Reliability-based optimization of imperfect preventive maintenance with Bayesian estimation

Abstract

In this study, we present a sequential imperfect preventive maintenance model for a component subject to degradation. We use an age reduction reliability model for scheduling preventive maintenance, which is performed whenever the component’s reliability falls below the reliability threshold level, R. The problem is considered under lack of data, in which the Bayesian methodology is more appropriate than the frequentist view for estimating the unknown parameters of the model. We assume a fixed duration for preventive maintenance, whereas the duration of corrective maintenance is an exponential random variable. We model the total expected cost over all cycles and find the optimal preventive maintenance plan until a replacement based on the reliability threshold value. We also conducted a numerical study for sensitivity analysis of the developed model.

Keywords:

• Bayesian inference
• optimization
• preventive maintenance
• reliability
• unreliable system

Acknowledgment

The authors thank the editor and the anonymous reviewers for their valuable comments and suggestions helped improve the exposition of this article.

Additional information

Notes on contributors

Selma Gürler

Selma Gürler received her B.S., M.S., and PhD degrees in Statistics from the Dokuz Eylul University in years 1998, 2002 and 2006, respectively. She currently works as a Professor at the Department of Statistics at Dokuz Eylul University, Türkiye. Her research interests are including reliability theory, order statistics, applied probability and statistics.

Dinçer Göksülük

Dinçer Göksülük graduated from the Department of Statistics in 2008 and completed his master degree in Statistics in 2011. He completed his Phd in Biostatistics at Hacettepe University in 2019. He currently works as an Assistant Professor in the Biostatistics department of Erciyes University. His research interests are machine learning, artificial intelligence, transcriptomics, proteomics, and metabolomics. He currently works on developing novel applications, computer algorithms, and analysis-tools for various problems, mainly in medicine and bioinformatics.

Deniz Türsel Eliiyi

Deniz Türsel Eliiyi is Professor and Chair of the Department of Industrial Engineering at Izmir Bakırçay University in İzmir, Türkiye. She obtained her B.S., M.S., and Ph.D. degrees in Industrial Engineering from the Middle East Technical University in Ankara, Türkiye. She worked at the Middle East Technical University, Dokuz Eylül University, Izmir University of Economics and Yaşar University, where she was Professor and Chair of the Department of Industrial Engineering. She also was a visiting researcher in the Department of Business Information Technology at the Virginia Polytechnic Institute and State University in the U.S. in 2013 and 2017, and in the Department of Computer Science at the University of St. Andrews in the U.K. in 2018. Her research interests include mathematical modeling and optimization, scheduling and vehicle routing, container port operations management, and the scheduling of IoT devices. She has authored over 100 journal and conference papers, and participated in over 15 scientific and industrial research projects on these topics.