BAYES ESTIMATION OF THE PIECE-WISE EXPONENTIAL-DISTRIBUTION

A Bayes method to infer an unknown failure-time distribution is presented. The method is based on the piecewise exponential distribution and a relationship between values of the failure rate in successive intervals; it provides smooth estimates of the survival and hazard functions of the distribution. This is accomplished in a model-based framework without resorting to smoothing procedures that require ad-hoc specification of parameters that have no bearing on the data. It is a useful procedure whenever the failure rate is anticipated to be reasonably continuous. Incorporating these beliefs into the model allows a more rational solution to the nonparametric estimation problem. The advantages are illustrated using a real data-set where a smooth estimate of the failure rate is obtained. The method can be used with any possibly-censored data-set and is easily implemented on a microcomputer. The Bayes solution is compared with the classical solution for the problem.