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

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& OR unit, Kolkata for other necessary assistance. I am thankful to Professor Sankar K. Pal, the Director of Indian Statistical Institute, for allowing me to undertake this research and provide the necessary resources for preparation of this thesis. Kolkata, September 7 2005 Anup Majumdar iii
Contents 0.1 Purpose of sampling inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0.2 Theory and application of sampling inspection - a short review . . . . . . . . . . . . . . . . . 2 0.3 The relevance of sampling inspection in today’s economic scenario: . . . . . . . . . . . . . . 8 0.4 Scope of the present inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 0.5 Summary of the dissertation : Sampling inspection schemes by attribute for multiple quality characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.1 Introductory concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.1.1 Relevance of sampling inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.1.2 Multiattribute sampling inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.1.3 The type B OC function for a generalized multiattribute single sampling plan . . . . 35 1.1.4 Poisson conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.1.5 Expressions of type B OC function under Poisson conditions . . . . . . . . . . . . . . 39 1.2 Multiattribute sampling schemes based on AQL . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.2.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1.2.2 Using published plans in a multiattribute situation . . . . . . . . . . . . . . . . . . . . 40 1.2.3 The consequence of using MIL-STD-105D in a multiattribute situation - two live examples 41 1.2.4 The properties of the OC function of the MIL-STD-105D normal inspection when used in a multiattribute situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.2.5 The C kind plan and the properties of its OC Function . . . . . . . . . . . . . . . . . 47 1.2.6 An alternative sampling scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.2.7 Construction of A kind MASSP’s using the sample size and AQL from MIL-STD-105D 52 1.2.8 The D kind plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 1.3 Multiattribute sampling plans of given strength . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.3.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.3.2 Single attribute situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 1.3.3 Construction of C kind plans of given strength . . . . . . . . . . . . . . . . . . . . . . 65 1.3.4 Construction of A kind plans of given strength . . . . . . . . . . . . . . . . . . . . . . 70 1.3.5 D kind plans of given strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 1.3.6 Comparing sample sizes of A kind C kind and D kind MASSP’s of given strength . . . 74 1.3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 2.1 General cost models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2.1.2 Existing cost models for multiattribute acceptance sampling . . . . . . . . . . . . . . 78 2.1.3 Cost model - some practical considerations . . . . . . . . . . . . . . . . . . . . . . . . 80 2.1.4 A generalized cost model for nondestructive testing . . . . . . . . . . . . . . . . . . . . 81 iv
Page 1 and 2: Multiattribute acceptance sampling
Page 3: e) the cost functions are linear an
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
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increasing in each a i . Note that
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Figure 1.2.1 Absolute value of Slop
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Table 1.2.5: Three attribute A kind
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Table 1.2.5 (contd.): Three attribu
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Table 1.2.5 (contd.) : Three attrib
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Table 1.2.5 (contd.) : Three attrib
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1.3 Multiattribute sampling plans o
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Let M 2 < M 1 . Then G(c 1 , M 1 ρ
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α, β, and ρ. For α = 0.05, β =
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ma β (a 1 , a 2 , ρ) = m ′ ...(
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Table:1.3.2: Construction parameter
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1.3.5 D kind plans of given strengt
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Figure 1.3.1: The sketch of the fun
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2.1 General cost models 2.1.1 Scope
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(j) Interaction of scrappable attri
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use of defective item is additive o
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2.1.5 Approximation under Poisson c
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2.2 The expected cost model for dis
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P (p (j) ) denotes the probability
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250 200 Figure 2.2.1 : Lot Quality
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Table 2. 2. 1 Testing goodness of f
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2. 3 Cost of MASSP's of A kind 2.3.
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From (2.3.2) we observe that γ 2 1
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( γ / ) 2 γ − ( m′− m e ) /
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We now consider the following funct
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….(2.3.12) Here S A denotes the s
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∴There exists an optimal A plan f
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Hence, Q(m) = 1 − P (m) has the s
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where a 0 and n 0 are the parameter
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where, p = (p 1 , p 2 , ..., p r )
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situations as above. For the third
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2.5.3 Optimal Bayesian plans in sit
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Table 2.5.2 : Optimal multi attribu
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Annexure Microsoft Visual Basic pro
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If Regret,OMREGRET(c3-1) Tjem Prevo
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3.1 Bayesian single sampling multia
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f(p i , ¯p i , s i )dp i = e −v
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easonable to assume that the p i
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the minimum cost is obtained at a 1
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Table 3.1.1 (Contd.) : Results of 1
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Table 3.1.2 : Testing goodness of f
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Figure 3.1.1 : Scatter plots of num
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Figure 3.1.2: Sketch of the cost fu
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Annexure Microsoft Visual Basic pro
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References Ailor, R. B., Schmidt, J
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Copenhagen. Hamaker, H. C. (1950).
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Taylor, E. F. (1957). Discovery sam
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