Optimal preventive maintenance of coherent systems: A generalized Pólya process approach

Abstract

We propose optimal preventive maintenance strategies for n-component coherent systems. We assume that in the early time of the system operation all failed components are repaired, such that the state of a failed component gets back to a working state, worse than that of prior to failure. To model this repair action, we utilize a counting process on the interval $(0,\tau ],$ known as the generalized Pólya process (which subsumes the non-homogeneous Poisson process as a special case). Two generalized Pólya process-based repair strategies are proposed. The criteria to be optimized are the cost function formulated based on the repair costs of the components/system, and the system availability, to obtain the optimal time of preventive maintenance of the system. To illustrate the theoretical results, two coherent systems are studied for which the optimal preventive maintenance times are explored under different conditions.

Keywords:

• Preventive maintenance
• corrective maintenance
• minimal repair
• generalized Pólya process
• signature

Acknowledgments

We would like to thank the associate editor and four anonymous referees for their constructive comments and suggestions which improved the presentation of this article.

Additional information

Funding

Asadi's research work was performed in IPM Isfahan branch and was in part supported by a grant from IPM, Iran (No. 99620213).

Notes on contributors

Marzieh Hashemi

Marzieh Hashemi received BS, MS and PhD in statistics from the University of Isfahan, Isfahan, Iran. She has published six research papers. Her research interests are reliability theory, maintenance of coherent systems, and ordered random variables.

Majid Asadi

Majid Asadi is a professor of statistics at the Department of statistics, University of Isfahan, Iran and a senior associate researcher, School of Mathematics, IPM. He is an elected member of International Statistical Institute. He received BS and MS in statistics from Ferdowsi University of Mashhad, Iran and PhD in statistics from the University of Sheffield, UK. His research interests include reliability theory, reliability modeling of systems and networks, information-theoretic probability modeling, and ordered random variables. He served as the Dean of the Faculty of Sciences, University of Isfahan (2012-2016) and Head of the Department of Statistics, University of Isfahan (2008-2009). He received Isfahan Province Governor Research Award in (2010) and was recognized as the Distinguished Lecturer at the University of Isfahan (2014) and as the Exemplary Professor of the Country in Iran (2015).