ct in aecordaace
with paragraph C14.3. Ay lot .bdl be incitided
md, ante (m rt.dnutfri~ chmproc...
avera~c. The e.timate of thepmcc.. average
i. de. igriated by p“ wbem cwnpuc.d with
rempect tc. ●n upper .pecific.tion limit, by
(JL -b.. ..mP.ted rnth respect to a lower
.p. cifi..tic.n limit, and by p when computed
with respect to ● double .pecifi..t ion Ilmft.
.
C13.1 Abnormal R.. uft.. Th. ra.ult. of
ic!. pectitin of product rnamuf. cmred under
ccanditions aot typica3 of u.tmf production
hall b. excluded from the emtimaled proctm.
●verage.
Cl 3.2 Compufatio. of tbe EsUnmted Pro-
Ce.. Average. Th e estmuted pracemm ●vmr-
.;. 18the a%hrnetic mean of 4(I. e-hated
lot percent d. fecti.=m computed from tbe
●ampliag i.. pectioa re. ufto of the precedlmg
ten ( 10) lot. er ●. may be otberwi. e de. ig -
matad. & order to eatim.t. the lot p.rcem
defective, the qua3ity hdie.. Q“ andlcw OL
9ball be Coin ●d for aach lot. Tb... ua:
Ou = (u-X)C r X and
parwraph Cl 1.2. )
Ot, = (X- L)c/IL (See
C13.7..1
6
S&l* Specific& 3An& Tbe
emilmuea lot percent d ●1eetlva ●bQ b. d.-
Iarmin.d from Tabl. C-S forth #_ ti.d
on the r~c tuetbod. T& qdity M-x Ou
●bd k uood for tbae~e ti u-r •~.
Ific.tlmiMrnft er Q~ ler tb8 cu. d . tir
●p.cuictiom ulmlL T&l* c-s b tirti
dfb C)uor QL ●nd (h* ●rnfla ●ti=. d ~*
corresponding e.limated lot prcent dcf. c-
Uve p or p . rempecfivel~, is red from
the ta~)e. Tk ..tirnated proce.. .ver.~e
% i~ the -it f-=*ic M-= Of the individu~
-.titn.ted lot percent d. fectiva. pu’s. Sim -
itarly. tbe estimti.d proces8 ●.=r8ge PL
i. fbe srifhmetic mean of the individual estimated
lot perceot defective. pL’..
C13..?.2 Dc.uble Spccificatioa Umit. The
e.timateii lot pe,=.nl de fcct, ve shall be determi~ed
{mm Table C-5 fc.r the Plan. baaed
cm the rmt~. method. The quality iridice.
OU and OL shall be computed. Table C-5
is cmter.d #.parately with Cfu ad QL ●nd
the .ampfe .izc, and the c.rrespohdi:g Pu
-d PL ●re read from the table. The ●stim.ted
lot percem defective i. P . PU + P .
Tb. e.lirnated proce.. ●verage p i. ct+ ●
● rithmetic mea. of the i.divid.af ..tinuted
10I percemt defective. p,..
C13. Z.3 Special C.. e. If the quality iade.
Ou or 01. i. . aegativ. amber, lhen Table
C-5 i. entered bydi. regarding the negative
.iar.. Howcwer , ii. thi. c-.. the ..timat=d
lot perce.m defective above the uppar limit
or below the lower limit i. obthic.ed by .ub -
Cr.cting fh~ percentage lc.und in the table
from 100%.
C14. NORMAL TIGHTENED, AND RE-
“DUCED IkSPECTION
Tbia Standard esmblisbed ●u’nplfng
P(U far normal, tightened. and reduced
IEmpectk.n.
C14. 1 At Start of fa. pectiom. Normal inspection
.hd3 be used ●t the start of ias Pee-
U& uateoc otb.rwise dacignated.
C14. Z ZturirIg 3aspection. Qurimgfhe courm
of iwrnctiim, normal &xctio. sbdl be
UDd vba. imspoctian Coaiitimms are ●uch
(&85 tibteaed or reduced iMmcc?ion io not
r.4dTd Lm ●ccordume -itb” paragrmpfu
C14.3 d C14.4.
Cl 4.3 Tisbtened fxukmcfion. Tishw..d ia-
9D0ct10m 91M31be ttmtituted wbem tbe estj J
&t&f procemi ●verage computed from td

I
1.
prec.di.# t.. ( 10) lots (or ●uch other aember
of lot. de.i~nat.dl in ●ccmrdaoee .ith
para~raph Cl 3-Z is greater than th= AQL,
sod when mere than ● cc.rlaln ~r T of
theme hats have emtimatea O! the percem
delecctve .xecedisg the AQL. Tba T-values
●r.give. ln Table c-6 for tbeprocem ●wer,r
age compted from 5, 10 or 15 101*. 8 r40rmal
in. p.ctioa hall be reiiut.ted i[ the
e.tinuted proces. ●verane of Iota her
Cightea.d im.pecxic.n is ●qtd to or le.. tkn
the AQ t..
Cl 4.4 Reduced ln9PccUon. Iled=ced in-
●pecti.a rrmy b. uutitutad providd that all
of the following conditions ● rc catiafied:
Conditioa A. The preceding ten {10)
lot8 (or .uch other number of Iota deaigrmted)
have bee. under norm81 inspection and non.
ha. be.m rejected.
thmdicioa B. The ecttnu:ed pereemt
defective for each d theme preceding Ietm ile..
than tbe applicable lower limit #bow.
in Table C-7; or for certain ●ampiius plar.a.
Qa
the ●stimat.d lot percent defective i- ~
to sero for b ●vclfied ~r of towautiv.
10CC(see Table C-?).
COmdItkl c. Production i- ●t ●
●teady rata.
Normal Iaspectlen ●hall be reinstated M ‘my
one of the following cooditiea. eccvra ti.r
reduced ia.~ctiOU.
Cmditbm D. A M k rejected.
condition E. Tbe ●ettmatad procema
●va age 1. greater tbao tite ML
tkmditi.. F. Prehcttom become,
irregular or delayed.
Camdittc.aG. Dtber condition. w
may warrant Umt normal impaetio. . bauld
b. r.ltwtated.
Cl 4.5 S- Pling PIUIO for Tfuhta.d or Re -
dimed LompeCroon. Sam #w P~ ior tightened
-d reduced in@p@ctioa ●re provided in
Sectio. C, Partm 1 aad U.
... ,... .. .. .. .. .. .

MIL-sTD-414
11 Jme 19s7
,-
3 “3’ -3 3 4 4
H 5 b 6 6
: ; 7 7 e s
3 3 3 4 4 ,4
.1 5 b 6 6 6
7 : 7 8 8 9
4 4 4 4
J ; : 6 6 6
7 7 0 8 9 :
4 4 4 4 4
K : 6 6 6
7 8 8 8 : ;
4 4 4 4 4 4
L 6 6 6 6 7 7
a a 9 9 9 9
4 4 4 4 4 4
M 6 6 7 7
a 9 9 : ;1 0
4 4 4 4 4 4
N 7 7 7 7 7 7
9 9 91 01 0, 10
4 4 4 .4 4 4
0 7
9 Ii 1:1 :1 :1 :
TABLE C-6
VA.e. of T for Ti~ht.ned k.spcction
Sample #ix.
code letter
B
c
D
.04
.
●
●
.065
.
.
.
Acceptable DIM
.10 .15 .25 .4(
. . ● .
. ● ● .
. ● . .
Sy Lewd
T.6s 1.0
. .
T E . ● . .
z
>
4
z
4
s
F . . .
z
4
5
3
4
5
3
5
6
G 1: ! ; : ! :
?.
2
● 3 4
5 6
23 3
44 5
56 7
‘ectke]
6.5 10.0
44
:
8 :
: :8
9 10
4 .4
1 7
F10
10
15.0
1:
4
11
4
8
11
3
5
7
:7
89 -L4 4
‘7
10
4
7
10
4
8
11
2
8
—
4 d-
44 44
67 78
99 10
4,4 4
11
:
11
4
6
:
9
-t--t 1; 11 1:
44
77
99
44
:9
7
4
7 :
+ 9 10
4
7
10
—
4
7
10
—
4
7
10
—
;
10
—
4
1!
—
m
4
1:
—
4
7
JO
—
:
10
—
4
a
11
—
4
8
11
—
4
7
10
—
4
7
10
4
7
10
—
4
1:
—
4
7
10
—
4
e
11
4
a
L1
—
4
,?
44
7
10 1:
$44
7
10 1:
4 4
78
10, 11
$44
80
11 11
44
a
11 1:
44
88
11 11
4
8 :
11 11
44
80
11 11
*
4 4 4
n 8 8
11 11 11
4 4 4
-8 8 8
11 11 11
4
: : 8
11 11 11
4 4 4
8 8 8
11 11 11
4 4 4
8 a a
11 11 11
4 4 4
8 8 8
11 11 11
4 4 4
8 a 8
11 11 11
Range Me3b0d
Number
of Wm
5
5
5
-
5
5
5
5
5
5
5
5
10
10
10
10
10
10
10
15
15
15
15
1s
15
15
10 15
10
10
10
5
10
15
15
15
15
uid MLvm3umm.
----

