Mean Time to Achieve a Failure-Free Requirement

A common reliability test procedure is to test until a given, consecutive, failure-free time has passed. This paper gives expressions for the mean time to test completion, for both elapsed and operating time, for general probability distributions. The situations in which the test is monitored periodically and the repair time is not zero are considered. The standard deviation of completion time is also discussed. The special case in which the time-to-failure distribution is exponential is treated in some detail.