Monte Carlo variance reduction in applications to Systems Reliability using Phase Space Splitting

Abstract

Splitting is a widely known Monte Carlo variance reduction method (VRM). It has been successfully applied for a long time in Monte Carlo applications to neutral particles transport in Nuclear Engineering. In this field splitting is usually referred to as a Geometric Splitting method since it relies on geometric properties of the medium, namely distance and direction. Splitting is remarkable in the sense that it is a "safe" method. Unlike VRMs based on biasing it can not cause the sow tooth phenomenon in which a wrong result appears with very small statistical error. The only risk of using this method is increasing computation time. This makes the application of this method to such areas as safety-critical systems reliability and risk assessment a very attractive option.Suggested work concerns application of splitting to systems reliability problems. The system's structure based metric is used instead of the geometric approach. This metric takes into account importance of each system's component for the target event. Multiple disjunctive surfaces splitting, and splitting combined with the Cluster-Event biasing are considered. The optimal splitting parameters are predicted using the mathematical apparatus developed for applications of splitting in neutral particles transport. Provided numerical examples show considerable benefit of the method.

Some acceleration methods for Monte Carlo simulation of rare events

“…Furthermore, in order to handle the dependencies, an ongoing work consists in adapting the Dissociation method to systems with dependencies. Finally, another perspective is to combine EMCT with multilevel splitting techniques [16].…”

“…Eqs. (15)- (16) Let R be such that Rc is the last instant of renewal before sc (including sc). We denote by l k = (l 1 , .…”