Burn-in via shocks for avoiding large risks

Burn-in is usually performed for items that have decreasing or bathtub failure rates in order to eliminate early failures. This can be done in either the normal environment or an accelerated environment that uses high environmental stresses, which are often referred to as shocks. Mixtures of distributions present a useful survival model for lifetime distributions in heterogeneous populations. They often result in decreasing failure rates in some time intervals, which can often justify the implementation of the burn-in procedure. This paper considers shocks that eliminate weak items in heterogeneous populations. It is assumed that a larger failure rate of an item corresponds to a larger probability of this elimination. Approaches are developed that can help to minimize the risks of selecting items with large levels of individual failure rates for missions of high importance, where failures can result in substantial economic losses. The optimal burn-in time which minimizes average losses for different criteria is considered using simple examples.