The frequency distribution of availability

Availability is probably the most informative indicator of performance for repairable devices. The construction and study of availability measures is usually focused on understanding the time evolution of device status-often relative to the efficiency of the repair process. It is not generally acknowledged that the resulting availability measure is actually an expected value with respect to frequency. At any point in time and with any associated value for availability, the number of copies of a device that is functioning is a random variable. The behavior of this random variable is the subject of the study described in the paper. The intuitive view that the frequency distribution of operating devices is binomial is confirmed. This is done using a combination of direct analysis and simulation for negative exponential and Weibull life distributions under the assumption of negative exponential repair time distributions. An efficient numerical strategy for computing availability in the Weibull case is constructed and provided as an ancillary result. The implications of the analysis are that more accurate models of device behavior in terms of frequency are defined including exact confidence bounds for availability at any point in time. In addition, the time evolution of the frequency distribution is described and the implications of this evolution for decision analysis are identified. The result of the analyses presented is a new perspective on availability that should prove quite useful