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Higher moments and probability distribution of maintenance cost in the delay time model

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  • Mahesh D Pandey
  • Tianjin Cheng
  • JAM Van der Weide

Abstract

The delay time model is a practical way to model random occurrences of failures and the effect of inspection and maintenance actions on the reliability of a repairable system. The delay time model involves two random variables describing the time of initiation of defects and time to failure after the defect initiation. This article presents a clear and structured approach to the evaluation of maintenance cost using the theory of stochastic renewal processes. This article derives the mean, variance, skewness and kurtosis of the maintenance cost in a finite time horizon. Furthermore, the probability distribution of cost is accurately estimated using the Hermite polynomial model. Using the cost distribution, the value at risk is estimated and proposed as a measure to optimize the maintenance program.

Suggested Citation

  • Mahesh D Pandey & Tianjin Cheng & JAM Van der Weide, 2016. "Higher moments and probability distribution of maintenance cost in the delay time model," Journal of Risk and Reliability, , vol. 230(4), pages 354-363, August.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:4:p:354-363
    DOI: 10.1177/1748006X16641767
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    References listed on IDEAS

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    1. Wang, Wenbin, 2012. "An overview of the recent advances in delay-time-based maintenance modelling," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 165-178.
    2. Cheng, Tianjin & Pandey, Mahesh D. & van der Weide, J.A.M., 2012. "The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 65-76.
    3. A H Christer, 1999. "Developments in delay time analysis for modelling plant maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(11), pages 1120-1137, November.
    4. Aven, Terje & Castro, I.T., 2009. "A delay-time model with safety constraint," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 261-267.
    5. Massimiliano Giorgio & Maurizio Guida & Gianpaolo Pulcini, 2015. "A condition‐based maintenance policy for deteriorating units. An application to the cylinder liners of marine engine," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(3), pages 339-348, May.
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