DANGER OF EXCLUSIVE RELIANCE ON ERGODIC ANALYSIS FOR A CLASS OF PREVENTIVE MAINTENANCE POLICIES

概要

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In the literature, the study of preventive maintenance policies has been largely focused on ergodic analysis where the expected economic performance measure per unit time would be optimized in a long run. When the planning horizon τ is not large, however, the optimal preventive maintenance policy in [0,τ] 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 the dynamic analysis of the semi-Markov model, the asymptotic expansion of the expected reward in [0,τ] is obtained explicitly in an affine form. The optimal preventive maintenance policies in [0,τ] are then compared with the ergodic counterparts, thereby demonstrating danger of exclusive reliance on ergodic analysis when τ is not sufficiently large.