On reliability analysis in priority standby redundant systems based on maximum entropy principle

ABSTRACT

There are many studies on standby redundant systems, since those are the most standard models for ensuring reliability in systems. Particularly, two-component priority standby redundant systems are one of the most fundamental and important redundant models in the reliability theory. In recent years, the procedure for evaluating the mean time to failure (MTTF) of the two-component priority standby redundant system has been proposed by using mixed Erlang distributions as approximate distributions. In this study, by expanding the idea on evaluating MTTF proposed in the previous research, an evaluation method for the variance of failure times (VOFT) in the two-component priority standby redundant system has been presented. Furthermore, we have proposed a procedure for deriving the reliability function in the system based on the maximum entropy principle by utilizing MTTF and VOFT. Through some numerical applications, the validity of the procedures for deriving the reliability function developed in this study has been shown.

KEYWORDS:

• Method of Lagrange multiplier
• maximum entropy principle
• reliability function
• system reliability
• two-component priority standby redundant system

Acknowledgments

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 18K04611: “Evaluation of system performance and reliability under incomplete information environment”. We would like to appreciate the grant for our research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Ryosuke Hirata

Ryosuke Hirata received his BE and ME from Okayama University, all in the Graduate School of Natural Science and Technology, in 2018 and 2020, respectively. His research interests centre in the reliability theory and statistics.

Ikuo Arizono

Ikuo Arizono received his BE, ME and PhD from Osaka Prefecture University, all in the Department of Industrial Engineering, in 1982, 1984 and 1988, respectively. From 1985 to 1990 he was a research associate, from 1990 to 1994, he was an assistant professor and since 1994, he was an associate professor in the Graduate School of Engineering, Osaka Prefecture University. Since 2011, he is a professor in the Graduate School of Natural Science and Technology, Okayama University. His research interests centre in the statistical quality control and operational research.

Yasuhiko Takemoto

Yasuhiko Takemoto received his BE, ME and PhD from Osaka Prefecture University, all in the Department of Industrial Engineering, in 2000, 2002 and 2004, respectively. From April 2004 to September 2007, he was a research associate in the Department of Strategic Management, School of Business Administration, University of Hyogo. Since October 2007 to March 2017, he was an associate professor in the Faculty of Management and Information Systems, Prefectural University of Hiroshima. Since April 2017, he is an associate professor in the Faculty of Science and Engineering, Kindai University. His research interests centre in the statistical process control and supply chain management.