# Condition-based Maintenance for Multi-component Systems:Modeling, Structural Properties, and Algorithms

## TL;DR

This paper addresses the complex problem of condition-based maintenance for multi-component systems by developing a stochastic model, analyzing its properties, and proposing efficient algorithms to optimize maintenance costs.

## Contribution

It introduces a multi-stage stochastic integer model for multi-component CBM and designs two algorithms, including an optimal and a heuristic, for solving the model.

## Key findings

- Algorithm 1 finds optimal solutions efficiently.
- Algorithm 2 provides high-quality solutions quickly.
- The rolling horizon approach effectively manages multi-stage problems.

## Abstract

Condition-based maintenance (CBM) is an effective maintenance strategy to improve system performance while lowering operating and maintenance costs. Real-world systems typically consist of a large number of components with various interactions between components. However, existing studies on CBM focus on single-component systems. Multi-component condition-based maintenance, which joins the components' stochastic degradation processes and the combinatorial maintenance grouping problem, remains an open issue in the literature. In this paper, we study the CBM optimization problem for multi-component systems. We first develop a multi-stage stochastic integer model with the objective of minimizing the total maintenance cost over a finite planning horizon. We then investigate the structural properties of a two-stage model. Based on the structural properties, two efficient algorithms are designed to solve the two-stage model. Algorithm 1 solves the problem to its optimality and Algorithm 2 heuristically searches for high-quality solutions based on Algorithm 1. Our computational studies show that Algorithm 1 obtains optimal solutions in a reasonable amount of time and Algorithm 2 can find high-quality solutions quickly. The multi-stage problem is solved using a rolling horizon approach based on the algorithms for the two-stage problem.