ON THE NUMBER OF FAILED COMPONENTS IN AN OPERATING COHERENT SYSTEM

This paper is an investigation on the number of failed components in a coherent system. First, we consider an (n¡m+1)-out-of-n system, (m · n). Under the condition that the system is operating at time t, we calculate the probability that there exist exactly i failure, i = 0; :::;m ¡ 1, in the system at t. Several properties of the proposed time dependent probability are investigated. The results are then extended to coherent systems consisting of n components with an arbitrary signature vector. Several examples and illustrative graphs are also provided.