Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system

TL;DR

This paper compares two imperfect maintenance models for a gamma deteriorating system, analyzing their stochastic properties and optimal maintenance strategies, with a focus on how repairs impact system degradation and virtual age.

Contribution

It introduces a stochastic comparison framework for two repair models and explores optimal maintenance strategies for each, enhancing understanding of maintenance effects on gamma deteriorating systems.

Findings

Stochastic comparison results between the two repair models.

Conditions where the models yield identical expected deterioration.

Development of optimal maintenance strategies for each model.

Abstract

This paper compares two imperfect repair models for a degrading system, with deterioration level modeled by a non homogeneous gamma process. Both models consider instantaneous and periodic repairs. The first model assumes that a repair reduces the degradation of the system accumulated from the last maintenance action. The second model considers a virtual age model and assumes that a repair reduces the age accumulated by the system since the last maintenance action. Stochastic comparison results between the two resulting processes are obtained. Furthermore, a specific case is analyzed, where the two repair models provide identical expected deterioration levels at maintenance times. Finally, two optimal maintenance strategies are explored, considering the two models of repair.