A unified performance reliability analysis of a system with a cumulative down time constraint

We discuss unified performance and reliability analysis of a system which operates in a critical environment, in the sense that a catastrophic condition is reached when the accumulated down time exceeds a given threshold. Assuming that the system must process a task with a specified work requirement, we evaluate the probability that the task will be completed at a given time before the system reaches the catastrophic state. We show that several other important measures (like the distribution of the lifetime, the distribution of the interval availability, and the instantaneous availability) can be derived from the knowledge of the distribution of the completion time. A numerical example, based on the use of Phase (PH) type distributed random variables, concludes the paper.