Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.