This report presents the logic leading to a mathematical expression for mission availability. Mission availability is treated as the probability that the cumulative downtime occurring during a mission of given length will be less than the time constraint. This is opposed to more general approaches such as steady state or instantaneous availability or operating time versus real time. We intend to present a practical and usable mathematical model by deduction and demonstration. The development is based on exponentially distributed downtimes. Experience shows that certain systems follow exponential downtime distributions except near zero. This error is often so small that it may be neglected. A future report will present a downtime distribution which will account for this small error.
