Bayesian Methods in Estimating a Distribution from Failure Data JAYARAM SETHURAMAN Florida State University Failure data on a system can consist of data on failure times of a newly replaced system or of the repaired system after a previous failure. Hollander, Presnell and Sethuraman (1994) established a counting process framework to study the Whittaker and Samaniego (1989) estimate of the failure distribution from such data, when the repairs are ``minimal repairs'' which are done randomly according to the Block, Borges and Savits (1985) scheme. This estimate is based on failure times of N systems which are maintained by minimal repair till the time of a scheduled perfect repair. It may be noted that this frequentist estimate does not depend on the random mechanism which dictates minimal or perfect repair. In this talk, we will present a Bayesian view of this problem. This leads us to investigate posterior distributions under data consisting of failure times of repaired items, where we can allow repairs that are more general than minimal repairs. Perforce, the posterior distribution will not depend on the random mechanism dictating minimal or perfect repair and also on whether the next scheduled repair is a perfect repair or not.