Probability distribution of maintenance cost of a repairable system modeled as an alternating renewal process

This paper presents the derivation of the probability distribution of maintenance cost of a repairable system that is modeled as a stochastic alternating renewal process. The key idea of the paper is to formulate a renewal equation for computing the characteristic function of the maintenance cost incurred in a fixed time interval. Then, the inverse Fourier transform of the characteristic function leads to the complete probability distribution of cost. This approach also enables the derivation of probability distributions of the down time and the number of failures in a given time period. The distribution of the cost can be used to evaluate the Value-at-Risk (VaR) and other measures needed for the financial planning of a maintenance program.