‘=%!7
A. ce
z.10 .15
44
77
10 10
TABLE C-6-CooUfoJad
Vale. d T for Ti@t-.d Lmspcuoa
Q-lx
The S-D fiiwm in each block refers to the precedim 5 lot., the middle li~rc to the
4
7 :
10 10
ble Ouatit 5A ,.1s [ill
..?5 .40 .6s
4
788
“4 4
w10
11 11
laa
11 11 11
IT44
z1.0 1.5
44
f5a
11 11
44
a8
II 11
: :
4
a :
11 11 + !1 11
preceding.-
10 lots and lhc bottom figure to the pre&ding I S-lot..
mI I 1
MlL%Tn414
11 Juna 10S7
R.-g. Method
4 4 45
a a 10
11 11 1: 15
Tightened inspection i. required when the number of lots with ●.timatem of percent
defective above th= AOL from the precedin~ 5, 10. or 15 lots i. ~rester fhan the given vtiue
of T in the table, and the pr-.e=m averaae from these lat. exceeds the AQL.
Aff estimates of the lot percem defective are obtained from Table C-5.
al

TABLE C-7 RWISQMethod
Llmit# of htimxcd Lot Percent Defective (or f2educcdfn,pectk
Ssrnple *ize Acceptable Oudity Levels Number
code letter ,04 .065 .10 .1$ .25 .40
!
.b5 I ,0 1.5 .?.5 4.0 6.5 10.0 15,0 or z.ato
B ● ● o * ● ● ● ● ● [42]*. [28]** [18]** [121.. [ 9]**
Is
.17 s
c ● ● 4 ● ● ● ● [45]** (31)** [221.. [15j** [[O]** ( 7]** IS.oo 10
&
0.00 .74 6.06 s
● ● ● * ● ● [)1]** [25].* [18].* [II]** [ 9]** 4.40 9.96 15.00 10
6.50 10.00 , 15
D
.00 0.00 .19 3.s2 8.45 5
● [JO]** [23]** [17/.. [13].. [IO}** .35 1.84 5.74 10,00 J5.OO Jo
1.84 4.00 b. 50 b A Is
● ● ●
E
.000 .000 ,00 .061 .s3 .?.04 4.92 9.66 5
r ● a * [191** [141** [II]** .008 .104 .40 1.37. 3.01’ 6.06 10.00 I5.00 10
.158 .50 1.14 ,2.30 4.00 6.50 & i 15
.000 .000 .000 .006 .040 .148 .5)6 1.41 3.27 6.30 11.01 5
G [12]** [loI** [ 8)** .002 .015 ..060 .19z .449 .90 1.94 3.63 6.50 to.oo 15.00 10
.0.?0 .014 .199 .466 .90 1.50 2.s0 4.00 A & 1 15
.000 .000 .002 .004 .014 .04Z .112 .Z48, .498 1,12 2.20 4.27 1.40 12.13 5
H .003 .009 .020 .047. .101 .209 .422 .755 1.26 2.)4 4.00 ..50 10.00 I 5.00 10
.011 .025 .052 .096 .199 .174 .65 1,00 1.50 2.s0 , , A & 15
.001 .002 .004 .010 .028 .069 .16.2 .326 .600 1.27 2.42 4.52 7.68 12.43 5
I .006 .015 .032 .061 .110 ..?52 .478 ..522 1.34 2.42 4.00 6.50 I0.00 15.00 10
.017 ,037 .067 .118 .230 ,40 .65 I ,00 1.50 2.s0 L a A A 15
.001 .004 .007 .017 ,042 .094 .202 .Jsb .691 1.39 2.S7 4.11 7.91 12.65 5
.010 ,021 .042 .075 .151 .281 .51b .861 1.39 ?..47 4.00 6,50 10,00 15.00 10
.0.?2 ,044 .079 .131 .24B .40 .65 I ,00 1.50 2.s0 b A i A 15
1
●Th-rc ~rc no tunpllng plmo provided In this Standard for the-e code Iettera and A(3L vduos.

.
I
TABLE C-’I-C.mthtued RUIIO Method
Llmltc of ZZctlm~tedLX Pereent Defective for Reduced fmpectimi
2.5
T
y
333
.076 .140 .Z88 ,509 .857
4:00
i
1.40
2.50
&
.0Z4
.087
.144
.002 ,00s .012
.013 ,021 .049
.0Z6 ,010 .088
TF
,04 ,06S ,10
5.01 8.11 11.o~ 5
6.50 10.00 19.00 10
A k b 15
2.86
4.00
k’
1.6,?
2.s0
&
.190 .332 .581 .94.? 1.47
.Z5 .40 .65 1.00 1.s0
.036
.1OZ
.1s
.004 .010 .020
.010 .016 .062
.033 .0s9 .09?
L
5.2Z 8.48 13. z7 5
6.5o 10,00 15.00 10
tt-t- 1 bd 15
2.99
4.00
b
1,7Z
Z,50
A
.09Z .174 ,326 .562 .92i
.z06 .35Z .6o4 .968 1.50
.Z5 .40 .65 1.09 b
.046
,112
.15
.007 .014 .07.6
.023 .041 ,069
.036 .064 .10
5.5
3.19
4.00
A
—
1.32
4.00
1
1,87
2

,
TABLE C-8
Vducs Of f for h{dmum Average Range (hfARl
:ceptable Ouallty Le !It (in perct
6.50 I 10.00 115,00
de/cctive)
2.50 4.00
$ample #lz* Slrnple
CO* Ienor 91s* .04 .065
1,028
.907 .958
’77
B 3
.96S 1.0s6 I 1.180
.811 .865
+
.816 .891
c 4
1.011 I 1.118 I 1.26j
.756 .78.9
—
.764 !801
.857 .923
+
.910 I .985
D 5
.804 .846
--t-%
695I 727I 765
E 1
.730 .19)
,64z .677
442!3
.529
r 10
.6OZ ,637
.517 ,542 .572
.49J
,477
G 15 .444 .460
.785 I .879 I 1.004
.68.9 .748
-t-
.649 I .707
.567 .6OO
.486 ,509 .537
.463
.447
n 15 .4[6 .412
.642 I .699
.56o .593
,480 .503 .531
.457
.442
I 30 .411 .426
*
.6)7 j .694
.556 .588
,416 .49? .527
.454
.438
1 35 .408 .4?.3
.628 I .684
.548 ,580
.469 .4’?2 .519
.441
.4JZ
% K 40 .402 .417
,752 .843 .96)
.621 .676
.542 ,573
,463 .486 .503
.441
.426
L 50 .396 .411
.949
,740 .830 I
.533 .564
,455 .478 .505
it-
.434
.419
M 60 .190 .405
.129 I .618 I ,934
.608 .666
+
.6OZ I .656
-1-
.594 .64S
.504 .637
.525 .555
i--l--
.442 ,464 .490
44’I 470I 497
.427
.412
N 85 .J8Z .398
.720 I ,s08 ] ,923
.517 .540
.421
—
,411
.406
0’ 115 .318 .)92
.708 I .194 I .908
.300 .5)8
.434 .455 .481
.399
P 175 .371 .384
.507 .516
.43.? ,454 .480
.41z
.197
+
a 230 .369 .384
The MAR may ba obtdaod by multlplyin~ the factor f by the difference between the upper .pecificati.an limit u .nd lew. r
speciflcallon Ilmif L. The formuh 1- MAR . lIU-L). The htAR serveB as a guide for the magnitude Of the average rang, of
Iha ounpla when uaia# plant for the double opecUicatian Ilmit .ca#e, based on the average range of the munpla of .mbm.wn
varlabUity. Tha werap ruge of the .smple, tl It.ls Ieoo than the 5dAR, helpc to inoure, bd doe- not [utrantee, lot accept.
abiflty.
NOT&: There h t eorreopoadkg occepfablllty constant In Table C. I for eqch .aZue of f. For reduced hirpection, find
tht ●ccepttbillty comtant of T-ble C-Z in T~ble C- I md u-e the corre~pmtding value or f.

I
I
I
I
SY@.?!
m
Read
f
APPENDIX C
mMlmitfO.s
sample ●ike far ● single lot.
Definition.
mL-SlW414
.11 June 19s7
x X bar %rnple mean. Arithmetic meam of ●mple mea.. r.m.rm
from . .ingle lat.
R Range. The difference betweer. the Iarge. t and ●rnalle.t
mea.ur. mests in . .. bgroup. & this Smitdard, the #ubg.o.p
site scuf C-4. (For use wbem differenf AOL valuca for U and
L ● re specified.)
p bar
p bar #ub V
p bar suh L
~uxn mflowmble pert..t de f.cti.. blew f. Siv.m in Tabfe.
C-3 and C-4. fF~r u.e -ha. different AQL value. for U ad
f. ● re cp=dfied.)
S-pi. ..tinut. @f the p.ece.. p.rc.m defective. i.e.. Cbe
estinmt=d prc.ee.. average.
The estimumd proce.. ..era~e for UI upper ●pecUication lf-mit.
The ●stimated pro . . . . ●verage for a lower .pecific.tion limit.
The m- um number of emtin’tated proces. a.er4ea w~cb
may exceed the AOL given in Table C-6. (For use in deffr-
_ WW+fiCafiL= U fi~ht=aod Ampeefloa)
8s
.—.

