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.