ON THE NUMBER OF COMPONENT FAILURES IN SYSTEMS WHOSE COMPONENT LIVES ARE EXCHANGEABLE.

Consideration is given to a system that is composed of finitely many independent components each of which is either ″on″ or ″off″ at any time. The components are initially on and they have common on-time distributions. Once a component goes off, it remains off forever. The system is monotone in the sense that if the system is off whenever each component in a subset S (called a cut set) of components is off, then that is also true for every subset of components containing S. The authors are interested in studying the properties of N, the number of components that are off at the moment the system goes off. They compute the factorial moments of N in terms of the reliability function. Also proven is that N is an increasing failure rate average random variable and a duality result is presented. An application to a shock model is presented.