A Multi-objective Joint Burn-in and Imperfect Condition-based Maintenance Model for Degradation-based Heterogeneous Populations

For some engineering design and manufacturing applications, particularly for evolving and new technologies, there can exist substantial heterogeneity in populations of manufactured components. The co‐existence of n subpopulations and unit‐to‐unit heterogeneity can be common in devices when the manufacturing process is still maturing or highly variable. In this research, we not only model the heterogeneity at the subpopulation‐level but also at the unit‐level. A mixture degradation framework is developed to model this multi‐level heterogeneity. Based on the proposed mixture degradation model, we develop a multi‐objective optimization model to jointly determine burn‐in and condition‐based maintenance policies for populations composed of distinct subpopulations with random effects. We allow the condition‐based maintenance to be imperfect, which is more realistic. Our joint models are entirely appropriate for companies that are the providers of both products and services, and can also produce optimal collective results and decisions that can quantify potential savings or benefits through cooperative efforts between producer and user. Numerical examples are provided to illustrate the proposed procedure.