The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation ÊSS of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, ÊSS, has become an essential p...

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 importance of predictors is characterized by the extent to which their use reduces uncertainty about predicting the response variable, namely their information importance. The uncertainty associated with a probability distribution is a concave function of the density such that its global maximum is a uniform distribution reflecting the most difficult prediction situation. Shannon entropy is...

In this paper new measures of joint importance two and three components for repairable multistate systems based on the classical Birnbaum measure, are proposed. By considering system, first relevancy conditions given. Then probabilities each measured. The proposed method is applied a data set. An illustrative example As in generic since they depend probabilistic properties system structure. The...