Maintenance importance measures incorporating tripartite component dependence

Importance measures are very useful for reliability enhancement of engineered systems at both design and maintenance phases, and they have therefore been extensively studied. The existing importance measures are largely introduced from the perspective of system structure, reliability, and maintenance related costs. It is known that three types of component dependence: stochastic, economic, and structural, exist in many engineering scenarios and must be taken into account in optimising maintenance policies. Neglecting this tripartite dependence may result in erroneous evaluations of the benefit, time, and cost associated with a maintenance policy, thereby causing negative consequences. Nevertheless, to the best of our knowledge, all the three types of dependence measures are not considered jointly in the existing importance measures. To fill this research gap, a novel importance measure accounting for all the three types of dependence is proposed in this paper and further extend it to a joint importance measure of two components to quantify their interaction due to tripartite component dependence. Some interesting properties regarding the proposed importance measures, such as the relationship between both importance measures, the influence of the neglect of stochastic dependence, the monotonicity of the proposed measures, and the value range of the joint importance measure, are proved. Illustrative examples, including a numerical case and a landing gear system, illustrate the proposed importance measures and show that the proposed measures can effectively quantify the effectiveness of maintenance policies when the maintenance on a multi-component system is affected by the tripartite component dependence.