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 measures 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 measures 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 measures, as well as the advantages of proposed evaluation approaches.