From differential to difference importance measures for Markov reliability models

This paper presents the development of the differential importance measures (DIM), proposed recently for the use in risk-informed decision-making, in the context of Markov reliability models. The proposed DIM are essentially based on directional derivatives. They can be used to quantify the relative contribution of a component (or a group of components, a state or a group of states) of the system on the total variation of system performance provoked by the changes in system parameters values. The estimation of DIM at steady state using only a single sample path of a Markov process is also investigated. A numerical example of a dynamic system is finally introduced to illustrate the use of DIM, as well as the advantages of proposed evaluation approaches.