Adaptive Maintenance Policy for Gamma Degrading Units with Bathtub-Shaped Degradation Rate Function in the Presence of Random Effect

The main goal of this paper is to investigate, in the field of maintenance optimization, the performances of a new gamma process with random effect and bathtub-shaped degradation rate function. Maintenance costs are determined by applying an adaptive hybrid age-/condition-based policy recently proposed in the literature, which consists in measuring the degradation level of the unit at a first (age-based) inspection time and using a condition-based rule to decide whether to immediately replace the unit or to postpone its replacement to a future time. The policy is denominated adaptive, since the future replacement time is decided, unit by unit, based on the outcome of the inspection. The optimal maintenance policy is defined by minimizing the long-run average maintenance cost rate. After each replacement the unit is considered as good as new. The lifetime of the unit is defined by using a failure threshold model. Maintenance costs are computed by accounting for preventive replacement cost, corrective replacement cost, inspection cost, logistic cost, and downtime cost (which depends on the time spent in a failed state). An example of application demonstrates the affordability of the approach. A study is also performed, by using simulated data generated under the model with bathtub-shaped degradation rate function, to investigate the effect on maintenance costs of fitting the data by using a gamma process with random effect where the age function has a classical power law shape.