Analytical vs. Monte Carlo Methods of Calculating Reliability

Differential equations are derived to obtain analytically the reliability and mean life of a simple system with redundancy and replacement. They are solved for a simple case. The reliability and mean life of the system in more complex cases is obtained using a Monte-Carlo method. An excellent agreement between the two methods is obtained in the simple case. Increases by a factor of five in system mean life over the mean life of a single machine are obtainable using a simple replacement policy.