Optimal multi-level condition-based maintenance policy for multi-unit systems under economic dependence

The study aims to work on multi -level condition-based maintenance (CBM) policy for multi-unit systems under economic dependence. Failure modes of units are classified as hard failure or soft failure and taken into account in this paper. Unlike previous works which only considered setup cost dependence with a single failure mode, two types of economic dependence are considered, which are setup cost-saving, and additional cost and time that can be saved when identical maintenance tasks and expertise are needed. In this study, hard failure provides an opportunity for additional inspection and repair of soft-type units, and soft failure creates an opportunity for replacement of the hard-type unit as its age exceeds opportunistic threshold. They both undergo preventive maintenance (PM) when the level/age exceeds preventive threshold at inspection epochs. The objective of this study is to determine the optimal opportunistic control limit and preventive control limit for each unit such that the system's average long-run maintenance cost per unit time is minimized. The optimization problem is formulated in a semi-Markov decision process (SMDP) framework. The explicit formula for the mean residual life is derived for the proposed model which enables the estimation of the remaining useful life and allows maintenance engineers to plan maintenance early based on the observed information. Finally, the method is illustrated by an industrial case study of a feed system of a machine tool. A comparison with other methods is given, which illustrates the effectiveness of our approach.