Statistics Seminars: Mixing Bayes and Empirical Bayes for Modelling Reliability Growth during Engineering System Design and Development
6 February 2009 14:15 in CM107
Many engineering system designs are variants of earlier generations which have been changed to incorporate innovation and modification. Reliability assessment, conducted during design and development, will inform management decisions concerning, for example, test and analysis regimes to prove fitness of the system for use. This talk develops mixed Bayes and empirical Bayes inference for a reliability model that uses relevant data generated through a variant design process. Structured expert judgment is elicited to specify a subjective prior distribution for mutually exclusive and exhaustive classes of potential faults, while service records provide event histories for heritage designs to characterize the distribution of time to fault realization. The methodology forms a distribution by pooling classes of event data, permitting adjustments from the pool to provide a unique distribution for each class. Alternative approximations for the reliability are examined and their relative accuracy evaluated for subjective prior distributions from the Katz family of counting distributions. These include the Binomial, Poisson and Negative Binomial distributions. The model is extended to update estimates when further design change occurs during development. General forms of the posterior distribution are proven to exist for the selected class of subjective priors and it is shown that the distributions within the Katz family are closed under updating. An application to an industrial problem illustrates how analysis can support planning decisions.
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