n Subpopulations experiencing stochastic degradation: reliability modeling, burn-in, and preventive replacement optimization

Abstract

For some engineering design and manufacturing applications, particularly for evolving and new technologies, populations of manufactured components can be heterogeneous and consist of several subpopulations. The co-existence of n subpopulations is particularly common in devices when the manufacturing process is still maturing or highly variable. A new model is developed and demonstrated to simultaneously determine burn-in and age-based preventive replacement policies for populations composed of distinct subpopulations subject to stochastic degradation. Unlike traditional burn-in procedures that stress devices to failure, we present a decision rule that uses burn-in threshold on cumulative deterioration, in addition to burn-in time, to eliminate weak subpopulations. Only devices with post-burn-in deterioration levels below the burn-in threshold are released for field operations. Inspection errors are considered when screening burned-in devices. Preventive replacement is employed to prevent failures from occurring during field operation. We examine the effectiveness of such integrated polycies for non-homogeneous populations. Numerical examples are provided to illustrate the proposed procedure. Sensitivity analysis is performed to analyze the impacts of model parameters on optimal policies. Numerical results indicate there are potential cost savings from simutaneouly determining burn-in and maintenance policies as opposed to a traditional approach that makes decisions on burn-in and maintenance actions separately.

Keywords:

• n Subpopulations
• stochastic degradation
• mixture degradation
• burn-in
• preventive replacement
• inspection errors

Acknowledgements

The authors thank three anonymous referees for their helpful comments and suggestions. The work of the first author was supported by the Chinese Ministry of Education under grant 11YJC630228 and by Natural Science Foundation of Guangdong under grant S2011040002092. The work of the second and third authors was supported by the National Science Foundation under grants CMMI-0970140 and CMMI-0969423.