The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution

The stochastic gamma process has been widely used to model uncertain degradation in engineering systems and structures. The optimization of the condition-based maintenance (CBM) policy is typically based on the minimization of the asymptotic cost rate. In the financial planning of a maintenance program, however, a more accurate prediction interval for the cost is needed for prudent decision making. The prediction interval cannot be estimated unless the probability distribution of cost is known. In this context, the asymptotic cost rate has a limited utility.This paper presents the derivation of the probability distribution of maintenance cost, when the system degradation is modelled as a stochastic gamma process. A renewal equation is formulated to derive the characteristic function, then the discrete Fourier transform of the characteristic function leads to the complete probability distribution of cost in a finite time setting. The proposed approach is useful for a precise estimation of prediction limits and optimization of the maintenance cost.

► An efficient method to derive the probability distribution of maintenance cost is presented.
► The characteristic function of maintenance cost is calculated using the renewal equation.
► Optimization of the condition based maintenance policy is presented.
► Probability distribution of cost and the value-at-risk are evaluated.
► The advantage of distribution of cost over the expected value in decision making is highlighted.