Importance analysis considering time-varying parameters and different perturbation occurrence times

Importance measures are integral parts of risk assessment for risk-informed decision making. Because the parameters of a risk model, such as the component failure rates, are functions of time and a perturbation (change) in their values can occur during the mission time, time dependence must be considered in the evaluation of the importance measures. In this paper, it is shown that the change in system performance at time t, and consequently the importance of the parameters at time t, depends on the parameters perturbation time and their value functions during the system mission time. We consider a nonhomogeneous continuous time Markov model of a series-parallel system to propose the mathematical proofs and simulations, while the ideas are also shown to be consistent with general models having nonexponential failure rates. Two new measures of importance and a simulation scheme for their computation are introduced to account for the effect of perturbation time and time-varying parameters.