Abstract In this paper we consider systems made of components with time-dependent failure rates. A proper analysis of the time-dependent failure behaviour is very important for considerations of life-extension of safety critical systems such as nuclear power plants. This problem is tackled by Monte Carlo simulation which does not suffer from the additional complexity introduced by the model parameters' time inhomogeneity. The high reliability of the systems typically encountered in practice entails resorting to biasing techniques for favouring the events of interest. In this work, we investigate the possibility of biasing the system failures to be distributed in time according to exponential laws. The drawbacks encountered in such procedure have driven us towards the adoption of biasing schemes relying on uniform distributions which distribute failures over the system life more evenly.