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

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for j = 2. ...(2.2.7) We assume that all the above functions are nonnegative and none are identical to 0. We also assume that k s (p (j) ) ≥ k m (p (j) ), j = 1, 2. Further, let k s , k a , k r and k m denote the expected values of the corresponding cost functions defined in (2.2.4), (2.2.5), (2.2.6) and (2.2.7) w.r.t. the prior. Note that these functions are expressed as costs per unit. The average costs for the three cases without sampling inspection i.e. the cases where, (a) all lots are classified correctly, (b) all lots are accepted, and (c) all lots are rejected then become k m , k a and k r respectively. Sampling inspection should only be taken recourse to if k Avg − k m < min[k a − k m , k r − k m ] where k Avg = K(N, n)/N. Taking case (a) as the reference case we define the regret function R(N, n) R(N, n) = [K(N, n) − K m (N, n)]/(k s − k m ) where K m (N, n) is the average minimum unavoidable cost per lot a multiattribute analogue of what is given by Hald (1965). ...(2.2.8) We may further simplify the above expression for R(N, n) as R(N, n) = n + (N − n)[γ 1 Q(p (1) ) + γ 2 P (p (2) )] as γ j = w j |k a (p (j) ) − k r (p (j) )|/(k s − k m ); j = 1, 2. Note that if R 0 = S 0 and R i = S i ; i = 1, 2, then k s = k r and γ 1 = 1. ...(2.2.9) 2.2.5 Using the model In the above model γ j ’s are functions of the cost parameters and the prior distributions. The change of acceptance criteria affects the cost function through the probability of acceptance. This model therefore enables us to consider different kinds of MASSP’s and compare them in terms of costs, which is the primary focus of our inquiry. We shall continue our discussions to this end in the next chapters. 89
250 200 Figure 2.2.1 : Lot Quality Distribution of 552 inspection Lots for Functional defects of RS closures 150 Frequency 100 50 0 0.000- 0.001 0.003- 0.004 0.006- 0.007 0.009- 0.01 0.012- 0.013 0.062- 0.063 0.065- 0.066 0.068- 0.069 0.071- 0.072 0.074- 0.075 0.077- 0.078 0.08 - 0.081 0.083 - 0.0840 Proportion defectives 90
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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
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 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: P (p (j) ) denotes the probability
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
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
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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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