Product acceptance models for Weibull distribution of lifetime under parametric uncertainty
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Date
2011
Authors
Nechval, K.N.
Nechval, N.A.
Purgailis, M.
Strelchonok, V.F.
Berzins, G.
Moldovan, M.
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Conference paper
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Proceedings of the 11th International Conference Reliability and Statistics in Transportation and Communication (RelStat'11), 2011, pp.72-81
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11th International Conference Reliability and Statistics in Transportation and Communication (RelStat'11) (19 Oct 2011 - 22 Oct 2011 : Riga, Latvia)
Abstract
Product acceptance models include sampling, inspection, and decision-making in determining the acceptable or rejection of a batch of products by experiments for examining the continuous usage time of the products. The most popular lifetime distribution used in the field of product acceptance is either a one-parameter exponential distribution (because it has relatively simple functional forms for both the probability density function and the cumulative distribution function), or a two-parameter Weibull distribution, with the assumption that the shape parameter is known. Such oversimplified assumptions can facilitate the follow-up analyses, but may overlook the fact that the lifetime distribution can significantly affect the estimation of the failure rate of a product. The choice of an appropriate product acceptance model is a crucial decision problem because a good model not only can help producers save testing time and reduce testing cost, but it also can positively affect the image of the product and thus attract more consumers to buy this product. Therefore often the Bayesian approach is used to solve the above problem. Unfortunately, in this case the subjectivity of investigator (a limitation of the Bayesian approach) is introduced through a priori distribution. In order to rule out the subjectivity of investigator and to consider comprehensively the relevant risks, in this paper a frequentist (non-Bayesian) decision analysis is employed.
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Copyright 2011 Transport and Telecommunication Institute