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Parameter estimation in a condition-based maintenance model

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  • Kim, Michael Jong
  • Makis, Viliam
  • Jiang, Rui

Abstract

A parameter estimation problem for a condition-based maintenance model is considered. We model a failing system that can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is assumed to follow a hidden, three-state continuous time Markov process. Vector autoregressive data are obtained through condition monitoring at discrete time points, which gives partial information about the unobservable system state. Two kinds of data histories are considered: histories that end with observable system failure and histories that end when the system is suspended from operation but has not failed. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm and a closed form expression for the pseudo-likelihood function is derived. Numerical results are provided which illustrate the estimation procedure.

Suggested Citation

  • Kim, Michael Jong & Makis, Viliam & Jiang, Rui, 2010. "Parameter estimation in a condition-based maintenance model," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1633-1639, November.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1633-1639
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    References listed on IDEAS

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    1. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    2. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
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    Cited by:

    1. Pan, Donghui & Wei, Yantao & Fang, Houzhang & Yang, Wenzhi, 2018. "A reliability estimation approach via Wiener degradation model with measurement errors," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 131-141.
    2. Wang, Wenbin, 2012. "A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems," European Journal of Operational Research, Elsevier, vol. 218(3), pages 726-734.
    3. Moghaddass, Ramin & Zuo, Ming J., 2012. "A parameter estimation method for a condition-monitored device under multi-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 94-103.
    4. Rui Jiang & Michael Kim & Viliam Makis, 2012. "A Bayesian model and numerical algorithm for CBM availability maximization," Annals of Operations Research, Springer, vol. 196(1), pages 333-348, July.

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