The use of availability measures is very informative when analyzing the performance of repairable components. The derivation and evaluation of such measures is usually focused on describing the status of the component over time. It is not generally acknowledged that the resulting availability measure is in fact an expected value with respect to frequency. In a population of n independent, identical components, the number functioning at any point in time is a random variable. The distribution of this random variable is determined and described here. The intuitive view that this frequency distribution is binomial is verified. This is accomplished using direct analysis and Monte Carlo simulation. Two general cases are considered: (1) components with exponential life and repair time distributions, and (2) components with Weibull life distributions and exponential repair time distributions. The analysis leads to more accurate models of component behavior in terms of frequency including an exact confidence bound on the number of components functioning at any point in time. In addition, the time evolution of the frequency distribution is described and the relationships between the frequency distribution and the life and repair time distribution parameters are explored. Finally, the implications for availability decision analyses are shown. The overall result is a new perspective on availability which should prove to be very useful. / Master of Science