Optimizing Reliability through Infrequent Periodic Repairs in First-Order Degradation Systems

Abstract

Degradation systems deteriorate over time due to physical, chemical, or environmental factors, leading to progressive loss in performance and increased likelihood of system failure. These systems are commonly found in industries such as manufacturing, transportation, energy, and infrastructure, where reliability and uptime are critical to safety and economic efficiency. In practical applications, degradation often follows predictable patterns, and one of the most widely used models to describe this behavior is the first-order degradation process, where the degradation rate is linear over time in the absence of intervention. Traditionally, maintenance strategies have relied on frequent inspections or scheduled repairs to restore system performance. However, such approaches can be cost-intensive, labor-demanding, and operationally disruptive.

In this study, we propose an optimization model that incorporates infrequent periodic repairs to manage system degradation while balancing two competing objectives: maximizing system reliability and minimizing maintenance costs. Rather than assuming continuous monitoring or frequent servicing, our model explores the feasibility of maintaining system integrity with fewer but strategically timed interventions. The model integrates a mathematical representation of degradation progression and a stochastic reliability function that accounts for uncertainty in the degradation process.

By introducing a repair factor to simulate partial restoration at fixed intervals, we analyze how system reliability evolves across multiple repair cycles. The model evaluates the impact of various repair intervals on the probability of failure and provides a quantitative basis for selecting optimal maintenance schedules. Furthermore, we incorporate cost considerations by comparing the trade-off between repair frequency and the associated risk of failure. The approach is particularly suitable for systems where full restorations are not feasible or where minor, cost-effective maintenance actions are preferred.

Through analytical derivation and numerical simulations, we demonstrate that carefully chosen, infrequent repairs can significantly prolong system life without compromising critical reliability thresholds. The results confirm that there exists an optimal repair interval where the benefit of reduced risk outweighs the cost of repair, thus offering a pragmatic solution for asset managers and engineers. This research contributes to the growing field of predictive and preventive maintenance by offering a simplified yet effective tool for reliability-centered decision-making in resource-constrained environments