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This paper models the deterioration process of a multi-component system. Each deterioration process is modelled by the Wiener process. The purposes of this paper are to address these issues and consider the cost process based on the multi-component system.

Condition-based Maintenance is a method for reducing the probability of system failures as well as the operating cost. Nowadays, a system is composed of multiple components. If the deteriorating process of each component can be monitored and then modelled by a stochastic process, the deteriorating process of the system is a stochastic process. The cost of repairing failures of the components in the system forms a stochastic process as well and is known as a cost process.

When a linear combination of the processes, which can be the deterioration processes and the cost processes, exceeds a pre-specified threshold, a replacement policy will be carried out to preventively maintain the system.

Under this setting, this paper investigates maintenance policies based on the deterioration process and the cost process. Numerical examples are given to illustrate the optimisation process.