Numerical Evaluation of Instantaneous Availability

Instantaneous availability (the probability that the system is operational at any time t) is calculated via renewal theory by representing the system as a 2-state stochastic process; the defined states are on-time and off-time which are combined to form the total cycle time. The analytic solution to the above problem is quite general and can be applied to any system adjusted cycle time and on-time distribution. Using this model, a numerical solution is obtained. If the on-time and cycle-time are gamma distributed, then the analytic solution, in both complex and real forms, can be derived for the instantaneous availability of a system. if they are not gamma distributed then the analytic approach is difficult (if not impossible) and an alternative method is required. Thus a numerical approach is used, since it is distribution-free. A numerical example of small sample size illustrates the numerical approach.