Differential Importance Measures estimation through MonteCarlo and Importance sampling techniques

: We propose a general procedure to be applied for the estimation of the First and Total order Differential Importance Measures when the evaluation of the reliability / availability performances of the system requires the application of MonteCarlo techniques. By means of the application of Importance sampling techniques, all the output variables (system Unavailability for different values of the input variables) are computed contemporaneously, on the basis of the same sequence of the involved components, events type (failure / repair) and transition times for each trial. The failure/repair probabilities are forced to be the same for all components; the transition times are sampled from the unbiased probability distributions or by forcing the oc-currence of at least a failure within the (residual) system “mission time”. Different counters are incremented by different weights, according to the introduced biases. Without loss of generality, a networked system is considered as case study