A burn-in scheme based on percentiles of the residual life

Many commercial products sold with warranties suffer from infant-mortality problems. Burn-in is a common means to mitigate the impact of early failures on warranty costs. After burn-in, the p-percentile function of the residual life (PRL-p function) is of particular interest as, in some cases, there exists a change point at which the PRL-p function reaches a maximum value. When the failure probability during the warranty period is prespecified, this change point naturally gives rise to an optimal burn-in duration. Moreover, the maximal PRL-p represents the maximum allowable warranty period when the expected field return is set at p. We present some properties of this change point, and derive the asymptotic distribution of its parametric maximum likelihood estimator and that of the corresponding PRL-p. The procedure is then applied to estimate a set of desirable burn-in durations and the corresponding warranty periods when life-test data are available. An example using the modified Weibull extension model is given to illustrate the procedure.