On optimal burn-in procedures - a generalized model

Burn-in is a manufacturing technique that is intended to eliminate early failures. In this paper, 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 the burn-in process, two types of burn-in procedures are considered. In Burn-In Procedure I, the failed component is repaired completely regardless of the type of failure; whereas, in 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. Under the model, various additive cost functions are considered. It is assumed that the component before undergoing the burn-in process has a bathtub-shaped failure rate function with the first change point t₁, and the second change point t₂. The two burn-in procedures are compared in cases when both the procedures are applicable. It is shown that the optimal burn-in time b^* minimizing the cost function is always before t₁. It is also shown that a large initial failure rate justifies burn-in, i.e., b^*>0. The obtained results are applied to some examples.