A computational method for finding the availability of opportunistically maintained multi-state systems with non-exponential distributions

Abstract

Availability is one of the most important performance measures of a repairable system. Among various mathematical methods, the method of supplementary variables is an effective way of modeling the steady-state availability of systems governed by non-exponential distributions. However, when all the underlying probability distributions are non-exponential (e.g., Weibull), the corresponding state equations are difficult to solve. To overcome this challenge, a new method is proposed in this article to determine the steady-state availability of a multi-state repairable system, where all the state sojourn times, as well as the maintenance times, are generally distributed. As an indispensable step, the well-posedness and stability of the system’s state equations are illustrated and proved using C₀ operator semigroup theory. Afterwards, based on the generalized Integral Mean Value Theorem, the expression for system steady-state availability is derived as a function of state probabilities. Then, the original problem is transformed into a system of linear equations that can be easily solved. A simulation study and an instance studied in the literature are used to demonstrate the applications of the proposed method in practice. These numerical examples illustrate that the proposed method provides a new computational tool for effectively evaluating the availability of a repairable system without relying on simulation.

Keywords:

• Availability
• multi-state system
• non-exponential distributions
• corrective maintenance
• preventive maintenance

Acknowledgments

The authors would like to thank the Department Editor, Associate Editor and three reviewers for their insightful comments and suggestions that greatly improved the quality of this paper.

Additional information

Notes on contributors

Naichao Wang

Naichao Wang received his B.S. degree in solid mechanics and Ph.D. degree in system engineering from Beihang University, China. He is currently a lecturer assistant professor of the School of Reliability and Systems Engineering at Beihang University. His research interest is in the area of stochastic modeling with applications in logistics, reliability, discrete event simulation, and stock optimization.

Yu (Chelsea) Jin

Yu (Chelsea) Jin received her B.S. degree in 2014 from the Department of Information Science and Technology at Jinan University, Guangzhou, China. In 2017, she received her M.S. degree in manufacturing engineering from the University of Michigan, Ann Arbor. Currently, she is pursuing her Ph.D. degree at the University of Arkansas, Fayetteville. Her research focuses on sensing and analytics, advanced manufacturing, as well as data mining and machine learning for manufacturing and service applications. She received the IISE Gilbreth Memorial Fellowship in both 2018 and 2019, and Kuroda Graduate Fellowship in Engineering and Graduate Research Award from the University of Arkansas in 2019. Her work has been published in IISE Transactions and ASME Journal of Manufacturing Science and Engineering. She is a student member of IISE and INFORMS, and she served as the president of INFORMS student chapter at the University of Arkansas.

Lin Ma

Lin Ma received a B.S. degree in 1997 and a Ph.D. in 2003, both in aircraft design, from Beihang University, P.R. China. He is currently an associate professor in the School of Reliability and Systems Engineering at Beihang University. His research interests include maintenance modeling, virtual maintenance, and complex system analysis and evaluation.

Haitao Liao

Haitao Liao is a professor and John and Mary Lib White Endowed Systems Integration Chair in the Department of Industrial Engineering at the University of Arkansas – Fayetteville. He received a Ph.D. degree in industrial and systems engineering from Rutgers University in 2004. He also earned M.S. degrees in industrial engineering and statistics from Rutgers University, and a B.S. degree in electrical engineering from Beijing Institute of Technology. His research interests include: (i) reliability models, (ii) maintenance and service logistics, (iii) prognostics, (iv) probabilistic risk assessment, and (v) analytics of sensor data. His research has been sponsored by the National Science Foundation, Department of Energy, Nuclear Regulatory Commission, Oak Ridge National Laboratory, and industry. The findings of his group have been published in IISE Transactions, European Journal of Operational Research, Naval Research Logistics, IEEE Transactions on Reliability, IEEE Transactions on Cybernetics, The Engineering Economist, Reliability Engineering & System Safety, etc. He received a National Science Foundation CAREER Award in 2010, IISE William A. J. Golomski Award in 2011, 2014 and 2018, SRE Stan Ofsthun Best Paper Award in 2015 and 2019, and 2017 Alan O. Plait Award for Tutorial Excellence. He is a Fellow of IISE, a member of INFORMS, and a lifetime member of SRE.