Monte Carlo analysis of the time behavior of complex modern systems is rapidly becoming a commonplace tool in the design and life cycle control. This is due to the inherent complexity of such systems both in terms of their multiple dimensions and interactive stochastic behavior. Predictions of system characteristics such as reliability, availability, spare parts requirements, maintenance scheduling etc. are essential at the earliest stages of design in order to achieve optimal system performance at the lowest possible cost. The applications of Monte Carlo methods to this field are the only effective approach. Within this area the estimation of rare events (with significant consequences) is a most difficult problem. Variance Reduction Methods (VRM) are, therefore, important.Although a vast amount of effort has been invested in the development of variance reduction methods in the transport of neutral particles and a large variety of such methods exist, their transfer into the area of systems engineering is not at all trivial. This, mainly, due to the profound differences in the phase space and the addition of the "aging" phenomena in the case of systems transport.In this work a number of variance reduction methods is considered. The method of forced events is applied to the time crossing estimator and to the event type estimator. The latter case is shown to yield a method parallel to the leakage estimation method. Also, geometrical splitting is considered. The questions of splitting surface and 'distance to detector', which are essential for this method, are discussed and an approach that accounts for these elements is suggested. In each case it is shown that the VRM method is unbiased and numerical examples are presented to demonstrate the efficiency of each method.
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.
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