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

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Table:1.3.1 Construction parameters for fixed risk C kind MASSP’s for α = 0.05, β = 0.1, ρ = 0.1. Sl. c 1 c 2 m 0.95 (c 1 , c 2 , ρ) m 0.10 (c 1 , c 2 , ρ) R (c 1 , c 2 , ρ, α, β) 1 0 0 0.051 2.303 44.89 2 0 1 0.266 3.786 14.23 3 0 2 0.437 5.075 11.61 4 1 1 0.392 4.224 10.78 5 1 2 0.882 5.72 6.49 6 1 3 1.423 7.11 5.00 7 1 4 1.958 8.427 4.30 8 1 5 2.449 9.688 3.96 9 1 6 2.867 10.904 3.80 10 1 7 3.184 12.081 3.79 11 2 5 2.858 10.125 3.54 12 2 6 3.554 11.447 3.22 13 2 7 4.243 12.734 3.00 14 2 8 4.914 13.991 2.85 15 2 9 5.551 15.22 2.74 16 2 10 6.143 16.424 2.67 17 2 11 6.676 17.604 2.64 18 2 12 7.137 18.763 2.63 19 3 9 5.957 15.591 2.62 20 3 10 6.735 16.865 2.50 21 3 11 7.504 18.12 2.41 22 3 12 8.26 19.356 2.34 23 3 13 8.994 20.574 2.29 24 3 14 9.7 21.776 2.24 25 3 15 10.371 22.96 2.21 26 3 16 10.999 24.13 2.19 27 3 17 11.574 25.283 2.18 28 4 14 10.159 22.134 2.18 29 4 15 10.983 23.373 2.13 30 4 16 11.797 24.599 2.09 31 4 17 12.598 25.813 2.05 32 4 18 13.381 27.014 2.02 Similar tables for other values of α, β, and ρ can be constructed. With the tables provided 69
ma β (a 1 , a 2 , ρ) = m ′ ...(1.3.14) construction of fixed risk C kind <strong>plans</strong> for r =2 as demonstrared is simple. No attempts are made to investigate the case r > 2. The approach will be similar in essence, but numerically the problem is sure to turn clumsy for r > 2 1.3.4 Construction of A kind <strong>plans</strong> of given strength In this case we want to satisfy the equations : P A(a 1 , a 2 ; np 1 , np 2 ) = 1 − α P A(a 1 , a 2 ; np ′ 1, np ′ 2) = β Restricting to the situation where p 1 /(p 1 + p 2 ) = p ′ 1/(p ′ 1 + p ′ 2) = ρ , for a given ρ we define ma P (a 1 , a 2 , ρ) as the value of m satisfying the equation P A(a 1 , a 2 ; mρ, m(1 − ρ)) = P. We must have n, a 1 , a 2 such that, ma 1−α (a 1 , a 2 , ρ) = m Introducing the auxiliary function Ra(a 1 , a 2 , ρ, α, β) = ma β (a 1 , a 2 , ρ)/ma 1−α (a 1 , a 2 , ρ), we note that ma P (a 1 , a 2 , ρ) is an increasing function of a 1 and a 2 , Ra(a 1 , a 2 , α, β, ρ) is a decreasing function of a 1 and a 2 and We obtain the smallest a 2 = a ∗ 2 for which, then find a ∗ 1 such that Ra (0, a ∗ 2 − 1, ρ, α, β) > p ′ /p ≥ Ra(a ∗ 2, a ∗ 2, ρ, α, β) ...(1.3.15) Ra(a ∗ 1 − 1, a ∗ 2, ρ, α, β) > p ′ /p ≥ Ra(a ∗ 1, a ∗ 2, ρ, α, β) ...(1.3.16)[5pt] To facilitate the above tasks we may construct a table containing a 1 , a 2 , ma β (a 1 , a 2 , ρ), ma 1−α (a 1 , a 2 , ρ) arranged in descending order of Ra(a 1 , a 2 , ρ, α, β) for 70
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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
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: α, β, and ρ. For α = 0.05, β =
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
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
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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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