01. SAMPLfNG PLAN FOR SINGLE
sPEC1 nCATfON LfhffT
This part of the Stand~rd de.tribes tbe
prOc=

mL-snb414
11 June 1957
(21 Obtain PI*. from Master Table 33-I
or D-Z by sel=ctitag the ●ample .i%e rI ●nd
the .Cceptabitity Coti.ta-t k.
(3) Seleti at random ~ha .unple ef ❑
units from the lot: inspect ●nd record the
tn. amur. merit of the quality characteristic
Ior each unit of the ●ample.
[4) Cornput. the .unpl. me.. X, ●nd
●lso compute the quantity (u-X)/e for an
u per specification limit U or the quamtity
{f- L)/. for ● lower .peciiicatiaa limit L
(5) lf the quatitity (U-X)/. O. (x- L)/a
i. equal to or greater lhas k, the lC.I meet.
the acceptability criterion; U (u-X)1. or
(X- L)/W is Icaa :han k c.r eesative, them the
101do=. not meal the acc.ptabillty criserbn.
D5. SELECTING THE SAMPL3NG PLAN
WHEN FORM 2 3S USED
D5. I Master Samplirm T. bles. The ma.t.r
m.rnpling tables for plans ba. ed on vari. -
bilily knc.un (~r ● .ingle specification Iirnil
●rc Table. D-3 ●nd D-4 of Part IL Table
D-3 is used {or normal .ad tightened inspection
and Table D-4 for reduced inspection.
D5. Z Obtainin~ the Samplinff Plan. The
sampl.ug plan .onsi. ts c.{ ● ample .iz. ●nd
an ●ssociated maximum ●llowable perccnl
defective. The .amplimg plan is obtained
from Master Table O-3 or D-4.
D5. Z.1 Sample Sise. The .ampl. .i=e ~ i.
.hown in the rnasler table .x. rreaportdine to
each s~mple .i=e code letter,
D5.2. Z Maximum Allnr.. able P.rcecIt Defeormae.ce c.f ● quality eha~aeterimtic
with respect m ● .iagi. .pecifi. atio~ limit
.hdl be judpd by the prc=a of ~~conformimg
producl nutside tbe upper Or lm.er
‘S=. EXamPI. D-2 far . complete exunple of thl. precedure.
88
●Pecificalion limit. The p.rc.mtag. ef nomc.nferming
product i’ ●.;imamd b~ ●nfcr-
Tablt D-5 with the quality index.
D6. Z Computation of Oualilv lade-. The
quality ic.de= QtI . [U-X) VI. .h.lf be corn.
puted if the 8pe; ification limit im u. upper
limit U, or C3L = fX-L) v/. if il is s lower
limit L. The quzc.litie.. ~ and . . ●re the
..mplc mean and known variability. respectively.
The laclor v i. provided in Tables
D-3 and D-4 corre. pc.ading to the .unpfe
size.
D6.3 Estimnte of Pert.nt Defective in Lot.
The quality of ● lot ●hall be exprem. ed by
Pu. the estimated percent delective in the
lot ●bove the upper .pecificstmn limit, or
by P the ●stimated percetit defective below
ih. l-” owcr specific alior. limit. The citimated
percent de~ective PU or pL i. obtaiztedby
cmte. img Table D-5 with OU or Cfti
D6.4 Acceptability Criterion. Compare the”
estimated 101 p=rcent defective p~ or pL
with th. maximum ●llowable percent de fcc -
ti. e M. lf pu or pL i’ equal to or le.. than
M, the lot meet. the acceptability criteriotx
if PU or PL is ~reater than M or U QU or
‘L ~S negative. ~h=n th= 10t do= C@ IIWCt
cn. acceptability crxterior..
.137. SUMMARY FOR OPERATION OF
SAMPLZNG PLAN WNEN FOffhf 2 IS
USED
The following steps summarice the Procedures
tO be followed:
(1) Dele. rninethe .m’nple size code 141cer
from TabIe A-Z by ..ing the lot .ise and
the in. pecliem level.
(2) Obtaia plmr. from Mater Table D-3
or D-4 by ●electing lhe ●unple ●i=e U. fbe
fbctor ., ●nd the mulmum df.wable percent
defeefiwe M.
(3) S4ect st ramdom tbe .unple of n
umits from the 10G irs. pect and record the
nma.ur.nmnt 01 the qualhty charutari9tic
on each umit of tbe ●empl..
(4) Compute tbe sample me- X.
[5) Compute the quality index f2u .
( U- X}v/- U ●. upper t cificatimn limit U
= (FL)v/. If ● ,-*
;F%%%$; %ai% i, .peeified.,
16) Determine the ●mtimsted lot prcasd
defective PU or pL fram Table D-5.
-——

I
I
I
I ..
I
I
I
I
I
MUA7D-414
11 Juoa 1SS7
(7) U the emthrmtcd lot percent de f.c -
UW* pU or pL im eqtml W or Ie*a ttmo tbe QL u ‘u h ‘r nesattve, “ “ ““”=’ thea the‘- let M deem “ ad ‘f ‘4Z
maximum atlowable percent defective M, the =ccopMbUitY criterion.
the lot meata thm ●ccaptabiii.~ cricerla~
EXAMPLE D-1
&Ample of Ca3ctiiiam
SiaCle Spec51ictii0a L%iit- Form 1
VariabiIlfy t(cw-n
Example The ●pecif ied minimum yield point for certain ●t4el c~-ttags is 50,000 psi. A lot
of 500 item. im wubmicted for inspection. lo bpection Level IV. normal Ia.poction.
with AOL . 1.5S i. to be u..d. The variability . i. knowm te be 3000 p-i. From
Table. A-Z and D-1 it i- seen that ● mample of ●kc iO io re.autred. SUPW9C fhe
yield point. of the ●unple specimen, ●re:
Lint
—
1
2
3
4
5
b
7
8
6Z,500; 60,500; 68,00(h 59.000; 65.500;
6z.000; 61,000; 69.000; S6.000; 64.500;
and rompliame with the acce?tabilitv criterion i- to be determined.
Information Ne.ded Value Obtained Expluulion
Sample Sise: n io
Known V.riabitity: . 3.000
Sum af Mes..rcmcnt.: IX 630,000
Sample Mm. X: ZXln 63.000 6J,000110
Speeificatioo Llmlc (Luwer): L 58,000
The Quantity: (X- L)le 1.67 (63,000-5.5.000)/3000
Acceptability CoLI. taat: k 1.70 See T-ble D- I
Acceptability Criter- Compare (X- L)/. 1.67 c 1.70 see Para. D>.3
with k
The lot does mot meet the =eceptabi3ity critmriom, dnce (X-L)!. is le.. th= ~
NOTE: If ● ●ksie upper specUiCatiOn ltrrdt u i. SWen. tbeh compute tbe quaatlfy (U-X)1. tm
— lb- b d compu~ it with k the 10C meet. the .cceptabiiify crit=rio. if ( u-X)k i.
equal to or greater tbui k.
89

54flL-sl’13-414
11 Jumd 1957
E~LE D-2
fkampfe of Cafcuhtfonm
Single Specification L4mit - Form 2
VariabUity Known
Example The specified mimimum yield poiuf f-r certain .teel
or 500 item. is submitted ror inspection. inspection
casting. .. . in S8.000 psi. A lot
Level Iv, normal lnspectlon,
with AQL = 1.5% is to be u.ed. The variability e is known to be 3000 psi. From
Table, A-2 and D-1 it is . ..cI that ● sample of ●ize 10 i. required. .SuPpa. e the
yield points of the sample mpecimen. are:
Line
—
I
2
3
4
5
b
7
8
9
10
62.500; 60.500: 68,000; 59.000; 65,500:
62,000; 61,000; 69,000; 58.000; 64,500;
and compliance with the ●cceptability criterion is m be determined.
biforr?mtirm Needed Value Obtaimed Explanation
sample size: n 10
Know. Variability: c 3.000
sun-l of Mr.a.urerncIll’: xx 6>0.000
sample Me- X: TXln 63.000 630,000/10
Factor, v 1.054
sp=cific aliOn ~mi, ltiwe r): f- S8.000
Ouality fnder: OL : (X- L)v/o !.76
‘m’” ‘f “ ‘Crcent ‘“1 ‘L
(63.000-58.000)1 .054
3,000
3.927. Se. Table D-5
Max. A1l.awabl, Percem Def.: M 3.63% See Table D-3
Acceptability Critcrian: Compare pL 3.92% a 3.63% S=. Par.. D6.4
with M
The lot d~es not rn. e$ the ●ccepf.abifity criterion, since PL is great=r than M.
F-
~E ff . sin 1. upper .pecific.tion Iii-nit ff i. given. the. compute the qu~lity index Qu =
(U. XIV . m lme 7 and ebtain the sstimale -f $he perceml defective PU. compare
with W. the 1.s rn. et. the ●cceptability criterion if pu i. ●qual 10.0. 1.*S than M-
PU
90
I ------- . . ..- .-

