SOME ROBUSTNESS ISSUES IN THE BAYESIAN-ANALYSIS OF A WEIBULL FAILURE MODEL

We determine the Bayes estimator of the reliability function for a hierarchical Weibull failure model, assuming the scale parameter is known, and treating the shape parameter, alpha, as stochastic. The shape parameter is generated from a mixture containing a point mass at alpha = 1, yielding exponential data, and alpha distributed as Beta Type II, yielding general Weibull data. The estimator is then evaluated for data from a series of different failure distributions, including the parent model, and simple exponential and simple Weibull models, Its robustness is measured by evaluating the root mean squared errors of the mixture estimator and comparing them to root mean squared errors for some competing models.