The asymptotic distribution of the number of failures of a separately maintained system

Abstract

Markov models are commonly used to analyze the reliability of complex systems with separately maintained components that operate and are restored independently. In such a model, a system failure occurs whenever a given class of states is entered from outside the class. This paper derives expressions for the expected value and variance of the number of system failures during a given time interval together with their asymptotic forms. Using these results, a central limit theorem for regenerative processes is applied to show that the number of system failures is asymptotically normally distributed. As an application of the results, a telecommunications system is considered, e.g., a switching system, of n components modeled by a binary structure.