Optimal Maintenance Policy for a Compound Poisson Shock Model

TL;DR

This paper develops an optimal maintenance policy for systems deteriorating due to random shocks, using a compound Poisson process and impulse control, to enhance system availability through monitored interventions.

Contribution

It introduces a novel model combining compound Poisson deterioration with impulse control for optimal maintenance planning.

Findings

Optimal intervention timing and size are derived based on system state.

The model effectively balances intervention costs and system reliability.

Permanent monitoring improves maintenance decision accuracy.

Abstract

Engineered and infrastructure systems deteriorate (e.g., loss capacity) as a result of adverse environmental or external conditions. Modeling deterioration is essential to define optimum design strategies and inspection and maintenance (intervention) programs. In particular, the main purpose of maintenance is to increase the system availability by extending the life of the system. Most strategies for maintenance optimization focus on defining long term strategies based on the system's condition at the decision time (e.g., $t=0$). However, due to the large uncertainty in the system's performance through life, an optimal maintenance policy requires both permanent monitoring and a cost-efficient plan of interventions. This paper presents a model to define an optimal maintenance policy of systems that deteriorate as a result of shocks. Deterioration caused by shocks is modeled as a compound Poisson process and the optimal maintenance strategy is based on an impulse control model. In the model the optimal time and size of interventions are executed according the the system state, which is obtained from permanent monitoring.