Danger of exclusive reliance on ergodic analysis for a class of preventive maintenance policies

In the literature, the study of preventive maintenance policies has been largely focused on ergodicanalysis where the expected economic performance measure per unit time would be optimized in a long run. When the planning horizon T is not large, however, the optimal preventive maintenance policy in [0, T] could be significantly different from that under ergodicity. In this paper, the classical semi-Markov model of Makabe is first examined thoroughly at ergodicity, yielding many new results. Then, through thedynamic analysis of the semi-Markov model, the asymptotic expansion of the expected reward in [0, T] isobtained explicitly in an affine form. The optimal preventive maintenance policies in [0, T] are then compared with the ergodic counterparts, thereby demonstrating danger of exclusive reliance on ergodic analysis whenT is not sufficiently large.