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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. 346 Michael Khazen and Arie Dubi

A Note on Variance Reduction Methods in Monte Carlo Applications to Systems Engineering and Reliability.