A transport framework for zero-variance Monte Carlo estimation of Markovian unreliability

Monte Carlo simulation has become an important tool for the estimation of reliability characteristics. However it may lead to unacceptable computation times. Variance reduction techniques have to be worked out. We show in this paper how to write the equations of Markovian reliability as a transport problem, and how the well-known-zero-variance scheme can be adapted to this application. But such a method is always specific to the estimation of one quantity, while a Monte Carlo simulation allows to perform simultaneously estimations of diverse quantities. We propound a method to reduce simultaneously the variance for several quantities, by using probability laws that would lead to zero-variance in the estimation of a mean of these quantities. Just like the zero-variance one, the method we propound is impossible to perform exactly. However we show that the use of simple approximations of it may be very efficient.