TABLE D-1
Matter Table for Normal and Tlghtenad Inspection for Planr Baoed on Varlablllty Known
(Single Specification Lkmlt-Form 1)
ccepttble Ouallty Level? (norma2 Inopaction]
.10
[
.1s
I
.25
[
.40
I ,65
a k [nklnklnkl ak
++”
. 1 1 , ,
4 2.39 4 2.30 4 2,14
I
5 2.05 5 1,25
I
S 2.46. 5,.,4 I 62.2, I 6Z.0* I ?. ‘“ 1,95
.06S
.04
Sample 91*c
code letter
n k
n k
B
—
c
—
D
E
F
F
—
49
—
3
3 2.58
G’
I
4 2.5s
4 2.63
H
6 2.49 I 6 2.37 I ? 2.25 I 8 2.13 I 8 1.96
6 2.59
5 .?,69
1
-1 2.s0 1 2.3s 8 2.26 9 2,13 10 1.99
6 2.58
6 2,12
J“
8 2.54 ‘? 2.4s 9 2.29 10 2.16 11 “2,01
7 2.63
1 2.7?
x
9 2.54 10 2.45 II 2.31 12 2.la 13 2.03
1 t
11 2.59 12 2.49 13 2.35 14 2.21 26 2.o7
I
I
16 2.65 I 1? 2.S4 I 19 Z.41 I 21 2.21 I 23 2.12
8 1.64
8 2.7?
5.,
11 2.12
10 2.81
M
14 2.88 15 2,77
19 2.92
1= r-
20 .?.80
27 2.96 10 2..94
37 2.97
~
.063
.10
N
30 2.14
27 2.29
25 Z.4J
I
I
22 2.69 2)- 2.57
I
31 2.72 34 2.62 31 2,41 40 2.33 44 2,11
42 2,71 45 2.62 49 2.48 %4 2,34 59 2.18
o
,’ ‘E
.15 .29 ~o .65 i ,00
Acceptable Oua21ty Levalo (tightened lnopectlon)

. ---
TABLE D-1-Conl[nud
=s
Maoler Table [or Normal and Ti~htenid Znopectionfor PlarJI Based On Variablllty l(nown
(Single Speclflc.tlon Limit-Form II ?1 ;.
l==
Acceptable I 31ty Level# (normal Inmpeetim)
d
z
Sample ●Ic*
~~
I .00 1.50 Z.50
4

.
I
TABLE D-2
1
F17
.40 .b5
n knk
Z 1.3b
z ,.581, z 1.42 I
3 1.b9 3 1.S.6
II
-=-H-i
5 l.aa b 1.7a
II
=-l-=-i
Msomr ~nbte for Reduced Zn8pectionfmr Plant Baiedon Variability bon
(Sinlle SpecUicaIlon Limit- Form 1)
ble Quality Levelo—
.15 I .25
.04 .065 .10
Sample aico
coda Inttmr
Rn knk
8 k m k n k
}
a25
c
D
E
—
r
G
z 1.94 z 1.01
1 2.07 I 3 1.91
3 2.07 3 1.91
4 2.14 s 2.05
6 2.23 b 2.0%
34
r1 1
3 2.19
I
J’
3 2.19
I
K 132.’ 914 39 4 Y..3O
L 4 2.ss 5 2.46 5 2.34
‘ k 2.23 b 2.08
M 4 2.55 5 2.46 5 2.34
7 2.25 8 2.13
N 6 2.59 b 2.49 6 2.37
10 [.99 I II 1.86 I
a 2.26 9 Z.13
0 6 2.58 7 2.50 7 Z.J8
13 2.35 14 2.21
19 z.41 21 2.21
*
P 11 2.12 11 2.59 la 2.49
Q 15 2.77 16 2.65 17 2.s4
I I
4*

.
:.
TABLE D-2-ConUnued
:s
Masltr Table {m Reduced kicpectbn f.? I?lan. Breed On Variability IGI.Wm
(Sin@Speciflcatlon Limit -F.atm 1) :8
..—
Acecptable C2uaIityLevelt
‘Smple Siso
code letter
n k 1
1.00
I
1.50 2.50 “ 4.0 6.5
n k n k
m k n k
!
!
n k
I
B
c
D,
E
=--l 6 ,515
a 1.2s 1 2 1.09 I 2 .936 I 3 .755 I J .573
F
3 .8.35 4 .641
a 1.33 1 1.17 3 1.01
G
5 .919 5 .1?.8
9 1.44 4 1.28 4 1.11
53
z .1
0 .584 I
6 .991 1 .797
4 t.5j 5 1.39 5 1.20
8 ,584
1 .797
6 .991
41.53 I 5,1.39 I 51.ZO
J
!2 .649
11 .877
9 1.01
7 1.45 8 1.28
b 1.62
II
K
16 ,685
14 .906
11 1.11
a 1.60 9 1.49 10 1.31
L
16 ,685
14 .906
12 1.11
S 1.60 9 1.49 10 1.31
EM
20 .706
17 .9?.4
15 1.13
13 1.34
I
11 1.51
I
10 1.70
N
2.4 .719
21 .942
18 1.15
12 1.?2 13 1.53 \s 1.35
o
18 .770
33 .995
29 1.21
19 1.79 22 1.61 25 1.42
P
56 .803
49 1.03
42 1.24
36 1.46
32 1.65
I
I
28 1.84
Q

I
I
I
...”
..:
--
DE. sAM’PU?JG PLAN FOR DO CfBCE
sPECIF3CAT10N _
This part Of the Standard describma the
procedures f.r use with pftis for ● double
Specific-tiom limit when variabttlty of the
lot =ith reopact to the qtmfky c~rscteristic
i. known.
DE. 1 U.* Of SUnplimc Plan,. TO determine
w%the r the lot meets the ●cceptability cri -
le.-ion with ?=*PCCX co ● XrtiCtIISr qu~i~
characleri~ tic and AOL v’azuels). the applicable
●ampliag plan shall bc u.ed in accordance
with the prwimic.nm cd .$ection A, Gea -
eral DeacriptiOm of SkrqdiW Plmns, md
those in this part of the Standard.
D9. SELECTWG THE fMkfPLfNG PLAN
A sampling plan for esch AQI. .ake
.h.11 be selected from Tab)e D-3 or D-4 ●
[0110-s:
D9. i Determination Of S=mple Sise Code
Letter. T he ●ample ●ma cade letter .bfi
b~.cte.d [ram Treble A-Z in mecordamce
with paragraph A7. 1.
D9. Z Master SamPlinE Table.. The maater
SUnpl-es ier w bs. ed on wuiabi3ity
known for ● double cpecific-tti Itit ●r=
T=ble- D-3 and D-4. Table D-3 11 u~ed for
.O rmal amd tightened izupection ud Tmblc
. D-4 for reduced inspect.ion.
D9. > Obtaining .sunpli.g P1_ A ●unpliag
plaa Celia, mt, 01 ● ●mple ●2*, d M ● s80-
.dated maximum aflowsble ~rc=m defectively).
The ●uf@ins PI- ti be ●pp3Aed Jo
inspection shall be ebtahed from 3dmcter
Table D-3 or D-4.
D9.3. 1 Sun 1. Si.e. The ●unple ●i.e m i-
#how. = ~ t e master ZAb3e. eorrecpondlag to
each ●unple ●txe code letter -d AOL.
~Iv* for .unpte .8Unut.* .of percent
dafeectwe for th4 Imr. nppe?. 0rb04b cp*ctfication
limits co~ta.d. eerr*mpOndbs fa
tb. sample ●ize memfiomed in parasrmpb
D9.3. 1. i. #ho_ in the cdunm of the W18mter
table eorreaponding co tba applicable AQ3.
wdte(s]. K dKferemtAQLos m aa~isad w
●xb speckficatlon Umlt. demtsuua th8 -tmmm
tile-able percent defective by ULIOZ
Psrt n
DOUBLE SP3ZC3SXATZON Lfb4ZT
es
kUL-sm-414
llJums 106?
the lover Itrnlt. M4 by MU for tb= UPWr
limit. u one AOZ. i- ●ssigned to bath l~ltc
combined. demipte tbe maximum A31.wable
p-rcerd defective by M. Table D. 3 is entered
from the zop for uornuz tipeczton and from
tbe bosom for ttghtened imopectdon. Sampli.s
plans for redoced imcpeczion sre prOvided
in Table D-4.
D1O. DRAWING OF SWLES
Samples #ball be selected In accord-
●nce with parasraph A7. Z.
D1l. #.&-T-Y~O T ACC~PTABIIXl%’
D! 1.1 Accepi.bility criterion. Tbe degree
et conformance al ● qutiltY c r.cleri~ tic
with respect to a do~le sF&c Ification limit
.ihll be judged .by tbe perce~ al ~confarmiog
product. The ~TCeIIUSS Of Wa-
.IJaforzniq product La estimated by enterkg
Table D-5 wAzh Z& quality M-x.
D 11.2 Computation of Quality lndice ■. The
qua3ity iadices Q . (U-xwi e and OL=
(X- L)v/c. ●ball be ~omputed, where
U is the upper specification limit,
L i- the 10wer ●peeificmion limit,
“ is a facsor providsd in Table* D- 3~d D-4.
X is tk .unple mean. and
. ia zbe ksowm wariabifizy.

