Optimal imperfect maintenance cost analysis of a two-component system with failure interactions

This paper considers a two-component system with failure interactions. Component 1 is repairable and component 2 is non repairable and is subject to an increasing degradation. One considers two different shock models. In model 1, component 1 failure causes random gradual damages to component 2 and increases its degradation level. In model 2, component 1 failure may cause the failure of component 2 with a given probability while the failure of component 2 is catastrophic and induces the failure of the whole system. For each model, three maintenance policies are proposed. In each policy, component 1 undergoes imperfect corrective maintenance actions and component 2 is perfectly repaired. An explicit expression of the long run average maintenance cost is developed and the existence of the optimal policy is discussed. Numerical examples are given to illustrate the effectiveness of the proposed models.