Bounding the optimal burn-in time for a system with two types of failure

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining bounds to the optimal burn-in time and optimal replacement policy maximizing the steady state availability of a repairable system. It is assumed that two types of system failures may occur: One is Type I failure (minor failure), which can be removed by a minimal repair, and the other is Type II failure (catastrophic failure), which can be removed only by a complete repair. Assuming that the underlying lifetime distribution of the system has a bathtub-shaped failure rate function, upper and lower bounds for the optimal burn-in time are provided. Furthermore, some other applications of optimal burn-in are also considered.