Statistical Estimation Procedures for the "Burn-In" Process

This study deals with the "burn-in" process. In this process, items whose failure rate is assumed to decrease with time are put on test (burnt-in) until a fixed amount of time has elapsed (truncated sampling) or until a fixed number of failures have occurred (censored sampling). The purpose is to identify and eliminate poor-quality or defective items. For both of the modes of observation described, we provide a conservative upper confidence bound for the failure rate at the time the burn-in process ends, and the maximum likelihood estimate (MLE) of the failure-rate function. These results are valid under quite general conditions. In particular, we do not require that the form of the life distribution be known. The MLE is obtained under the sole assumption that the failure-rate function is decreasing. The confidence bound is obtained under the even weaker assumption that the failure rate at the time observation ends is no larger than the failure rate throughout the period of observation. For the truncated sampling case, a computer program to calculate the confidence bound is given.