USE OF THE WEIBULL DISTRIBUTION IN BAYESIAN DECISION THEORY
RESEARCH ANALYSIS CORP MCLEAN VA
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The Weibull distribution is useful in analyzing the probabilistic lifetimes of many electrical components and complex systems. It is attractive for Bayesian decision-making because its right-hand cumulative function is of an exponential form which allows all life-test data to be easily incorporated into the decision-making process. Unfortunately no natural conjugate prior distribution exists if both the shape and scale parameters of the Weibull distribution are assumed to be unknown. If the shape parameter is assumed known, however, Bayesian analysis becomes little more difficult than for the exponential distribution, a special case of the Weibull. Prior, posterior, and preposterior analyses are given for the case of known shape parameter. In connection with preposterior analysis several sampling plans are discussed. The paper concludes with an analysis of a problem in optical sampling.
- Operations Research
- Manufacturing and Industrial Engineering and Control of Production Systems