Piecewise deterministic Markov process for condition-based imperfect maintenance models

TL;DR

This paper models condition-based imperfect maintenance using piecewise deterministic Markov processes, incorporating natural degradation, random shocks, and delayed maintenance decisions to optimize costs.

Contribution

It introduces a PDMP-based framework for modeling complex maintenance scenarios with stochastic shocks and delays, advancing the application of impulse control theory in maintenance optimization.

Findings

Optimal maintenance thresholds identified.

Sensitivity of costs to discount factor analyzed.

Numerical example demonstrates model effectiveness.

Abstract

In this paper, a condition-based imperfect maintenance model based on piecewise deterministic Markov process (PDMP) is constructed. The degradation of the system includes two types: natural degradation and random shocks. The natural degradation is deterministic and can be nonlinear. The damage increment caused by a random shock follows a certain distribution, and its parameters are related to the degradation state. Maintenance methods include corrective maintenance and imperfect maintenance. Imperfect maintenance reduces the degradation degree of the system according to a random proportion. The maintenance action is delayed, and the system will suffer natural degradations and random shocks while waiting for maintenance. At each inspection time, the decision-maker needs to make a choice among planning no maintenance, imperfect maintenance and perfect maintenance, so as to minimize the total discounted cost of the system. The impulse optimal control theory of PDMP is used to determine the optimal maintenance strategy. A numerical study dealing with component coating maintenance problem is presented. Relationship with optimal threshold strategy is discussed. Sensitivity analyses on the influences of discount factor, observation interval and maintenance cost to the discounted cost and optimal actions are presented.