Optimal Maintenance Strategy of a System Which Deteriorates in Accordance With a Gamma Process Over a Bounded Time Horizon

Abstract

This article discusses the mean and variance of discounted total maintenance cost of a system intended to operate during the finite time interval [0, t]. We implement the age replacement strategy under the assumption that the system deteriorates in accordance with a stochastic gamma process. Laplace transforms for the mean and second moment of the total maintenance cost are obtained. We apply the result to obtain an optimal period for preventive maintenance which minimizes the mean of the discounted total maintenance cost in the time interval [0, t]. Standard deviation for the optimal period for preventive maintenance is also calculated.

Keywords: Age replacement strategy; Gamma process; Discount factor; Renewal process; Laplace transform.

2010 Mathematics Subject Classification. 90B25; 60K10