A novel method for reliability evaluation of Markov systems

Yamei Zhang; Nikolaos Limnios; Bei Wu

doi:10.1088/3050-2454/ae587c

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A novel method for reliability evaluation of Markov systems

Papers | 更新时间：2026-05-08

- A novel method for reliability evaluation of Markov systems
- 马尔可夫系统可靠性评估的一种新方法
- Journal of Reliability Science and Engineering Pages: 1-12(2026)
- 作者机构：
  
  Northwestern Polytechnical University, Xi'an, People's Republic of China
  Université de Technologie de Compiègne, Compiègne, France
- 作者简介：
  
  [ "Yamei Zhang received her PhD degree from Northwestern Polytechnical University, Xi'an, China. She is currently a lecturer at the School of Physical Science and Technology, Northwestern Polytechnical University. Her research interests include system reliability modeling and maintenance optimization." ]
  [ "Nikolaos Limnios is a distinguished professor in France and worked at the Institute of Applied Mathematics of the Université de Technologie de Compiègne, France. Nikolaos In 2018, he received the ‘Academic Palm Medal’ in recognition of his academic contributions. His main research interests include modeling and estimation of semi-Markov systems, convergence properties of random evolutions, and fundamental theoretical issues in hidden semi-Markov models." ]
  [ "Bei Wu received her PhD degree in Beijing Institute of Technology. She is currently an Associate Professor and PhD Supervisor at the School of Management, Northwestern Polytechnical University. Her research focuses on system resilience, reliability, and maintainability management. Since 2017, she has published over forty papers in high-level research journals and conferences, including Naval Research Logistics, IISE Transactions, IEEE Transactions on Engineering Management, Reliability Engineering & System Safety, and International Journal of Production Research." ]
- 基金信息：
- DOI：10.1088/3050-2454/ae587c
  CLC：
- Received：02 November 2025，
  
  Revised：2026-03-09，
  
  Accepted：27 March 2026，
  
  Online First：09 April 2026，
  
  Published：2026-06
- 稿件说明：
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Yamei Zhang, Nikolaos Limnios and Bei Wu. 马尔可夫系统可靠性评估的一种新方法[J]. 可靠性科学与工程学报（英文）, 2026, 2: 025001.

Yamei Zhang, Nikolaos Limnios and Bei Wu. A novel method for reliability evaluation of Markov systems[J]. Journal of Reliability Science and Engineering, 2026, 2: 025001.
Yamei Zhang, Nikolaos Limnios and Bei Wu. 马尔可夫系统可靠性评估的一种新方法[J]. 可靠性科学与工程学报（英文）, 2026, 2: 025001. DOI： 10.1088/3050-2454/ae587c.

Yamei Zhang, Nikolaos Limnios and Bei Wu. A novel method for reliability evaluation of Markov systems[J]. Journal of Reliability Science and Engineering, 2026, 2: 025001. DOI： 10.1088/3050-2454/ae587c.

摘要

本文提出了一种基于指数运算和幂运算谱表示的方法，用于解决马尔可夫系统中与可靠性特征相关的复杂性问题。由于状态数量呈指数增长，传统公式变得不切实际，这在二元部件系统中成为一个显著挑战。在此背景下，本文在一个受控的数学框架内提出了一种近似方法，以实现对高可靠性系统的精确可靠性评估。本文推导了用于计算系统可靠性的公式，如可靠度、失效率、条件生存分布等，并证明这些公式在非遍历系统的可靠性评估中实用且精确，同时还推导了遍历系统的可用性。计算中唯一需要的元素是生成矩阵或子转移矩阵的最大特征值及其对应的特征向量，这些元素描述了可靠性的近似结果。最后，通过数值算例验证了近似结果与精确结果，证明了所提方法的正确性。

Abstract

This paper introduces a method based on the spectral representation of exponential and power operations to tackle the complexity issues associated with dependability characteristics in Markov systems. The conventional formulas become impractical due to the exponential growth in the number of states

which becomes a significant challenge in binary component systems. In such contexts

an approximation method is proposed in a controlled mathematical framework to realize accurate reliability assessment for highly reliable systems. In this paper

formulas for computing system dependability such as reliability

failure rate

conditional survival distribution

etc. are derived and proved to be useful and accurate for the reliability assessment of non-ergodic systems

while the availability of ergodic systems is derived. The only elements needed here are the largest eigenvalues and corresponding eigenvectors of the generate or subtransition matrix

which describes the approximation of reliability. Finally

the approximate results and exact results are verified through numerical examples

proving the correctness of the proposed method.

关键词

Keywords

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