Optimal burn-in decision for products with a unimodal failure rate function

Some lifetime distributions have a unimodal failure rate function, where a critical time separates the product's operating life into an increasing failure rate (IFR) phase and a decreasing failure rate (DFR) phase. Consequently, the customer may encounter a risk of high failure both in DFR and in IFR phases during the early operating life of the products. Moreover, since the corresponding mean residual life (MRL) function has an upside-down unimodal shape, the goal of maximized MRL, which is considered in traditional burn-in decision related to bathtub-shaped failure rate model, cannot be achieved. Therefore, how to eliminate IFR phase, economically determine the optimal burn-in time during DFR phase, and incorporate the MRL into consideration are essential to the burn-in decision for products with a unimodal failure rate function. In this paper, a minimum cost burn-in model is formulated to solve this decision issue. A lognormal distribution is used as an example to illustrate the proposed procedure and discuss the feasible range of parameters for conducting an effective burn-in.