Estimation of Survival Functions and Failure Rate

Abstract

The BAYESian estimation of the survival function and failure rate in the uncensored case has been treated in PROSCHAN and SINGPURWALLA [5]. In this paper the extension of estimation to randomly censored data is considered. The time interval is partitioned into fixed class intervals. Assuming constant failure rate on these intervals and using a DIRICHLET distribution as the prior, the resulting estimates of survival function and failure rate have nice and simple forms. If instead of the fixed time intervals, one uses the “natural” intervals formed by the observed failure times, this gives essentially the same result as in FERGUSON and PHADIA [3], SUSARLA and VAN RYSIN [7], but in a much simpler form. In this situation the limiting estimates are the KAPLAN-MEIER analog for the discrete situation (not the KAPLAN-MEIER product limit estimator (KAPLAN and MEIER [4]).

Keywords:

• BAYESian inference
• DIRICHLET distribution
• survival function
• failure rate