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

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Table 1.2.5 (contd.) : Three attribute A kind single sampling plans for normal inspection p ( ) /Total SL. n.(AQL 1 ) n.(AQL 2 ) n.(AQL 3 ) a 1 a 2 a 3 Over all Prod. 0. 10 No. risk AQL 274 5 12.56 31.55 13 27 61 0.050 1.5 275 0.1256 19.91 31.55 2 30 64 0.048 1.5 276 0.1991 19.91 31.55 2 30 64 0.050 1.5 277 0.3155 19.91 31.55 3 31 64 0.047 1.5 278 0.5 19.91 31.55 4 31 64 0.050 1.5 279 7.924 12.56 31.55 17 32 64 0.049 1.5 280 0.7924 19.91 31.55 5 34 64 0.050 1.5 281 1.256 19.91 31.55 5 32 65 0.049 1.5 282 1.991 19.91 31.55 8 32 66 0.050 1.5 283 3.155 19.91 31.55 9 35 67 0.049 1.4 284 5 19.91 31.55 12 37 69 0.050 1.4 285 7.924 19.91 31.55 18 42 72 0.050 1.4 286 12.56 19.91 31.55 26 49 77 0.050 1.4 63
1.3 Multiattribute sampling plans of given strength 1.3.1 Scope We considered in the last chapter two schemes: one, consisting of plans of A kind and, another consisting of plans of C kind, which differed in terms of acceptance criteria. In this chapter we try to construct MASSP’s defined by two equations Q(p) = α and P (p ′ ) = β, where p = (p 1 , p 2 , ..., p r ) is the process average vector for the satisfactory quality level and p ′ = (p ′ 1, p ′ 2, ..., p ′ r) is the process average vector for an unsatisfactory quality level; Q(p)is the probability of rejection at p and P (p ′ ) is the probability of acceptance at p ′ . Further, α and β are the stipulated producer’s and consumer’s risks, respectively. 1.3.2 Single attribute situation Before we start, we look at the method of obtaining the Poisson solution for sampling plan of a given strength for the case of single attribute as outlined by Hald (1981). For the case of single attribute, we define a sampling plan of strength (p, α, p ′ , β) as the plan satisfying two equations Q(p) = α, and P (p ′ ) = β, p and p ′ denote the process average values for the satisfactory and unsatisfactory quality levels, respectively. Allowing c and n to be real numbers, these two equations determine (c, n) uniquely. However, in practice c and n are integers. We therefore find a sampling plan such that the two conditions are satisfied as nearly as possible and actual risks are less than or equal to the stipulated risks. For this we define m P (c) as the value of m such that G(c, m P (c)) = P . Under Poisson conditions the problem boils down to solving the two equations: G(c, np) = 1 − α and G(c, np ′ ) = β. Let G(c, m P (c)) = P then we solve the equations and np = m 1−α (c) np ′ = m β (c). ...(1.3.1) The ratio R(c, α, β) = m β (c)/m 1−α (c) is a decreasing function of c for given (α, β). We may therefore obtain c uniquely from the equation: R(c, α, β) = p ′ /p since c is an integer we obtain c from : R(c − 1, α, β) > p ′ /p ≥ R(c, α, β) and obtain an integer n from m β (c)/p ′ ≤ n ≤ m 1−α (c)/p ...(1.3.2) ...(1.3.3) ...(1.3.4) 64
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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.
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: Table 1.2.5 (contd.) : Three attrib
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 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
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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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