..
nlL-s’nk414
11 JuIIe 1957
Pi +b *= s-Am .Uew*Ie ‘P~z~ti
delceuve M. 25p u equaf to or lea- 3baa U
the Id meeb the ●ccep3abUIty crUeri~ ff
p ic ‘re=ter tbm M or if Of) or Of. or both
.,* Itapfive. Umn the lot &es ml meet the
acceptabffity criteriam
D12.1. Z Suna~ryef OP erati.n of Sunplia
Plan. la caoe. where a .ingle AOLvtiue ~
~bliohed for tbe upper and lower ●pacification
limit cornbim.d (or a ●fwle quality
characterimtlc. the tolZowinS steps 8umma.
ri. e th.. procedtwe. to be u.ed:
(1) Determine the sunple ●ise code
letter from Table A-2 by u.ing the lot .ize
and the in. pectioa level.
(Z) Select plan fr.am Mater Table
D-3 or D-4. Obtti tbe .unpla si.e n. the
factor ., and the rruximurn allowable perced
defective M.
(3) .%], ct ●l ra=dem the .am~le of
n unit. from the lot; in. pect and record the
m... ttmeatat of tbe quality characcerimtic
on ●.cb unit of the sample.
(4) COmpute the .unple mean X.
(s) compute the quality indicem Qu
= (U-x)vl. ad QL . (X. L)v/..
(6) Determine the ●.tinmxed lot
percent defective p . pu + pL from TabIe
D-5.
(7) M tbe e. f.inuted lot percent defective
p i. ●qual to er le.. than the maxi.
mum allowable p.rceas defective M. tbe lot
me. t. tbe acceptability criterion: if p is
sreater than M or if Qu or OL o, both ●xe
=S~~V~. tfI*n *- let doa - not meet ~e
mccapc-bility criterion.
DIz. z Dlff8remt AOL Values for Upper and
&w.r .Sp.eUi.aUOO LiInlL
D1 2-2; 1 Aceap4abflUy Crit9ria. 5 COirtfu*e
the ●stdnuted 1ot pmrc~t defeetivem m.. h
PU dth the cerro@omd4ng ~ -a..-
=bI= Perta=t de f==ttvew M d Mfj alao
=Omi=r. P . Pfi + PU wittt k larger d ML
mmdMu. lf pL sequmt taarle*attmm ML. P
ic 9qtmf to or Ie*m tbul Mu. ad p i. q A
to or lam than the larger of ML aad Mu,
the lot meat. tbe ●ecepbility criterk
—--- . .
athrwi. t, tbe 10I doe. rat meet tb. ●ce.pl -
ability .rit. ria. Zf either OL O* O“ or both
ar. ae*.U.e, UMrI the 10; &e. 03%rpe.t the
●ccep3abUtty criteria.
: D12.Z. Z summaryc.f operation ef s-
Plan. Za em=. wtmre ● diflereot AOL
~ctabliched f., the “p-r -d lower t~c.
Aficatiom limit for a •in~le qtmii17 character -
imtic, tbe ;dfow- .tcp. . urnnmrime tbe
prmcedurem fn be u.ed:
(1) Determlae the ●unple ●k. code
letter from Table A-Z by uefa, the 105.&e
d in.peetio. level.
{Z] Select tbe san-tpliag plan front
Mate. Table D-3 or D-4. Obtaio tb. ample
.ise tI .ad the I.cter ., eorre.podirq
to the lar~erof lb. two AQLva3ue.. dal. o
the maximum .U.Ywable percerit delecgive.
●nd M corresponding to the AOL
va ‘Y ue. for 1# e apper and lower specificatiea
limit., respectively.
13) Select at random the ●mple of
n unit. from tbe 10C irIap. ct ●md record the
mcaauremcm of the quality characteristic
on each unit in the .arrtple.
(4) compute tie .8mpIe mean x.
(5) Compute the q~ty indiee. QU
= (U- fov/. and CZL = (X- L)v/&,.
(6) Determine the ●.tImued @t
p.rceat defectl.es p“ mud pL, correspond -
ins to tha pa rc.af d. f.ctivec tie tb. upper
and b.lmw the lower .pecific.tkm limit..
Afmo d.te rmine th. combined percent de f.c -
tive p = p“ + p~ .
diuolta :
%.
Mu
(7) u all three of tbe fallowing cc,n-
l.) ~u i’ equaf to or 1... tbma
(b) pL i. mquaf 1. or lR.8 ffun
(CJ p b equaf ts Or Ie*#fzlamthe
larger of ML and Mu,
u. satiaficd, th. lot umato the ~C~tdiii~
criterk other+se. the lot does MC meet the
“’=~ or both am aesativ~ “’’”’A’* tbeo ‘*’ * lot%::%
m..t tbe acc.ptiifiiy criterb

I
..:
E.mtple
Lb.
—
1
?.
3
4
5
6
7
8
9
10
11
J2
13
14
.
EXAMP= D-S
fsxanlpze of Cdcufat,ioms
DOEbh sp4c3d&az10a ZAm2t
varhbmfy XmOwm
Dm. AC3L Vahie for Seth Upper @ &w.r SpeeUiea320a 2AMA1 Combined
bn~14
11*2ES7
The ●peclfie.d maximum ad mitdmnun yield 3,0311u[m cemd. steel rutimzN are
67.000 p. i and 58,000 psi, rucpceUvel y. A lot of 500 items is ●tbmitted for impec -
tloa. 3nop.ct30n &val ZV. aornd insPct3aa, W3UI AQL = 1.5% 1- to be ..4. T&
variability c is &o-n to be 3,000 psi. Frati ?abka A-2 ●nd D-> it i. seem fzut a
.unpl. of ●i.e 10 i. required. SuPpu. e the yi.ld point. of the ●ample specimens
● re:
6z, SOO; 60,500; 68.000; s9,000; 65.500;
6z.000; 61,000; 69.000: 58.000; 64.500;
●nd compliance with the ●cceptability criteriom is to b, determined.
Sample Size: n
lnIornutio. Needed
Know. Variability: o
Sum of Meaaurem6ats: ZX
Sample Mean X: sXln
Factor, v
Upper Specification Untie: U
Zmwer Specific=cion Limiti L
QuaIity Index: Qu = fU-X)V/.
Quality Lufex: Z3L . (~- Z.).1.
Est. of Lot Percen: Def. Above U: pu
12tc. of &t PerccnI D*I. Below IA P&
TelaJ ~*t. P=r=e=t D-f- ~ ~~ P -
Pu + P~
Max. A310w~ble Percent D.[.: M
AcceotablI1tv C.ite rioa: cmn~r= n .
. .
pu + “pL with M
V. I.e Obtaim.d
3,000
630,000
10
63, o0O
67,000
56,OOO
1.054
1.41
l.?b
7.93%
1.92%
11.85%
3.63S
11.85% > 3.63%
Explanation,
630,000/10
See Table D-3
(67,000-61,000)1.054/3,000
(63,000-58.000)1.054/3.000
See Table D-5
See Table D-5
7.93% + 3.92%
Seo T*1c D-3
See Para. D13.4
The 3ot doe ● not met the ●ccepzcbiflty criterion. da.. p = pu + PL io sreater than ~
97
------ . . . -—

um=slv-414
11 Jnne 19S7
Lime
—
I
~
3
4
5,
6
7
8
9
10
11
17.
11
14
15
EXAMPLK D-4
Exampte of Cafcutatimu
ml= sp0dfka3A9n ZAmtt
V.rkatduty KaOwt!
Difiere.t AQL. Vti.ss for Upp.r & lmwer SpeeUicDtinm ZAmlt.
The .pecified maximum and minintum yield p0&39 for cer3mim oteel ca.tl~o ●re
67.000 psi -d 58,000 psi. reapectivdy. A lot d S00 item, is submitted for inspee-
UO.. znspctko. *CI IV, uarnuf knspctinn with ML = 1%. for the uPP8r aad
AOZ. . 2.5% for the lower tipecificuiom lkmit im m. be u..d. The vari.bilicy . is
kcuaw. m be 3.000 pi. Frern Table. A-Z ●d D.> it i. .... that ● .unple cd ais.
11 c~rre. poridir..g to the s.rnple .ise code letter, 1, ●nd the AQL value Of 2.S% i.
required. S.ppc.. e the yield Pc.itis d the ●mple specimen- ●re:
6Z.500; 60.500: 64.000; 59,000; 65.500:
6Z.000; 61.000; 60.631; 68.000; 62.000; 63,000
and cmnplisnce with the ●cceptability criteria 1. to be determined.
Sample Size-: n
Kn~wn Variability: o
Sum .f Me... rernen:.:
Information Needed
.%rnple Mean X: XXIC.
Factc. r: v
UPPe r Specific atiort Lirnic u
faw. r Speci[ieatiea Limit: L
Ix
Quslity Index au = (u-X)v/.
Ou-lity htdex: QL = (X- L)*/a
=.~ ‘f ‘t ‘“’cent Def” -’e u: Pu
E.1. of bt Percent Def. Selow b pL
T.atal Cat. Percent Del. h bt: p = pu +
Pz.
Value Obtained Expl-ation
11
3,000
67.9,131
61,64.9
67,000
58,000
1.049
1.07
1.28
3.07%
10.01%
13.10%
Mu. Allowabi. Pe r..mt Del. Abo.e U: % 2.59%
- A31.wable Pe rcest De[. B=lmu k
‘L
s.60%
Acceptabilit~ Criteriw (al Compare PLI 3.07s ~ 2.59s
with Mu -
(b] Compare PI. 10.05% > 5.60%
with ML
(c) Cemoare 0 13.10% >5.609
with “ML
678.131/11
See Table D-3
(67,000-61,648)1.049/3,000
(61.648 -SB.000)l.0491J. oOO
See Table D-5
See T-ble D-5
3.07% + 10.03%
Se. Tabl. D-3
See Table D-3
see Par*.
DIZ..Z. Z(7)(a)
see Para.
1312.Z, Z(7)lb)
s.. P.**.
D12. Z. Z17)(C)
The 10: dins. not meet the mccep~bUity crIterl.. .tnce 15(a), (b) - (c) ●re Dot ●*fied;
i.e.. pu ●64U. pL > Mb ●nd p wM~
08
-.
,:
-.. .—

