Regime-Dependent Value of CVaR in Preventive Maintenance Scheduling under RUL Uncertainty

Abstract

We study preventive-maintenance scheduling for a small fleet when several assets compete for a limited number of maintenance slots and their remaining useful lives (RULs) are uncertain. The planning horizon is divided into discrete periods; each asset may be maintained at most once, and at most $K$ assets may be maintained in any one period. Future usage and RUL errors are represented by scenarios. We compare a risk-neutral policy that minimizes expected cost with a risk-aware policy that minimizes expected cost plus conditional value-at-risk (CVaR), where $\operatorname{CVaR}_{0.90}$ is the mean cost among the worst 10\% of scenarios. Both policies are solved exactly by enumerating all capacity-feasible schedules. A $3\times5$ experiment combines capacities $K=1,2,3$ with five increasing levels of RUL uncertainty, with ten paired replications for each combination. The risk-aware policy provides its largest benefit when RUL uncertainty is low-to-moderate and more than one maintenance action can be executed per period. In the best observed case, it reduces CVaR by 13.4\% with an expected-cost increase of only 0.2 relative cost units. At high uncertainty, the benefit becomes negligible and the two policies can select identical schedules. The results show that risk-aware scheduling creates operational value only when prognostic information is sufficiently informative and the maintenance system has enough flexibility to act on it.