Optimal Age-Replacement in Anticipation of Time-Dependent, Unpunctual Policy Implementation

In many maintenance settings, it is assumed that the preventive maintenance policy prescribed by the maintenance planner is implemented without error. However, in practice, the party who implements the policy often deviates from the intended maintenance times. We study an age-replacement setting in which the maintenance worker may be unpunctual. That is, the actual preventive replacement times may deviate from the prescribed replacement times in a probabilistic manner. Previous work on this problem assumes that the degree of unpunctuality is not influenced by the length of time between scheduled replacements. We relax this assumption and let the degree of deviation depend on the prescribed replacement time. In this article, we formulate a long-run cost-rate minimization model and present analytical and numerical results that compare its optimal solution and performance to those when the unpunctual behavior is assumed to be either absent or independent of the prescribed replacement time. We also provide insights that can help maintenance planners adjust their policies in anticipation of nonstationary, unpunctual implementation.