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

Mahesh D. Pandey, Tianjin Cheng, J.A.M. Van Der Weide

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)354-363
Number of pages10
JournalProceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
Issue number4
Publication statusPublished - 2016


  • Delay time model
  • finite time cost analysis
  • Hermite moment model
  • maintenance cost
  • probability distribution
  • renewal integral equation
  • stochastic renewal process

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