Abstract A method was developed for the reliability analysis of systems of components whose failure rates may be time-dependent. A special case of such systems is the one whose components are under aging. The hypothesis of minimum repair is adequate in many cases, especially in heavy industries, such as the nuclear industry. The method employs the technique of supplementary variables to cast the modeled Nonmarkovian systems into Markovian ones. Use is made of the Laplace transform technique, in order to reduce the number of equations, which are then solved by numerical methods. The inverse Laplace transforms to obtain the final solution of the set of differential equations is also done by using the Gauss–Legendre quadrature method which is very fast. Applications to safety systems, like the auxiliary feedwater system of a typical PWR plant show that the method is very fast and accurate as compared to other simulation methods.