A Hybrid Maintenance Policy for a Deteriorating Unit in the Presence of Random Effect and Measurement Error

In this paper, a hybrid condition/age-based maintenance policy is proposed for a deteriorating unit whose observed degradation path is affected by three forms of variability: time variability, unit to unit variability, and measurement error. The perturbed degradation process is modelled by using a gamma-based model with random effect. The unit is assumed to fail when its (hidden) degradation level exceeds a (fixed) given threshold. Failure is assumed to be not self-announcing. So, it is also assumed that a perturbed measurement does not allow to say with certainty whether a unit is failed or not. The maintenance policy is defined by considering two different scenarios. In the first one, we assume that an optimal age-based replacement time and a single intermediate inspection time are initially planned and that based on the outcome of the inspection it is possible either to immediately replace the units or to postpone its replacement to a given (a priori defined) successive time. After each replacement, the unit is considered as good as new. However, being unable to detect failures, we assume that replacements can occur either at inspection or at the a priori planned replacement time only. The second scenario extends the first one by assuming that a more expensive, not perturbed measurement can be optionally performed at inspection. Finally, results obtained under the considered scenarios are analysed and compared in terms of long-run average cost rate, to evaluate whether (assumed that the option exists) it is convenient to perform the more costly inspection.