  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.
