Optimizing block-based maintenance under random machine usage

Existing studies on maintenance optimization generally assume that machines are either used continuously, or that times until failure do not depend on the actual usage. In practice, however, these assumptions are often not realistic. In this paper, we consider block-based maintenance optimization for a machine that is not used continuously and for which the usage is random. We propose to govern the random machine usage by a Markov switching (on-off), and present a method to determine the optimal maintenance interval. Various problem instances are considered, and the optimal maintenance intervals are compared with two benchmark intervals that result from the limiting cases with a very high and a very low switching frequency. Based on this analysis, we identify under what circumstances it is particularly important to take the properties of the usage pattern into account when scheduling maintenance.