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

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Case II a 0 < a ′ 0, n 0 > n ′ 0 In this case we choose the SSP (a ′ 0, n ′ 0) as a competitor to the C kind optimal plan. We note, Q(p) ≃ 1 − G(a 0 , n 0 p) ≥ 1 − G(a ′ 0, n ′ 0p) and, P (p ′ ) ≃ G(a ′ 0, n ′ 0p ′ ). Thus by the same logic the regret function for the SSP (a ′ 0, n ′ 0) will be less than the optimal C plan. Case III a 0 > a ′ 0, n 0 > n ′ 0 Consider the function d(m) = G(a 0 , mλ) − G(a ′ 0, m). For λ > 1, d(m) has one change of sign only from positive to negative for m > 0. [ This result is due to T.Tjur as quoted by Hald(1981) ] If now these two OC’s for the two SSP’s intersect at p 0 such that p G(a 0 , n 0 p ′ ). In the event p 0 p ′ neither of the SSP (a 0 , n 0 ) and the SSP (a ′ 0, n ′ 0) may have lesser regret than the optimal C plan. We may therefore choose a plan (a ′′ 0, n ′′ 0); such that a ′′ > a 0 , n ′′ 0 > n 0 such the OC’s of plan (a 0 , n 0 ) and that of (a ′′ 0, n ′′ 0) intersect at p 0 and p < p 0 < p ′ . In this case the the OC of the plan (a ′′ 0, n ′′ 0) and that of the plan (a ′ 0, n ′ 0) will intersect at a point p ′ 0 G(a ′′ 0, n ′′ 0p ′ ). This plan will have lesser regret if n > n ′′ 0. Obtaining the D kind plan We note that the OC of the D kind plan (k, n) at P (p) and at P (p ′ ) under Poisson conditions is identical with that of a SSP at p and at p ′ , where p = p 1 +p 2 +...+p r , p ′ = p ′ 1 +p ′ 2 +...+p ′ r with acceptance criterion: x ≤ k. It, therefore, follows that given an optimal MASSP of C kind it should be possible to construct a D kind plan with lesser regret values in first two 111
situations as above. For the third situation we may have to satisfy the additional condition mentioned as above to obtain such a D kind plan. In the next chapter we will demonstrate numerically the comparative superiority of the D kind plan to the C kind plan. 112
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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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different sampling schemes in terms
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curves i.e. the OC curve as a funct
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0.5.3 Part3 Bayesian multiattribute
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K(N, n)/(A 1 − R 1 ) = nk ′ s +
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example, a sample of finished garme
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...(1.1.2) If now X i is assumed to
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(i) Poisson as approximation to bin
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1.2 Multiattribute sampling schemes
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We take this case and the case of t
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highest with respect to critical de
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...(1.2.4) Note that, for single at
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...(1.2.7) To compare the relative
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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
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 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: where, p = (p 1 , p 2 , ..., p r )
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
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