Shocks as burn-in in heterogeneous populations

Burn-in is usually performed for items with decreasing or bathtub failure rates in order to eliminate early failures. This can be done in a "normal" or accelerated environment or with the help of high environmental stresses, which can often be referred to as "shocks". The latter method of burn-in was not considered so far in the literature on burn-in modeling. Mixtures of distributions present a useful survival model for modeling lifetime distributions in heterogeneous populations. They often result in decreasing failure rates in some time intervals. In this article, we consider shocks that eliminate items in heterogeneous populations with probabilities that depend on the corresponding frailty parameters. We assume that the larger the failure rate of an item in a heterogeneous population is, the larger the probability of this elimination. The optimal level of severity of shocks that minimizes the corresponding total expected costs function is analyzed. Some meaningful examples are discussed.