Optimal burn-in policies for multiple dependent degradation processes

Abstract

Many complex engineering devices experience multiple dependent degradation processes. For each degradation process, there may exist substantial unit-to-unit heterogeneity. In this article, we describe the dependence structure among multiple dependent degradation processes using copulas and model unit-level heterogeneity as random effects. A two-stage estimation method is developed for statistical inference of multiple dependent degradation processes with random effects. To reduce the heterogeneity, we propose two degradation-based burn-in models, one with a single screening point and the other with multiple screening points. At each screening point, a unit is scrapped if one or more degradation levels pass their respective burn-in thresholds. Efficient algorithms are devised to find optimal burn-in decisions. We illustrate the proposed models using experimental data from light-emitting diode lamps. Impacts of parameter uncertainties on optimal burn-in decisions are investigated. Our results show that ignoring multiple dependent degradation processes can cause inferior system performance, such as increased total costs. Moreover, a higher level of dependence among multiple degradation processes often leads to longer burn-in time and higher burn-in thresholds for the two burn-in models. For the multiple-screening-point model, a higher level of dependence can also result in fewer screening points. Our results also show that burn-in with multiple screening points can lead to potential cost savings.