Simple Test of Hypotheses on System Availability and Mean Time to Repair

A method is developed for testing hypotheses on system availability and mean time to repair, under the assumption that the failure times and repair times are, respectively, independent exponential and gamma random variables. System is assumed to be in a steady state; availability is defined in usual manner as the ratio of mean time to failure to the sum of mean time to failure and mean time to repair. Testing hypotheses on system availability is achieved by simple application of the F distribution, provided: a) the system mean time to repair is known or determinable from other assumptions, or b) the ratio of system mean time to failure to the gamma scale parameter is known. Similarly, hypotheses on system mean repair time can be tested using the chi-square distribution, if the gamma scale parameter is known.