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Estimating parameters of proportional hazards model based on expert knowledge and statistical data

Author

Listed:
  • A Zuashkiani

    (University of Toronto)

  • D Banjevic

    (University of Toronto)

  • A K S Jardine

    (University of Toronto)

Abstract

Proportional hazards model (PHM) is a convenient statistical tool that can be successfully applied in industrial problems, such as in accelerated life testing and condition-based maintenance, or in biomedical sciences. Estimation of PHM requires lifetime data, as well as condition monitoring data, which often is incomplete or missing, and necessitates the use of expert knowledge to compensate for it. This paper describes the methodology for elicitation of expert's beliefs and experience necessary to estimate the parameters of a PHM with time-dependent covariates. The paper gives a background of PHM and review of the literature related to the knowledge elicitation problem and gives a foundation for the proposed methodology. The knowledge elicitation process is based on case analyses and comparisons. This method results in a set of inequalities, which in turn define a feasible space for the parameters of the PHM. By sampling from the feasible space an empirical prior distribution of the parameters can be estimated. Then, using Bayes rule and statistical data the posterior distribution can be obtained. This technique can also provide reliable outcomes when no statistical data are available. The technique has been tested several times in laboratory experiments and in a real industrial case and has shown promising results.

Suggested Citation

  • A Zuashkiani & D Banjevic & A K S Jardine, 2009. "Estimating parameters of proportional hazards model based on expert knowledge and statistical data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1621-1636, December.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:12:d:10.1057_jors.2008.119
    DOI: 10.1057/jors.2008.119
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    References listed on IDEAS

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    1. Mazzuchi, Thomas A. & Linzey, William G. & Bruning, Armin, 2008. "A paired comparison experiment for gathering expert judgment for an aircraft wiring risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 722-731.
    2. Shafiqah Al-Awadhi & Paul Garthwaite, 2006. "Quantifying expert opinion for modelling fauna habitat distributions," Computational Statistics, Springer, vol. 21(1), pages 121-140, March.
    3. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    4. Wang, W., 1997. "Subjective estimation of the delay time distribution in maintenance modelling," European Journal of Operational Research, Elsevier, vol. 99(3), pages 516-529, June.
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    Cited by:

    1. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    2. Kiassat, Corey & Safaei, Nima & Banjevic, Dragan, 2014. "Choosing the optimal intervention method to reduce human-related machine failures," European Journal of Operational Research, Elsevier, vol. 233(3), pages 604-612.
    3. de Jonge, Bram & Teunter, Ruud & Tinga, Tiedo, 2017. "The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 21-30.
    4. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    5. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2015. "Optimum maintenance strategy under uncertainty in the lifetime distribution," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 59-67.

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