This paper analyses in detail a system with an exponential reliability function and a constant repair time. It first presents the availability and its variance for a given number of cycles, a finite length of time, and a steady state. Then, it shows how the variance of the availability can be used to support an economic evaluation of start-up operations, presents some design criteria based on a total system cost model that includes a function of the availability (a down-time that is the complement of availability), gives optimal values of the mean time to failure and the mean repair time, and exhibits methods for a sensitivity analysis of these optimal values and of the total system. The paper concludes with a numerical example.