Performance-based Burn-in for products sold with warranty

To protect users from early failures, manufacturers often use burn-in to screen out weak units and meanwhile providing warranty to customers. Some performance-based burn-in models have been proposed in the literature. However, relations between these indices are not clear. In this study, we look into this problem and reveal the internal relations between these indices. More specifically, we focus on the probability of failure within the warranty period, mean number of failures within the warranty period and the percentile residual life that maximize the warranty period given a specified proportion of field failure. It is found that there are some dual relations between these indices. An illustrative example is used to demonstrate our results.