NON PARAMETRIC QUASI-BAYESIAN ESTIMATION OF RELIABILITY AND PRIOR DISTRIBUTION

The purpose of this study is to examine from a nonparameter point of view and in a Bayesian setting failure models which depend on stochastic parameters whose distribution G((theta)) is unknown. The problem of estimating G when a priori information about G is specified in the form of an initial guess G(,0), is considered. First, assuming that the unconditional failure time distribution is a Dirichlet process, estimators of the prior G and reliability function are obtained based on censored data. Also, assuming that the unconditional failure time distribution is a mixture of Dirichlet process, Bayesian estimators are obtained for reliability and the prior distribution. Monte Carlo simulation is employed to compare the estimators for some specific failure models.

The results are extended to multiparameter models, under the assumption that the unconditional failure time distribution F(,G) is a Dirichlet process or a mixture of Dirichlet processes. In both cases, some examples are given to illustrate the usefulness of the theoretic results. Some possible extensions are mentioned.