A bayesian approach to inference for monotone failure rates

In reliability theory, the notion of monotone failure rates plays a central role. When prior information indicates that such monotonicity is meaningful, it must be incorporated into the prior distribution whenever inference about the failure rates needs to be made. In this paper we show how this can be done in a straightforward and intuitively pleasing manner. The time interval is partitioned into subintervals of equal width and the number of failures and censoring in each interval is recorded. By defining a Dirichlet as the joint prior distribution for the forward or the backward differences of the conditional probabilities of survival in each interval, we find that the monotonicity is presenved in the posterior estimate of the failure rates. A posterior estimate of the survival function can also be obtained. We illustrate our method by applying it to some real life medical data.