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

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We have therefore arrived at a model as applicable to a multiattribute situation discussed in section 2.1.3. for r > 1. This may be considered as a generalization of the cost model of Hald(1965) for the single attribute situation i.e. for r = 1 85
2.2 The expected cost model for discrete prior distributions 2.2.1 Assumptions By Bayesian plans we understand the plans obtained by minimizing average costs which has three identifiable components viz. inspection costs, acceptance costs, and rejection costs. For these plans the process average defective is taken to be a random variable. In our present context the prior distribution (i.e. the distribution of process average) is the expected distribution of lot quality vector on which the sampling plan is going to operate. For the multiattribute Bayesian plans considered by others [See chapter 2.1], the process average for each attribute has been assumed to follow a beta distribution so that the lot quality distribution for each attribute becomes a beta binomial.Thus, in a situation when defect occurrences are jointly independent the product of individual beta distributions are chosen as an appropriate prior. We may, however, note that even when the process is in control with respect to such a prior, the process will occasionally go out of control and some lots of poorer quality will be produced before the process gets corrected. We then have a situation of a beta prior with outliers. As an alternative to these models, consider the process average vector as a random variable which may take on two values,(p 1 , p 2 , ..., p r ) and (p ′ 1, p ′ 2, ..., p ′ r), a satisfactory and an unsatisfactory quality level with given probabilities. This two point prior may be considered as a simplification of the one point prior with outliers, because the model contains some information about the distribution of the outlier. When the process performs at an unsatisfactory level it generally happens (e.g. for a manufacturing operation) that the quality level is poor for all the attributes. We cite one example from a real life situation. 2.2.2 A real life example The example given below constitutes a typical example picked up from the author’s list of similar applications in factories rendered by him as a QC professional. For the general discussion intended here, the details relating to the particular application are not included and only the relevant calculations are presented. A company manufactures about 1.5 lakhs of 25 mm RS closures in a shift. A shift’s production by a group is being packed in cartons, each carton is considered as an inspection lot for verification after the end of the shift. The two important sets of attributes for the product are functional defects and surface defects. On the spot observations have been made using a p-chart data format on these attributes. In a typical scenario one observes, that most of the time the process is stable at a certain 86
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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 +
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 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: 2.1.5 Approximation under Poisson c
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
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
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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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