Sequential burn-in procedures

In Reliability Theory, the 'burn-in' period is intended as the period in which a component is tested before its operative life, in order to eliminate early failures. The problem of optimally choosing the burn-in period is considered for several components with exchangeable times-to-failures. From a Bayesian point of view, this reveals to be a sequential statistical decision problem. We give the definitions of sequential burn-in strategies and optimal burn-in strategies and prove an existence result relating to the optimal burn-in strategy, by applying the general ideas of dynamic programming. The latter result also establishes relevant aspects in the structure of the optimal solution.