Lower Confidence Limits and a Test of Hypotheses for System Availability

Any estimate of system availability calculated from time-to-failure and time-to-repair test data will be subject to some degree of uncertainty due to the uncertainty associated with the sample estimates of MTTF and MTTR. Although decisions about the true availability of the system should take this uncertainty into account, a point estimate of availability is usually the only statistic calculated. This paper derives techniques for placing a lower confidence limit on system availability and for deciding if the true system availability differs significantly from a specified value when MTTF and MTTR are estimated from test data. These techniques could be used to analyze existing test data or to design a test program for demonstrating system availability and/or detecting significant deviations from specified values of system availability. To facilitate utilization of these techniques, curves of the lower 0.90 and 0.95 confidence limits and power curves for the test of hypotheses at the 0.05 and 0.10 levels of significance are presented. Examples illustrating the use of the curves are given.