Accounting for components interactions in the differential importance measure

A limitation of the importance measures (IMs) currently used in reliability and risk analyses is that they rank only individual components or basic events whereas they are not directly applicable to combinations or groups of components or basic events. To partially overcome this limitation, recently, the differential importance measure (DIM), has been introduced for use in risk-informed decision making. The DIM is a first-order sensitivity measure that ranks the parameters of the risk model according to the fraction of total change in the risk that is due to a small change in the parameters’ values, taken one at a time. However, it does not account for the effects of interactions among components. In this paper, a second-order extension of the DIM, named DIMII, is proposed for accounting of the interactions of pairs of components when evaluating the change in system performance due to changes of the reliability parameters of the components. A numerical application is presented in which the informative contents of DIM and DIMII are compared. The results confirm that in certain cases when second-order interactions among components are accounted for, the importance ranking of the components may differ from that produced by a first-order sensitivity measure.