In this paper, the generalized burn-in and replacement model considered by Cha (2001) is further extended to the case in which the probability of Type II failure is time dependent. Two burn-in procedures are considered and they are compared in cases when both the procedures are applicable. Under some mild conditions on the failure rate function r(t) and the Type II failure probability function p(t), the problems of determining optimal burn-in time and optimal replacement policy are considered.

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.