A Monte Carlo Estimator Based on a State Space Decomposition Methodology for Flow Network Reliability

A Monte Carlo simulation of the flow network reliability using importance and stratified sampling

“…If these reliabilities are evaluated by estimators that belong to the variance réduction family, we will obtain more accurate estimator than f (7). As a conséquence, we propose to replace the standard estirnator by the recursive importance sampling one presented in [4,5]. This estimator is briefly recalled in the next subsection.…”

“…In [4,5], we proposed an efficient variance réduction method. It transforms the sampling in a given rectangular set R Ç ft of state vectors into the sampling is one subset among the undetermined subsets resulting from the DJD procedure when it is called to partition the rectangle R, This subset subsequently undergoes a similar step until the transformation is called on a …”

“…Moreover, the K samples are distributed on strata of U. Unfortunateïy, the trials within each stratum is accomplished by the standard sampling technique. The aim of our work is to show that if we estimate the contribution of each stratum by the importance sampling method proposed in [5], we induce additional accuracy in the évaluation of the measure of interest.…”