..— —,. ..—. .—.
TABLE D-fl;
Matter Table for Normti ●nd Tightened Ioapectlon ~or Plain Bamadon Known Vtriabllity
(Doubla 5pec{flcatlon Llmlt and Form Z-Single Specification Llmlt]
ImpI* -I*E
ode letter
—.
B
c
D
E
r
I
a
n
1
a
J
K
L
M
N
o
P
,.
Q
J!LJ__
AU AQ L id tabl~ who ●m In pmcaat defective.
● firm sunpllq plan balow arrow. that Id, bath mmpsa 01*4 as well as M valua. When ●ample ●Is* equdo or ●xe*sd* lot
I:la., @v*r, ‘Mm ,. tba 10, rnu,tb. SrIlpocied.
I
l!
IJ
1
I

,.
.
TABLE D-3-Con(lnued
MmIar Tcble for Normal and TI$ht~ned hmpectlon for Plma Baaed on Known VarlabIllty
(Doubl. Specllic8tl.m Umit -nd 5’orm Z-Single Speci[icztlm Limit)
Acceptable Quality Level# [normal In#pectio,
10.00 I 13,00 1
2.50 4.00 6,50
1.s0
1.00 “
mpl* 01:
oda ldtt
n 64 v m M v
n he v n M v n M v
TMv
v v ~
B
3 Z4.2Z 1.225 4 33.67 1.15s
v v v
?. 6.11 1.414 6 9.27 1.414 3 {1.14 1.ZZ5
3.90 1.414
m M v m
v 1 .?.13 1.414 ?.
c
4 22.91 1.IJ5 4 31.01 1.155
3 1.56 1.225 3 10.79 1..?Z5 3 15.60 1.ZZ5
t Z.23 1.414 2
D
5 Zo.ao 1,118 6 28.64 1.095
4 6.99 1.155 4 9.97 1.155 5 15,21 1.118
3 2.76 1.U5 1
E
7 19.46 1.080’ f5 2b.b4 1.0b9
5 6.05 1.110 5 B.9Z l.lia 6 13,s9 1,095
4 2.s8 1.155 4
r
11 I7.88 1.049 12 24.88 I.04s
7 5,83 1.080 B 8.62 1.069 9 12.88 1.061
*
1.77 1.095
b 2.s7 1.093 6
G
14 17.36 1,038 16 23.96 1.033
9 5.68 1.061 10 8.43 1.054 12 12.35 1.04s
}.b@ 1.069
1 2.’bZ 1.000 s
54
17 17.03 1,031 20 23,43 1,026
II 5,60 1.049 13 e.13 1.041 15 12.04 1.03s
),63 1.054
9 2.s9 1.061 10
1
21 16.71 1.025 24 23,13 1.022
13 5.50 1.041 15 8,13 1.035 la I l,n8 1.029
1.045
3.61
I 2.51 1.049 Iz
J
Z4 16.23 1.022 21 u;i) 1.019
1$ 5.34 1.035 18 1.72 1,029 20 11.57 1.o26
1.038
3.43
z 2.49 1.045 14
K
Z1 16.z7 1.019 31 Z2,51 1,011
18 5,29 1.0,?9 Zo 7.80 l.OZb z] 11.5b 1.023
1.03s
—
1,027
1.54
—
3.2$
4 2.51 1.038 1!
L
3~ 1S.61 1.016 30 21.77 1.013
z?. 4.98 1.024 25 7.34 1.021 39 10.93 1.018
1 2.3s 1.031 19
M
49 14.81 1.010 56 20,90 1.009
32 4.68 1.016 36 6.9S 1.014 42 I,).40 1.012
1.OIE
3.0!
s 2.19 1.02! 2a
N
64 14.s8 1

. .. ——. —
TABLE D-4
Matter Table for Reduced Znopectlonfar Plan@ Based on Known Varhbllliy
fDmhlo Specillcmion Limit and Form 2–Single Specllicatl.m Limit)
Acceptable (lualhy Levels
.04 I .065 [ .10 I .1s I .25 I .40 I .&<
mph Dim
ode letter
B
c
D
E
r
a
H
i
kJ
2(
L
M
1!
o
?
Q
AU AOL Ad Iabh VdUCi i?o in PO?CQ84dafactlvc.
I US* flrol mmPlkIs Plan hlOW ●rrow, that I*, both mnv.le slsa ●s well ●s M vahie. When mmplo tlse ●quala o? azewdc lot
{DISC, ●T*?F Itim k~ha lot mutt ba inspected,

.-. . .
TABLE D-4-Continued
.Mmter Tsb2e for Redue.d Zn*p.ctl.n lor PlarM Bated on Known Vsrisbllity
(Doub18 Specillcmtion Umit and Form Z-Single Specl{~cItiOn Umit]
ACCI
1.50 2,50
1.06
Ssmplo BI*9
cod- lqtt@r
“ II
v a M v n M
n M
B
~.
1
D
FIJ.67 1.225
1.Z25 i 4
T1.Z?.5 3
t
17.74
1.414 J
v T
1.414 1 6.11 1.414 2 9.27
12
v
k 1 3.90
)l.O1 1.155
1.155 4
lZ.91
1.ZZ3 4
15.bO
1.2z5 )
1.414 3 7.5b 1.225 3 10.79
G 2 3.00
28.64 1.095
).11.3 6
ZO.80
1.118 5
15.Z1
1.155 5
1.ZZ5 4 6.99 1.1s5 4 9.97
H 3 3.85
zi.b4 1.069
1.080 8
19.46
1.095 ?
11.89
1.118 6
1.15s 5 6.05 1.118 5 8.92
1 4 1.87
t4.64 1.0$9
1.080 8
19.46
1,095 7 I
13..59
1.116b
1.155 $ 6.05 1.118 5 .9.92
J 4 3.81
24.08 1.045
1.049 1z
17.88
1.061 11
12.88
1.069 9
1.095 1 5.0) 1.080 8 8.62
K b 5.77
z3.96 1.033
1.o38 16
17.lb
1.045 14
IZ.35
1.054 Iz
1.0699 5.68 1.061 10 8.43
L, a l.be
Z3.96 1.033
1.038 16
17.36
1,045 14
12.35
1.05i IZ
1.0699 5.b8 1.061 10 8.43
M 8 3.68
23.43 1.026
1.031 Zo
17,05
1,035 17
12.04
1.041 15
1.05 4 11 5.6o 1.04 9 13 8.13
N 10 3.63
+ 23.13 1.022
1.0,?$ Z4
16.71
1,029 z!
11..58
1.035 “18
1.04 s 13 5.58 1.04 1 15 8.13
0 1z L61
21.77 1,013
1.016 M
1S.61
1,018 31
10.93
I.oz 1 .?9
1.02 7 22 4.98 1.02 4 7.5 7.34
P 19 3.26
?.0.90 1.009
I.O1O 56
14.81
I.olz 49
i
10.40
—
1.014 4Z
1.01 8 32 4.68 1.01 6 36 6.95
0 28 3.05
i

. —— –-— ——-
—— __
.
TABLE D-5
TabIc for CotlmstInS the lat Percentage Defective for Plans Bared on tiowa Varllbilityl
1

