Burn-in and the performance quality measures in continuous heterogeneous populations

Burn-in is a method used to eliminate initial failures in field use. To burn-in a component or system means to subject it to a period of use prior to the time when it is to actually be used. Under the assumption of decreasing or bathtub-shaped population failure rate functions, various problems of determining optimal burn-in have been intensively studied in the literature. In this paper, we assume that a population is composed of stochastically ordered subpopulations, described by their own performance quality measures and study optimal burn-in, which optimizes overall performance measures. It turns out that this setting can justify burn-in even when it is not necessary in the framework of conventional approaches. For instance, it could be reasonable to perform burn-in even when the failure rate function that describes a heterogeneous population of items increases and this is one of the main and important findings of the current study.