The Monte Carlo simulation technique, which uses well-developed neutron transport theory, is applied to study the reliability of engineering systems with either Markovian or non-Markovian properties. In order to extend the application of this Monte Carlo simulation technique to the study of the perturbed system behaviour, for example, after design changes have been made to the system, the correlated sampling technique is incorporated with conventional Monte Carlo simulation to achieve this purpose. We conclude that Monte Carlo simulation function becomes an attractive method for reliability studies, especially after the correlated sampling technique has been incorporated.