Development and optimization of PIR and QIR strategies of maintenance using Monte Carlo method

Abstract

The optimization of condition-based maintenance (CBM) strategies is conventionally formulated as the minimization of the long-run expected maintenance cost rate. While this criterion provides a rigorous and economically meaningful measure of asymptotic performance, it does not explicitly account for the variability of maintenance costs across renewal cycles. As a result, its applicability may be limited in industrial environments where budgetary stability, operational reliability, and risk mitigation are critical considerations. This study proposes a robustness-aware optimization framework for two representative CBM policies: Periodic Inspection and Replacement (PIR) and Quantile-Based Inspection and Replacement (QIR). The principal contribution lies in the formulation of a unified decision criterion that jointly incorporates the long-run expected maintenance cost rate and the dispersion of maintenance costs at the renewal-cycle level. This criterion enables a systematic and coherent comparison of maintenance strategies that extends beyond traditional average-cost-based evaluations. System degradation is modeled as a homogeneous Gamma process, a widely adopted stochastic model that combines analytical tractability with strong empirical relevance. Closed-form analytical expressions are derived for the PIR strategy, whereas a fully specified Monte Carlo–based estimation framework is developed for the QIR strategy to accommodate its state-dependent and non-periodic inspection structure. A comprehensive sensitivity analysis is performed with respect to the inspection cost, the downtime cost rate, and the robustness-weight parameter, providing a structured comparative assessment over a broad spectrum of economic conditions. The results reveal an intrinsic trade-off between economic efficiency and cost stability. They further demonstrate that the QIR strategy generally achieves a superior compromise between performance and robustness under moderate cost conditions, whereas the PIR strategy remains advantageous in operational settings characterized by elevated inspection costs or fixed scheduling constraints.