Evaluation and Comparison of Estimation Methods for Failure Rates and Probabilities
This paper compares some features of Bayesian estimation techniques developed recently to assimilate data from multiple units to obtain effective estimators of failure rates for individual units. Several problems have been identified recently in various“two-stage” super-population methods [1, 2]. Hofer et al. noticed that the results obtained with the method are sensitive to the order and ranges of multidimensional integration, and in the limit the results behave as if the components (or plants) were completely identical. Such lack of variation was also noticed in a common-cause failure study . Becker and Schubert obtained suspicious results with the 2-stage method . Meyer and Hennings  studied the impacts of different forms of the improper hyper-priors and integration limits. Hofer and Peschke re-formulated the method so that the population variability is better accounted for . Bunea et al  claim that this approach still has some mathematical problems, and the choice of super-population and integration ranges are not always uniquely established. One problem with all these 2-stage-methods is that numerical methods are needed to calculate multidimensional integrals. This is a burden with hundreds of components in realistic risk assessment studies (PSA).
KeywordsStandard Deviation Dirichlet Distribution Bias Term Gamma Density Multidimensional Integral
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