Multiattribute acceptance sampling plans - Library(ISI Kolkata ...

More documents

Recommendations

Info

Table 2. 2. 2 Testing goodness of fit of two point discrete distribution for the Visual defects for 552 inspection Lots of RS closures of size 10000 Number of defects /unit Observed Frequency ( O i ) Estimated Frequency ( E i ) ( O i -E i ) 2 / E i 0.000-0.040 4 4.12 0.003 0.040-0.042 43 34.24 2.240 0.042-0.044 120 124.97 0.197 0.044-0.046 195 192.23 0.040 0.046-0.048 126 124.97 0.009 0.048-0.050 31 34.24 0.307 0.050-0.115 6 6.17 0.005 0.115--0.120 8 14.51 2.920 0.120-0.124 12 12.94 0.069 More 7 3.62 3.167 Total 552 552 8.956 Estimated ( p 2, p ' 2 , W 1) = ( 0.0450, 0.1200, 0.94 ) Prob ((χ2 df = 6 >= 8.95) 0.176 93
2. 3 Cost of MASSP's of A kind 2.3.1 Scope In this chapter we examine the properties of optimal A kind MASSP’s and also examine how the ordering of the attributes affects the costs. We evaluate the costs in terms of the regret function as defined in the last chapter for discrete two point prior distribution of the process average vector. We do this under the assumption that the Poisson conditions hold so that the type B OC function can be expressed in terms of the sum of products of the individual Poisson probability terms with parameter np i , i = 1,2,...,r over the domain of x i values satisfying the acceptance criterion. At the outset we recall that given two levels of the process average vectors, p and p' and the values of γ 1 , γ 2 and N, the regret is a function of sample size (n), and the acceptance numbers as applicable to a specific acceptance criterion. The expression for the regret function has been given in (2.2.9). In the discussions that follow we consider the optimality of a sampling scheme in terms of n and the acceptance parameters given p, p' , γ 1 , γ 2 and N . Notations We introduced in Part 1 the MASSP’s of A kind as the one where we take a sample of size n, observe the number of defectives (defects) for the i th attribute as x i for i = 1, 2,..., r and apply the following acceptance criterion : accept if x 1 ≤ a 1 ; x 1 + x 2 ≤ a 2 ; ... ; x 1 + x 2 + ...+ x r ≤ a r and reject otherwise. Similarly for a MASSP of D kind we take a sample of size n, observe the number of defectives (defects) s for the i th attribute as x i for all i = 1, 2,...,r and apply the following acceptance criteria : accept if x 1 + x 2 + …+ x r ≤ k and reject otherwise. We use the following notation as before : x ( j ) = x 1 +...+ x j ; j = 1, 2, ..., r. For the prior the process average vector can take two values viz. p and p' , where p = (p 1 , p 2 ,..., p r ) p' = ( p' 1, p' 2 ,..., p' r ) ; p' i > pi for i = 1, 2,..., r . Let , p ( j ) = p 1 + ... + p j ; j = 1, 2 ,...,r; p = p 1 + p 1 + ... + p r ; p ′ = p ′ + p ′ + ... + p r ′ 1 2 ; m = np , i = 1, 2 ,..., r; i i m' i = npi , i = 1,2,..., r ; m = np ; m ′ = np ′. 94
Page 1 and 2:
Multiattribute acceptance sampling
Page 3 and 4:
e) the cost functions are linear an
Page 5 and 6:
Contents 0.1 Purpose of sampling in
Page 7 and 8:
Part 0 : Introduction 0.1 Purpose o
Page 9 and 10:
ectification is defined by setting
Page 11 and 12:
procurement of materials of the US
Page 13 and 14:
average defective from such a proce
Page 15 and 16:
0.4 Scope of the present inquiry 0.
Page 17 and 18:
0.4.6 A generalized acceptance samp
Page 19 and 20:
sembled units the general practice
Page 21 and 22:
with the above purpose in mind. The
