Cost optimization of Gamma distribution accelerated burn-in

The burn-in process is operated under severe (stress) conditions involving high temperature, voltage, etc. and the product's residual life depends on the burn-in stress level and the length of burn-in period. Accelerated burn-in before shipment will reject poor-quality products and improve product reliability within a warranty period. Accelerated burn-in saves time but may cost more. In this paper, our goal is to find the appropriate testing parameters to minimize the total of testing, manufacturing, quality and reliability costs. The upper and lower bounds for the optimal burn-in time are derived. It is assumed in our work that the failure pattern follows Gamma distribution and the burn-in process is operated under approximately the same environment as that of the early operating life of the product.