Bounds to optimal burn-in and optimal work size

Burn-in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn-in time and optimal work size maximizing the long-run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn-in time is derived for each fixed work size and a uniform (with respect to the burn-in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non-trivial lower bound for the optimal burn-in time can be derived if the underlying lifetime distribution has a large initial failure rate.