Page 23 and 24:
equals to p i in the long run. We a
Page 25 and 26:
m j , r∏ −P C j ′ = g(x j , m
Page 27 and 28:
show that if we increase c 2 keepin
Page 29 and 30:
independence and mutually exclusive
Page 31 and 32:
different sampling schemes in terms
Page 33 and 34:
curves i.e. the OC curve as a funct
Page 35 and 36:
0.5.3 Part3 Bayesian multiattribute
Page 37 and 38:
K(N, n)/(A 1 − R 1 ) = nk ′ s +
Page 39 and 40:
example, a sample of finished garme
Page 41 and 42:
...(1.1.2) If now X i is assumed to
Page 43 and 44:
(i) Poisson as approximation to bin
Page 45 and 46:
1.2 Multiattribute sampling schemes
Page 47 and 48: We take this case and the case of t
Page 49 and 50: highest with respect to critical de
Page 51 and 52: ...(1.2.4) Note that, for single at
Page 53 and 54: ...(1.2.7) To compare the relative
Page 55 and 56: Corollary For ρ 2 /ρ 1 > c 2 /c 1
Page 57 and 58: increasing in each a i . Note that
Page 59 and 60: Figure 1.2.1 Absolute value of Slop
Page 61 and 62: Table 1.2.5: Three attribute A kind
Page 63 and 64: Table 1.2.5 (contd.): Three attribu
Page 65 and 66: Table 1.2.5 (contd.) : Three attrib
Page 67 and 68: Table 1.2.5 (contd.) : Three attrib
Page 69 and 70: 1.3 Multiattribute sampling plans o
Page 71 and 72: Let M 2 < M 1 . Then G(c 1 , M 1 ρ
Page 73 and 74: α, β, and ρ. For α = 0.05, β =
Page 75 and 76: ma β (a 1 , a 2 , ρ) = m ′ ...(
Page 77 and 78: Table:1.3.2: Construction parameter
Page 79 and 80: 1.3.5 D kind plans of given strengt
Page 81 and 82: Figure 1.3.1: The sketch of the fun
Page 83 and 84: 2.1 General cost models 2.1.1 Scope
Page 85 and 86: (j) Interaction of scrappable attri
Page 87 and 88: use of defective item is additive o
Page 89 and 90: 2.1.5 Approximation under Poisson c
Page 91 and 92: 2.2 The expected cost model for dis
Page 93 and 94: P (p (j) ) denotes the probability
Page 95 and 96: 250 200 Figure 2.2.1 : Lot Quality
Page 97: Table 2. 2. 1 Testing goodness of f
Page 101 and 102: From (2.3.2) we observe that γ 2 1
Page 103 and 104: ( γ / ) 2 γ − ( m′− m e ) /
Page 105 and 106: We now consider the following funct
Page 107 and 108: ….(2.3.12) Here S A denotes the s
Page 109 and 110: ∴There exists an optimal A plan f
Page 111 and 112: Hence, Q(m) = 1 − P (m) has the s
Page 113 and 114: where a 0 and n 0 are the parameter
Page 115 and 116: where, p = (p 1 , p 2 , ..., p r )
Page 117 and 118: situations as above. For the third
Page 119 and 120: 2.5.3 Optimal Bayesian plans in sit
Page 121 and 122: Table 2.5.2 : Optimal multi attribu
Page 123 and 124: Annexure Microsoft Visual Basic pro
Page 125 and 126: If Regret,OMREGRET(c3-1) Tjem Prevo
Page 127 and 128: 3.1 Bayesian single sampling multia
Page 129 and 130: f(p i , ¯p i , s i )dp i = e −v
Page 131 and 132: easonable to assume that the p i
Page 133 and 134: the minimum cost is obtained at a 1
Page 135 and 136: Table 3.1.1 (Contd.) : Results of 1
Page 137 and 138: Table 3.1.2 : Testing goodness of f
Page 139 and 140: Figure 3.1.1 : Scatter plots of num
Page 141 and 142: Figure 3.1.2: Sketch of the cost fu
Page 143 and 144: Annexure Microsoft Visual Basic pro
Page 145 and 146: References Ailor, R. B., Schmidt, J
Page 147 and 148: Copenhagen. Hamaker, H. C. (1950).
Page 149:
Taylor, E. F. (1957). Discovery sam
show all

Multiattribute acceptance sampling plans - Library(ISI Kolkata ...

Create successful ePaper yourself

Delete template?

Save as template?