APPROXIMATE ZERO-VARIANCE MONTE-CARLO ESTIMATION OF MARKOVIAN UNRELIABILITY

Monte Carlo simulation has become an important tool for the estimation of reliability characteristics, since conventional numerical methods are no more efficient when the size of the system to solve increases. However, evaluating by a simulation the probability of occurrence of v ery rare events means playing a very large number of histories of the system, which leads to unacceptable computation times. Acceleration an d variance reduction techniques have to be worked out. We show in this paper how to write the equations of Markovian reliability as a transp ort problem, and how the well known zero-variance scheme can be adapte d to this application. But such a method is always specific to the est imation of one quantity, while a Monte Carlo simulation allows to perf orm simultaneously estimations of diverse quantities. Therefore, the e stimation of one of them could be made more accurate while degrading a t the same time the variance of other estimations. We propound here a method to reduce simultaneously the variance for several quantities, b y using probability laws that would lead to zero-variance in the estim ation of a mean of these quantities. Just like the zero-variance one, the method we propound is impossible to perform exactly. However we sh ow that simple approximations of it may be very efficient. (C) 1998 Pu blished by Elsevier Science Ltd.