Bayesian Nonparametric Estimation of Failure Rates with Censored Data

Abstract

The failure time distribution is estimated in the nonparametric context when some of tbe observations arc censored. The time interval is partitioned into fixed class intervals, and number of failures and number censored in each of these intervals are observed. Using a Dirichlet distribution as the prior, the resulting estimates of the survival function and the failure rate have a nice and simple form. If instead of the fixed time intervals, one uses the “natural” intervals formed by the observed failure times, this gives essentially the same results as in Ferauson IUld Phadia (1977), Susarla and Van Ryzin (1976), but in a much simpler way. Bayes estimation under the increasins and decreasing failure rates is also considered, and applications to accelerated life testing are discussed.