Mission Availability for Bounded-Cumulative-Downtime System

In this research, a mathematics model is proposed to describe the mission availability for bounded-cumulative-downtime system. In the proposed model, the cumulative downtime and cumulative uptime are considered as constraints simultaneously. The mission availability can be defined as the probability that all repairs do not exceed the bounded cumulative downtime constraint of such system before the cumulative uptime has accrued. There are two mutually exclusive cases associated with the probability. One case is the system has not failed, where the probability can be described by system reliability. The other case is the system has failed and the cumulative downtime does not exceed the constraint before the cumulative uptime has accrued. The mathematic description of the probability under the second case is very complex. And the cumulative downtime in a mission can be set as a random variable, whose cumulative distribution means the probability that the failure system can be restored to the operating state. Giving the dependence in the scheduled mission, a mission availability model with closed form expression under this assumption is proposed. Numerical simulations are presented to illustrate the effectiveness of the proposed model. The results indicate that the relative errors are acceptable and the proposed model is effective. Furthermore, three important applications of the proposed mission availability model are discussed.