System Structure and the Existence of a System Life

The reliability at time t of a system in sustained operation is often taken to be the probability that it functions continuously during the time interval [0, t]. The standard computation of system reliability finds the probability that the system functions at time t in terms of the probabilities that its components function at time t. This procedure is relevant only if the system, and its components, have lives (roughly speaking, a device has a life if it functions continuously until some time of failure, and remains failed thereafter). We show that if each component of a coherent system has a life, then the system has a life (again roughly, a system is coherent if its performance is not impaired by an improvement in the performance of its components). Our principal results are that, under reasonable conditions, converses are true. If a system has a life, only a very weak condition is needed to show that the system is coherent. With a somewhat stronger condition, we show that not only must the system be coherent, but that each component must have a life.