Computation of Mean Time to Failure for a System with Simple Redundancy

A system consisting of several independent components in series can be made more reliable by adding an "identical" component in parallel to some of the components. Two mathematical series are presented for computing the mean time to failure for the system when the failure times of the components are exponentially distributed. For large systems the evaluation of these series is not computationally feasible, but one of the series yields an accurate approximation if the series is truncated, and also yields an explicit solution if all components have identical failure rates. The explicit solution is then used to check the accuracy of solutions obtained using numerical integration. The method of numerical integration is highly accurate.