A Dempster-Shafer Theory-Based Approach to Compute the Birnbaum Importance Measure under Epistemic Uncertainty

Importance Measures (IMs) aim at quantifying the contribution of components to the system performance. In Process Risk Assessment (PRA), they are commonly used by risk managers to derive information about the risk/safety significance of events. However, IMs are typically calculated without taking into account the uncertainty that inevitably occurs whenever the input reliability data are poor. In literature, uncertainty arising from the lack of knowledge on the system/process parameters is defined as epistemic or subjective uncertainty. The present work aims at investigating on its influence on the Birnbaum IM and on how such an uncertainty could be accounted for in the components ranking. In particular, input reliability data are supposed to be elicited from experts in an interval form, and the Dempster-Shafer Theory (DST) of evidence is suggested as a proper mathematical framework to deal with such imprecise data. In the main part of the existing literature, IMs are supplied as crisp values. Instead, in the present paper, the Birnbaum IM is obtained in an interval form as it naturally arises from the use of DST. Then, a new approach based on plausibility curves is suggested to rank the system components. Finally, an application to a real industrial system is discussed.