,
Part Ill
ESTIMATION OF PROCESS AVDLAOE A34D CRfTER3A ~31
REDuCED AND TIGNTENW 1NSPECTION
D 13. ~:S#fATfON OF PROCESS AVER-
Th. ●ve rage percent defecti*e. baoed
UPOn A 8r0.P 0[ 10U ●tbmitmd for or~imal
in. pecticm, i. called Sbc proceaa average.
OrlgirIal inspection is the fir-t Inope.tion Of
● prticular quantity 01 product .ubmitted
[or .eceptahslity ●. di.tfngui.hed from the
in. pectian of product which ba. b=cm re. ubrnirted
after prior rajectimm. Th. procea.
●.eragc shall be ..tinuted frc. rn tbe re. ult.
of i.. pe. tion of wampl. mdrawn from . ●peeifi.d
murnber of preceding lot. for the purpose
of decermis.img severity cd inspection
during lhe tour. e of ● contract in accordance
with paragraph D14. J. Any Iot. .htil be included
OUZYonce io e.timatitig tbe proce. a
average. The estimate of theprec... ●ver -
●t?. is designated by $u what computed with
r.. pect to ●n upper ●pecific.tion limit, by
PL wb=n cOmp~t=d rnth r=~p=ct tO ● 10w=r
specification Iirnit, and by p when cmnput=d
with re. pect W. a dc.uble .pecificaciOm Iimit.
D13.1 Abtmrrr,a) Remult,. Th. re. ult. 0[
irmpectior. of product manufactured umdcr
conditions not typical cd tmual production.
shall be excluded from the estitrmted pre -
cemm’ average.
D1 3.2 Ccmputatiem d the Esf.inuted prcce.
a Avers e. Th ● e.tmuted proce.. aver-
●ge M the ●r~thrnetic mean of tbe estimated
10t pe rcem def ●ctive computed from the
.unpling itt*pecti.ma re.. tit. of the preceding
tea (10) low or S* may be .alhenvi. e d.miS -
❑ated. In order to estimate the lot percerat
dsf.cti.e, the quality kdicem Ou &\.ar QL
●lmfl be computed for each lot. Theme ●re:
(3u . (U-X)WI. and QL = (X- LWIO. (S8.
paragraph D] I. Z.)
D13.?.. I SiI@. Sp.cifieatlon Z.lml% 6 The
estimated 1ot percent dof ecu-e ●bal-1 b de-
Cennined frarn Table D. 5 ter the plum hawed
O. bnowa varbbi3ity. Tbe q-am3ityiadex Q“
hall be us.d far tbe ea.. of aocJppr .pec -
iiic.tiom limit c,r QLlor the c.. e of a 10X.
●pecifi..ticm limit. Table D-5 ii entered
!. with Q or QL 4 the corr. spondin~ .mtimuted
Y et perce,att defective Pu 0. P L. ?*spectively,
is read from #he ~bIe. The
e.tinuted proces. ●verage pu i. the arithmetic
m-u. of the Itidi.idual e.timated lot
percent defective. Pu’ ●. Sinaihrly. the e.ti -
nuted procems average p is the arithmetic
me- of tbeiadividdemt~atcd lot percemt
defect%ve. PL’..
D13. Z.Z Double Specification lAmit. Tbe
e.cim.ced lot percent dciectzve ●hall be .determim.d
from Table D-5 for the pluI. bm. ed
on variability b.swa. The quality Indic.s
0 and QL shall b. computed. Table D-5 i-
enY ered separately with QU and OL ad- the
carre.pomding pu snd pLare read frOm the
fable. The e.timtied ict percemt defective
is p = pU + pL. The e.tirnat.d pro . . . . a.er -
●ge p i. th= ●rithmetic rn.a.mof the individual
=atimsced lot percent defective. p’..
D13. Z.3 Special Case. U the quazity index
0,, or Q, ,s a nt~atm.e number. them Table
DY5 i..~~ter=d by-di. regarding the negative
si~n. However. io thi. case the e.timated iot
P. TC.nt defective ●bove the upper limit or
below the Jow.r limit i* obtained by ●ubtract -
~~~~ Per==at=ge found in the table from
AL TXGZiTENED, AND RE-
‘“ %%%dWPECITC)N
This S$azidard e.tabli. ha. wampling
pl*rsh for normal, tightened, and reduced
i-peetioa.
D14. 1 At Start of Inspection. Normal in-
.pectiom SW b. wed ●t the ●tart of inapec.
UOa IU13C.*Secberwim de#$gm4ted.
D14.Z OuriaS fn.xctiou During the co.r ●e
of In9puctia, -rmal uumction shall be
used when taapeecio. cmaditioo. ●re much
tbt t6sht.nod O. redncad iaapection is not
rqufred fn accordance with prmS.aphs
D14.3 and D14.4.
D1 4.3 Tight=imd 31Wpecttoa. Tiuhtermd tn-
Spectltl. .W1 be in. ututed wb. n the emti -
naat.d proce. m ●verage computed from’

’
I
prece4iag [e. (1OJ Iot# (.r much other smmber
of lma demig=atedl in ●ccordmce with
paragraph D1 3.2 i. greaur thaa the AQL.
and when more thao ● certAn number T Of
these 10ta ‘have ●stimmen of the percent
deiective exceeding ctaeADL. Tb* T-value.
are SiWeaI in Table D-b when tbe pr.acua
average is computed from 5, 10. or 15 lots. 8
Normal inspection still be reimtmted if the
.stinnted pro . . . . ..erage of Iota under
tightemed iiwpectio. i, equaf tc.c.,lem. than
the AQ L.
D14.4 Reduced fnsp=ctior.. Reduce4 bcpectien
may be instituted provided that all
of the following cOndiliOn. ● re ■atisf ied:
Condition A. The preceding tea (10)
lc.ts(or such other mmnberoflots designated)
have be.- under r.c.rrnsl i.. pecti.m -d no.e
has been rejected.
Condition B. The e.linuted percent
defective for ●ach of these preceding lots is
. .
10s
MUAID-414
11 Jftfld 10s7
Iesm than the ●pplicable loumr limit cbown
i- Table D-7.
Caufitiom c. Pr0dmct50n is ●t ●
●tcD4y rak.
Nonnsf impecthm *baff be retostate4 U my
one of tbe foIlowing eondftiom occurm tiad~r
redueed tic wctlon:
Condition D. A Iot-ic rejected.
fkradiiinm E. The estiunkd plwJce~-
. ..erage i. ~re.ter tbn the AQL.
Comditiom F. P.oductiom be=om.a
irregular or delay=d.
COtisti.n G. Dthe r ccmditiom u
may wtarrwt that normti inspection should
be reinstated.
D1 4.5 Sarnplin~ Plans for Tightened or Reduced
k,C.~=CtLOIl. S~PIIDS Pl~S fOr *lghl -
e~ed and reduced inspection ●re provided in
Section D, Parts I and 11

I
TABLE D-U
v.iu. mof T for Ti+t.oed k+spsctbon
Sample size Acceptable OustIty tavels (in percent deft!,
code letter .J-t .065 .10 .15 .25 .40 .65 1.0 1.5 2.5 ●-o
B . . . ● ● . . ● ● ● ●
3 3 3
c ● . ● ● . . ● 5 5 5 :
6 6 7 7
3 3 3 4 4
D ● ● ● . . ● 4 6 b
b : : a 9
2 3 3 3 4 4
E . ● . ● 4 4 5 6 : 6 7
5 6 7 7 8 9 9
3 3 3 4 4 4 4 4
F . . . 6 6 6 7
: : : 8 8 8 ; 9
3 3 3 3 4 4 4 4 4 4
G 4 4 5 5 : 6 6 ‘1 7 7 7
b 6 7 7 7 8 8 ,9 9 10 la
3 3 3 3 4 4 4 4 4 4
H 5 5 b 6 6 2 7 7 7 7 7
b 7 7 8 a 9 9 9 10 10 10
3 4 4 4
4 4 4 4 4 4 4
1 5 6 b b6
6 7 7 7 7 7 7
7 a 8 8 9 99
! 9 I.101 10110
—
i.e
—
,.5
—
●
4
7
9
—
4
7
9
4
7
10
4
7
10
—
4
8
11
—
4
8
11
10.0 15.0 of bm
● *
7FNu13160r
w
445
88 10
11 11 15
445
88 10
-++- II 11 15
445
88 10
11 11 15
J :
8
4
b
a
4
4 4
b b :
181819119101
444444
77
:1:1:
4
8
11
—
4
u445
K : b
a en 10
L
I
8
4
b
a
I
44d
8
4
6
q
I
9
4
6
9
t
9
4
7
9
4
7
9
4
7
9
4
9
4
7
10
4
10
4
7
10
4
10
4
7
10
4
10
;
10
4
10
44
88
11
4
II
11
4
11
—
4
8
11
—
4
8
11 11 1s
-l-J--
445
88 10
11 11 15
44=
a
1: 9 1: 1: 1: 1: 1: 1! l.: 11
—
4
a
II
4
8
11
— +E
445
88 10
11 11 Is
44’5
8 8 10’
.11 11 15
