Comprehensive evaluation of gamma process-based maintenance strategies through Monte Carlo simulation and cost-risk modeling

This study develops a comprehensive reliability-centered maintenance framework that integrates stochastic degradation modeling with cost-risk optimization. The degradation trajectory of engineering systems is represented using a gamma process, which aptly characterizes the cumulative and monotonic nature of physical wear over time. Within this context, three maintenance policies: Block Replacement (BR), Periodic Inspection and Replacement (PIR), and Quantile-Based Inspection and Replacement (QIR), are rigorously evaluated. Each strategy is assessed through a unified cost-risk objective function that jointly minimizes the long-run expected cost and its statistical dispersion, thereby capturing both economic efficiency and operational consistency. Given the analytical intractability of closed-form solutions, particularly for PIR and QIR strategies due to the path-dependent and nonlinear structure of their governing equations, Monte Carlo simulation is employed as the primary computational tool. This enables the estimation of critical performance indicators (including expected cost per renewal cycle, cost variance, and downtime) with high precision. The results demonstrate the superior adaptability of the QIR strategy in managing uncertainty and degradation variability across a broad spectrum of operational scenarios. Moreover, extensive sensitivity analyses underscore the responsiveness of maintenance performance to key system parameters, including inspection intervals, cost structures, and threshold settings. The proposed framework significantly advances current methodologies by offering a scalable and data-driven tool for decision support in maintenance planning. It facilitates the design of maintenance policies that are economically optimal, probabilistically robust, and operationally feasible, thereby enhancing the resilience, reliability, and lifecycle value of engineered systems. The proposed framework is particularly suited for reliability-critical engineering systems exhibiting cumulative and monotonic degradation, such as mechanical components subject to wear and fatigue (e.g., bearings and gears), structural systems experiencing corrosion or crack propagation, energy storage systems undergoing capacity fade, and industrial infrastructure exposed to progressive material deterioration.