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

Journal article (2016)

Authors

J.A.M. van der Weide Applied Probability -

Research Group

Applied Probability () (TU Delft)

Probability distribution Maintenance cost Delay time model Finite time cost analysis Hermite moment model Renewal integral equation Stochastic renewal process

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Published Date

2016

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.