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

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2.1.5 Approximation under Poisson conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.1.6 The genaralized cost model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.2 The expected cost model for discrete prior distributions . . . . . . . . . . . . . . . . . . . . . 86 2.2.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.2.2 A real life example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.2.3 The average costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.2.4 The regret function for the two point prior. . . . . . . . . . . . . . . . . . . . . . . . . 88 2.2.5 Using the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.4 Cost of MASSP’s of C kind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.4.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.4.2 The OC distribution and the OC moments of the C plan . . . . . . . . . . . . . . . . 105 2.4.3 OC moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.4.4 The moment equivalent plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 2.4.5 Sample size of the moment equivalent plan . . . . . . . . . . . . . . . . . . . . . . . . 107 2.4.6 Obtaining a D kind plan with regret value lesser than that of the optimal C plan . . . 109 2.5 Results of numerical investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 2.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.1 Bayesian single sampling multiattribute plans for continuous prior distribution . . . . . . . . 122 3.1.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.1.2 The cost model for continuous prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.1.3 The distribution of process average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.1.4 The verification for the appropriate prior distribution . . . . . . . . . . . . . . . . . . 125 3.1.5 The expression of average costs under the assumption of independent gamma prior distributions of the process average vector . . . . . . . . . . . . . . . . . . . . . . . . . 126 3.1.6 Bayesian Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 3.1.7 Annexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 1
Part 0 : Introduction 0.1 Purpose of sampling inspection The very purpose of quality management comprising of quality planning, quality control, quality assurance and quality improvement is to achieve simultaneously, improvement in customer satisfaction, improvement in productivity and reduction in costs of product at all stages. From the very beginning statistical methods have been developed, established and implemented as support activities for the above purpose. While Shewhart (1931) focused his attention on economic control of quality of manufactured product, Dodge and Romig (1929) attended to quality assurance activities of an organization for protection of the interest of the internal and external customers at reduced cost of inspection and cost of production, and also for attainment of uniform quality. The latter established methodologies of sampling inspection for separating lots or batches of mass produced items into lots of satisfactory and unsatisfactory quality. 0.2 Theory and application of sampling inspection - a short review In the following sections we try to underline the nature of major developments of techniques of sampling inspection for industrial quality assurance since the pre-war time. In this context we limit our discussions at the beginning to single sampling plans as employed for lot-by-lot inspection by attribute. The developments relating to double and multiple sampling plans for attributes, continuous sampling and chain sampling plans, sequential sampling plans and their modification and the whole subject matter of sampling plans by variables and all methods pertaining to bulk materials are scrupulously excluded from our discussions as they are not relevant as far as the scope of the present thesis is concerned. The historical perspective discussed focuses attention only to that part of the development which is conceptually and theoretically related to the problems studied in the present thesis. A single sampling plan is defined by means of three parameters c, n, and N and the following rule : From each lot of size N take a random sample of size n. If the number of defectives in the sample is less than or equal to the acceptance number c, accept the lot, otherwise reject the lot. 2
Page 1 and 2: Multiattribute acceptance sampling
Page 3 and 4: e) the cost functions are linear an
Page 5: Contents 0.1 Purpose of sampling in
Page 9 and 10: ectification is defined by setting
Page 11 and 12: procurement of materials of the US
Page 13 and 14: average defective from such a proce
Page 15 and 16: 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
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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
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Table 1.2.5 (contd.) : Three attrib
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Table 1.2.5 (contd.) : Three attrib
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1.3 Multiattribute sampling plans o
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Let M 2 < M 1 . Then G(c 1 , M 1 ρ
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α, β, and ρ. For α = 0.05, β =
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ma β (a 1 , a 2 , ρ) = m ′ ...(
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Table:1.3.2: Construction parameter
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1.3.5 D kind plans of given strengt
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Figure 1.3.1: The sketch of the fun
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2.1 General cost models 2.1.1 Scope
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(j) Interaction of scrappable attri
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use of defective item is additive o
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2.1.5 Approximation under Poisson c
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2.2 The expected cost model for dis
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P (p (j) ) denotes the probability
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250 200 Figure 2.2.1 : Lot Quality
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Table 2. 2. 1 Testing goodness of f
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2. 3 Cost of MASSP's of A kind 2.3.
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From (2.3.2) we observe that γ 2 1
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( γ / ) 2 γ − ( m′− m e ) /
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We now consider the following funct
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….(2.3.12) Here S A denotes the s
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∴There exists an optimal A plan f
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Hence, Q(m) = 1 − P (m) has the s
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where a 0 and n 0 are the parameter
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where, p = (p 1 , p 2 , ..., p r )
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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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