On the Computation of Contextual Distributionally Robust Preventive Maintenance Intervals

Heraldo Rozas, Nagi Gebraeel, Weijun Xie

Abstract: The optimization of preventive maintenance (PM) intervals traditionally follows predict-then-optimize (PTO) frameworks. These involve two sequential steps: training a statistical model to estimate the failure time distribution (FTD) and then integrating it into an optimization model for deciding the optimal PM interval. However, PTO models may have poor out-of-sample performance if the fitted FTD differs significantly from the true distribution or fails to capture covariate effects. To overcome these issues, this paper introduces a contextual distributionally robust optimization (DRO) model for computing PM intervals. The proposed model integrates empirical failure time data directly into the optimization framework without assuming specific distributions. Our setting assumes that the component FTD is affected by covariates. Therefore, our formulation seeks to exploit covariate knowledge to compute efficient PM decisions conditional on the observed covariates. We formulate a DRO model that accounts for potential misspecifications of the empirical FTD. This DRO formulation aims to minimize the long-term maintenance cost rate by optimizing PM decision policies over an infinite space, where these policies map covariate information to optimal PM intervals. We demonstrate that the proposed DRO model admits tractable mixed-integer linear programming reformulations in various practical cases. The efficacy of our model is demonstrated through computational studies involving simulated and real-world failure time data.

External IDs:doi:10.1109/tr.2025.3603869