Theory of maintained systems: Distribution of time to first system failure

The distribution of time to first system failure is considered for systems whose repairable components are separately maintained. It is shown that if repairable components have exponentiai failure distributions, repair distributions have decreasing failure rate, and non-repairable components have increasing failure rate, then the distribution of time to first system failure is new better than used. This result is used to provide useful bounds on the system failure distribution. Improved bounds are given for the exponential repair case.