Optimal burn-in with random minimal repair cost

Burn-in is a method used to eliminate early failures of components before they are put into field operation. Maintenance policy, such as block replacement policy with minimal repair at failure, is often used in field operation. In this paper burn-in and maintenance policy are taken into consideration at the same time. It is assumed that the cost of a minimal repair to the component which fails at age t is a continuous non-decreasing function of t. We consider the problems of determining optimal burn-in times and optimal maintenance policy.