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Goodness-of-fit tests in the multi-state Markov model

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  • Kong, Yaonan
  • Ye, Zhisheng

Abstract

The continuous time Markov process is commonly used to model state transitions in a multi-state system. However, it is hard to verify the Markov assumption by traditional goodness-of-fit techniques due to the multiple states. In this article, a goodness-of-fit test conditioning on a sufficient statistic is developed to test the Markov assumption. We propose a test statistic whose conditional distribution given the sufficient statistic is free of any unknown parameters. Therefore, the conditional distribution of the test statistic together with the corresponding percentiles could be obtained by Monte Carlo simulation. This conditional test outperforms two conventional goodness-of-fit techniques for the Markov assumption. Further, we consider a multi-state degradation system in which the operating conditions are available. An acceleration relation is often used to model the effects of the operating conditions on the degradation system. In this scenario, a goodness-of-fit test based on the Greenwood statistic is developed to test both the Markov assumption and the acceleration relation. The performance of the proposed goodness-of-fit tests in multi-state systems is demonstrated by extensive simulations and a numerical example.

Suggested Citation

  • Kong, Yaonan & Ye, Zhisheng, 2017. "Goodness-of-fit tests in the multi-state Markov model," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 16-24.
  • Handle: RePEc:eee:reensy:v:166:y:2017:i:c:p:16-24
    DOI: 10.1016/j.ress.2017.02.010
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    1. Soro, Isaac W. & Nourelfath, Mustapha & Aït-Kadi, Daoud, 2010. "Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 65-69.
    2. Lisnianski, Anatoly & Elmakias, David & Laredo, David & Ben Haim, Hanoch, 2012. "A multi-state Markov model for a short-term reliability analysis of a power generating unit," Reliability Engineering and System Safety, Elsevier, vol. 98(1), pages 1-6.
    3. Lisnianski, Anatoly, 2007. "Extended block diagram method for a multi-state system reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1601-1607.
    4. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    5. Chanseok Park, 2010. "Parameter estimation for the reliability of load-sharing systems," IISE Transactions, Taylor & Francis Journals, vol. 42(10), pages 753-765.
    6. Wang, Bing Xing, 2009. "Testing for the validity of the assumptions in the exponential step-stress accelerated life-testing model," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2702-2709, May.
    7. Zhi‐Sheng Ye & Min Xie, 2015. "Stochastic modelling and analysis of degradation for highly reliable products," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 16-32, January.
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    Cited by:

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    2. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
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