Deterioration state space partitioning method for opportunistic maintenance modelling of identical multi-unit systems

Abstract

We propose a deterioration state space partitioning method for opportunistic maintenance modelling of identical multi-unit systems with economic dependence. The proposed method presents a common description and model for multi-unit systems with identical units based on the mutual characteristics of opportunistic maintenance models with different maintenance strategies. In the method, all possible maintenance combinations of general multi-unit systems with a known number of identical units at each maintenance decision point and their corresponding probabilities are deduced on the basis of analysis of the scenarios of multi-unit systems with one, two and three units. Further, we develop a general representation of the stationary law of unit deterioration and its numerical solution. Numerical experiments verify the correctness of our deterioration state space partitioning method and its numerical solution. The proposed method is applicable to both single-unit and multi-unit systems, and provides a new generalised modelling method for maintenance optimisation of multi-unit systems with identical units.

Keywords:

• multi-unit systems with identical units
• opportunity maintenance
• deterioration state space partition method
• maintenance combination
• maintenance probability
• stationary probability density

Acknowledgments

The authors also gratefully acknowledge the helpful comments and suggestions from the anonymous reviewers which significantly helped to improve an earlier version of this paper.

Additional information

Funding

Funding. The authors would like to thank the support Shanxi Scholarship Council of China [grant number 2013-089], the Key Science and Technology Programme of Shanxi Province [grant number 20130321006-01] and the Natural Science Foundation of Shanxi Normal University [grant number ZR1410].