A Generalized Griffith Importance Measure for Components with Multiple State Transitions

The performance of the system is often influenced by the performance of a particular component. Hence, it is important to identify the state changing of which component dominates the system performance changing in a maintenance process. Motivated by the Griffith importance measure (GIM) model, this paper proposed the generalized GIM, which extends the application of GIM to complex multi-state components, to evaluate the accurate contribution of the components in the changing of the system performance by considering the transition probabilities of the states of each component. Furthermore, the generalized GIM method is successfully applied in the continuous-state systems by extending the system structure function in GIM model. As a result, the expression of the performance of continuous system and the generalized GIM of the continuous-state components are proposed. A numerical example and an application to an oil transportation system are presented to illustrate how the proposed method works.