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

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Part 2: Bayesian multiattribute sampling inspection plans - general cost models and discrete prior distributions 77
2.1 General cost models 2.1.1 Scope So far we have discussed the comparative features of A kind, C kind and D kind multiattribute acceptance sampling schemes based on OC function. We now attempt to do this on the basis of economic considerations. We first review the various cost models for dealing simultaneously with more than one attribute. We further develop a generalized cost model as appropriate to compare the costs of different sampling schemes proposed by us, under the assumptions of independence of defect occurrences and also under the assumption of mutually exclusive occurrences of defect in a lot/sample. We do this under Poisson conditions. 2.1.2 Existing cost models for multiattribute acceptance sampling Hald [ See Chapter 0.2.7 ] has been the major contributor in the field of economic design of acceptance sampling plans. He obtained general solutions for linear cost models under discrete and continuous prior distribution of process average for single attribute. Hald’s major emphasis has been on finding asymptotic relationships between n and c, and between N and n for a single attribute single sampling plan. The economic design of multiattribute sampling scheme was considered by Schimdt and Bennett(1972), and further by Case, Schimdt and Bennett(1975), Ailor, Schimdt and Bennet(1975), Majumdar(1980), Moskowitz, Plante, Tang and Ravindran(1984), Tang, Plante and Mokowitz(1986), and Majumdar(1997). We discuss some of them and examine their relevance in the context of our enquiries. i) Case, Schimdt and Bennett(1975) This model is developed under following assumptions: (a) Each attribute is assumed to have its own sample size n i and an acceptance number c i for i = 1, 2, ..., r; r being the number of attributes. (b) Any item inspected on one attribute may be inspected on all other attributes thus resulting in the total member of items sampled being maximum of (n 1 , n 2 , ..., n r ). Acceptance is realized only if and only if x i ≤ c i ; i = 1, 2, ..., r (c) The number of items inspected for the i th attribute is without exception n i . No screening/sorting is made on the rejected lots. (d) Irrespective of the lot size a rejected lot is ‘scrapped’ at a fixed cost. (e) The sampled items are replaced in the lot by additional items and are taken from a lot of the same overall quality as the sampled lots. 78
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Multiattribute acceptance sampling
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e) the cost functions are linear an
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Contents 0.1 Purpose of sampling in
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Part 0 : Introduction 0.1 Purpose o
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ectification is defined by setting
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procurement of materials of the US
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average defective from such a proce
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0.4 Scope of the present inquiry 0.
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0.4.6 A generalized acceptance samp
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sembled units the general practice
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with the above purpose in mind. The
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equals to p i in the long run. We a
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m j , r∏ −P C j ′ = g(x j , m
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show that if we increase c 2 keepin
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independence and mutually exclusive
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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: Figure 1.3.1: The sketch of the fun
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 and 98: Table 2. 2. 1 Testing goodness of f
Page 99 and 100: 2. 3 Cost of MASSP's of A kind 2.3.
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
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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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