.There are no .antplimg plMM provided in this Standard fer these code letters 8nd AOL.a3nOS.
I&
—

I
I
TABLE D4-CmtJmd
VAM., of T for Tl@umd f519~Cti00
Sample ●L. Accepmkle Ouatlty Lavelo (in PC rcemt ttefe
code letter .04 .065 .10 .15 .25 .40 .b5 I .0 1.5 2.5 4.0
4 4 .4 4 4 4 4 4 4 4 4
P 7 7 1 7
10 10 10 10 If< 1: i! 17 1: J: 1:
4 4 4“ 4 4 4 4 .4 4 .4 4
Q 1 7 8 s 8 s 8
10 10 lJ 11 11 11 11 1: 1: 1; 1:
hfnATD-414
11 June 1951
v ●riab.bMc7 ~
4445
888 10
11 11 11 15
The top rigure in cacb block refer. to tbe precedi~ 5 lot., the rniddlc figure m the
preceding 10 lot. ●nd the bottom figure to the precedi~~ 15 lots.
Tightemed i.. pectiom i. rquir.d wbem the aurnber af lotm with .stirn.tea of percent
defective ●bove the AQL from the preceding 5, 10, or 15 Iotm i. greater thaa the Eiven value
Of T iu tbe t.ble, and the proceos ●verage from th.. e lat. e=c=ed. th= AOL.
N] estinutea of the lot p.rcemt de fectiws ● re Obtaimed from Table D-5.
107

TABLE D.7 V. fIablllI~ Known ~~
Llmlto o{ Estimated Lot PerceIII D. f.c!Ivr ior Reduced Inspection *r
15.0
Acceptable C1. &litv Levels
*
,10 ,15 ,,?5 ,40 .b5 1.0
.J
—
. ● ● . ● .
Sample size
code letter .04 .065
*
35 ● *
5
10
1.714
14.z91
I 5.00
.021
.2, ?2
.558 !
.011
.109
,209
* ● ● ● ●
c ● *
Is
.769 1.645 4.386
Z.354 4.496 8.049
3.850 6.50 10.00 I 5.00 1$
I I
.369
I,Z48
2.145
.027
.222
.558
.011
.109
.290
.003
● ● ● ● .050
.144
D ● *
5
9.419
15.00
A
.631 1.225 z.q37 5.154
1.64J 2.9z4 5.69? 9.330
2.50 4.00 6.50 I 0,00
,16b
.62Z
1.124
.086
.)57
.669
.001 .002 .045
● * .009 .021 .197
.029 .064 .384
E ● *
5
10
10.436
15.00b
.046 1.560 1.3Z5 6.114
1.880 3.250 5.958 9.806
2.50 4.00 6.50 10.00
.311
.874
1.194
.178
.5Z8
.867
.005 .010 .021 .09n
* .025 ,052 .100 .309
J- ● 4
~
I
1$
11.470 5
15.00 10
A IS
1.1)6 t.166 4.o45 1.093
Z.141 3.698 6.342 10.00
2.50 4.00 6.50 J
.53J
I,IJ9
1.50
.056 .110 .204 .5.22
.-1-
.078 .147 .Jz Z
027 .049 .093 .Z17. .385 .718
055 .090 .167 .347 .6OZ .00
013 .02.? ,057 .103 ,ZZ3 .375
041 .0b7 .147 .252 .418 ,773
071 .114 .227 .382 .65 ,.00
l-l
007 .013 .0Z6
.001 .001
G .004 .008
: .010 .01.9
1.326 Z.40J 4,453 7.s02 12.054 5
z.Z17 3.8JI 6.5o 10.00 I 5.00 10
% 2.50 4.00 A A & Is
TF
1.461 Z,643 4.719 1,786 12.427 5
Z.J59 J.94z 6.5o 10.00 15.00
2.50 4.00 A i ~ [’015
1.562 2.758 4.909 8.05s 12,693 5
2.412 3.987 b.50 10.00 15.00 10’
2.50 4.00 A a A
15
1.641 2.89! 5.009 8.205 12.848 5
2.449 ,4.00 6.50 10.00 15.00 10
2.50 A A A A 1$
.677
1.Z70
1.s0 -L
.002 .004
53” .009 .017
.018 .033
.718
1.346
1.50
.451
.847
,.00
.
.252
.508
.65
.142
.298
.40
—
.15.9
.J13
.40
—
.171
.JZ6
.40
.070
,164
.244
—
.08Z
,177
.2s
018 .030
0s1 .081
082 .129
.004 .011
I .014 .011
.025 .051
.85J
1.J94
1.50
.316
.892
1.00
.298
.549,
.b5
OZJ .038
0s8 .092
090 .140
.006 .011
J .016 .011
.030 .051
—
.910
1.4z7
1.50
.540
.908
1.00
.3!7
.564
.b5
,09 I
.18B
.25
,028 .051
,064 .10’9
,09b + .1S
.008 .014
2( .021 .036
.033 .056
1 1 1
●There ●re no aampllng plant provided in lhh Standard far lhe. e :ode letter, and AQL va5ue#.
I
4

_—— .
TABLE D-7-Conllnued V~rIabIllty Knows
Llmlto of thtimited Lat Percent Defective lor Reduced fnnpectim
Numb-r
1 .0 of I/As
., .-. . .
we u“alftv La C19
T2.5 4.0 6.S T10.0
—
.348
---1-
.501 .934 1.732 z.96Q 5.131 8.3Z8
.586 .934 1.440 Z.406 4.00 b.io ko.oo
.65 I ,00 1.50 2.50 b A h
—
.383 .6zl I,o1O 1.821 3.093 5.310 8.516
.608 .959 1.415 2.50 4.00 6.50 10.00
.65 I .00 I 1.50 ha,
A
m.435 .705 1.113 1,959 3.Z7Z 5.546 8.0z2
.635 .994 1.50 2.50 4,00 6,5o 10.00
.b5 1.00 i A A * A
“X .40
13,017 5
I+ 5.03 10
.107 .191
,203 .344
.Z5 .40
A 15
1115
-1_
13-238 5
I S.00 10
-1-
13.588 s
15.00 - 3u-
.120 .211
.Z14 .557
.Z5 .40
.146 .Z51
.232 .38Z
? .25 .40
.017 .030 .049 .080
N .03Z ,054 ,086 .134
.04 .06S .10 .15
1 15
—
13.801 5
I 5.00 10
& 15
.(41 .277.
.241 .392.
.2s .40
14.034 5
IS,oo 10
& 14
.1s0 .299
.249 .41Z‘
.25 b
5
*
14.173 5
15.00 10
A 15
.191 .316
.25 .40
h b
,.
1
*
All A(3L ●nd tsble vduec ~r; In percent defective.
bUmethe flrot fl#ure In dlrectlon of arrow and correepondin~ number of 10M. In each block the top (Igura reform to the
precedlm[ 5 lott. the middle figure to the preceding IO lots. and Ihe bottom figure 10 the preceding 15 lots.
Rw!uc813 impectkon may b- tnalituled when every emtlmaled lot percent defective from the preceding 5, 10, or 15 lot- in
bdow the flsure glvon In the table. fn addition, III c.ther conditiom for reduced impection, In Part 323of Sectloa D, must bc
dtiltfled.
AN entknmteoof the lot percent defective ●re Obtained lrom ‘Table D-5.
=H
II

aL-sTD-414
11 June 1957
Sz@!s!!
n
x
.
u
1.
k
v
Q“
QL
m
PL
P
M“
Mu
‘L
P
P“
‘L
T
<
>
I
Read
X bar
Sigma
Q ,ub U
O .ub L
p sub U
p ●ub 1.
M ●.b u
M ●ub L
p bar
p bar ●ub U
p bo ●ub L
Less than
Greater tbM
SLunof
APPENDIX D
Defhiflmu
Sunple site for + ●ingle lot.
Def intt.io.s
S-pie rnemn. Arithmetic mean of ●unple rneawaremento from
8 tingle lot.
fbowa variability. The predetermined variability of the quaf -
ify cbaract.ristic which vill be u.ed rntb the .ariabifify bow.
●cceptabfltfy plus.
Upper specification Iimtit.
Lawmr ■pectficatian limit.
The .ceeptabi3ity constant givem in Table. D. 1 and D-z.
A factor tw.d in determining the quality indices when ua ing
the bnowLI variability acceptability plan, The v vafues., ●re
giv== in T~b10. D-3 -d D-4.
Quality Index for use with Table D-5.
C3uality Index for use with Table D-5.
Sample estinute 0[ the Iot percent defective ●bove U front
.Table D-5.
Sample escinute of the lot percent @ef.ctive below L fr.am
Table D-5.
Total ●unple emfirnsfe .af tbe 101percent defective p = p“ + PL.
Maxdmum dfowable percent defective lor sample eatimatea
given in T@bles D-3 and D-4.
Maxfmum allowable percent defective ●bove U ~ivem h Table.
D-3 and D-4. IForuce when different AQf- v81uec for W and
L ●re spactfjed. )
Maximum ●llow.blcpercent defective below 1. @em ia Table.
D-3 and D-4. (For usawhen different Mf- value. for U =d
L ●re ●~edfted. )
Sunpfe ewtdnnte Of the procemw merceut defective, i. e., the
amfimated procema average.
Tbe ●mfimuod pw..s. .Verq. [*. -n upper Spectficstlom unlit.
The estimated process average for a lower ●pecf3icatlon Umit.
Tbe maximum number of emttnuted pr.xeoa ●verage- which
may exceed tbe AQL given in Table D-6. {For u.e indetnr -
=1- applic~t~a Of ti8bt=n=d i=~p=ctiOa. )
L.eom than.
Greater than.
110
.—.—— . - ---- ----

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