Optimal inspection and replacement policy based on experimental degradation data with covariates

Abstract

In this article, a novel maintenance model is proposed for single-unit systems with an atypical degradation path, whose pattern is influenced by inspections. After each inspection, the system degradation is assumed to instantaneously decrease by a random value. Meanwhile, the degrading rate is elevated due to the inspection. Considering the double effects of inspections, we develop a parameter estimation procedure for such systems from experimental data obtained via accelerated degradation tests with environmental covariates. Next, the inspection and replacement policy is optimized with the objective to minimize the Expected Long-Run Cost Rate (ELRCR). Inspections are assumed to be non-periodically scheduled. A numerical algorithm that combines analytical and simulation methods is presented to evaluate the ELRCR. We then investigate the robustness of maintenance policies for such systems by taking the parameter uncertainty into account with the aid of large-sample approximation and parametric bootstrapping. The application of the proposed method is illustrated by degradation data from the electricity industry.

Keywords:

• Condition-based maintenance
• degradation modeling
• imperfect maintenance
• large-sample approximation
• maximum likelihood estimation

Acknowledgements

We are grateful to the editors and anonymous referees for their insightful comments that led to a substantial improvement to an earlier version of the paper.

Additional information

Funding

This work was supported in part by the Research Grants Council of Hong Kong under a theme-based project under Grant T32-101/15-R and a General Research Fund (CityU 11203815) and in part by the National Natural Science Foundation of China under a Key Project under Grant 71532008.

Notes on contributors

Xiujie Zhao

Xiujie Zhao is a Ph.D. candidate with the Department of Systems Engineering and Engineering Management at City University of Hong Kong. He received a B.E. degree from Tsinghua University, and an M.S. degree from Pennsylvania State University, both in industrial engineering. His research interests include accelerated reliability testing, degradation modeling, maintenance modeling and design of experiments. His papers have appeared in IEEE Transactions on Reliability, Reliability Engineering & System Safety, among others.

Olivier Gaudoin

Olivier Gaudoin is a professor of statistics at Grenoble Institute of Technology, Institute of Engineering, University Grenoble Alpes, France and researcher at Laboratoire Jean Kuntzmann. His research topics are stochastic modelling and statistical inference for reliability and maintenance, with special focuses on maintenance effect modelling, goodness-of-fit testing in reliability, competing risks, discrete reliability and software reliability. He has co-authored one book on Stochastic Modelling for Software Reliability, more than 40 papers in peer-reviewed journals, and 60 communications in international conferences. He is associate editor of Methodology and Computing in Applied Probability and Journal de la Société Française de Statistique, and former associate editor of IEEE Transactions on Reliability.

Laurent Doyen

Laurent Doyen received a Ph.D. degree in applied mathematics from Grenoble University, France, in 2004. He is an associate professor at Université Grenoble Alpes, France. His research interests include probability and statistics applied to reliability. He is particularly interested by the subjects of aging, imperfect maintenance modeling, competing risks, and random processes in reliability. He has co-authored 12 papers in peer-reviewed journals, three books chapters and 30 communications in international conferences.

Min Xie

Min Xie received his Ph.D. from Linkoping University, Sweden in 1987. He did his undergraduate study and received an MSc at Royal Institute of Technology in Sweden in 1984. He joined the National University of Singapore in 1991 as one of the first recipients of the prestigious Lee Kuan Yew Research Fellowship. In May 2011, he moved to City University of Hong Kong as chair professor of industrial engineering. He has published many journal papers and eight books, including Software Reliability Modelling published by World Scientific, Weibull Models published by John Wiley, Statistical Models and Control Charts for High Quality Processes published by Kluwer Academic, and Stochastic Aging and Dependence for Reliability published by Springer. He is an editor, associate editor and on the editorial board of many established international journals. He has organized many international conferences, and also 50 Ph.D. students have graduated under his supervision. He was elected a fellow of IEEE in 2005.