Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment

Importance measures of multi-state systems have been intensively investigated from different perspectives in the past few years as the results are able to provide a valuable guidance for effective reliability improvement and enhancement. The state assignment is oftentimes conducted to identify the state of a multi-state system when features and/or knowledge related to the health condition of the particular system are collected. However, due to the scarcity of sensor data, limited accuracy of sensing techniques, and vague/conflicting judgments from experts, conducting the state assignment is imprecise and inevitably produces epistemic uncertainty. In this paper, some composite importance measures of multi-state systems are extended by considering the epistemic uncertainty associated with component state assignment. To take account of such epistemic uncertainty, the proposed method contains three basic steps: (1) propagate the epistemic uncertainty associated with component state assignment to the reliability function of a multi-state system by dynamic evidential network models, (2) evaluate the intervals of the conditional reliability by inputting hard evidences and/or vacuous evidence into the tailored dynamic evidential network models, and (3) compute the extended composite importance measures by constructing a pair of optimization problems and properly handling the dependency among input intervals. A numerical example of a multi-state bridge system together with an engineering example of a feeding control system of CNC lathes is exemplified to demonstrate the impact of the epistemic uncertainty on the importance measures of components and their rankings.