A consecutive k-out-of- n reliability system in random environment

Abstract

Linear and circular consecutive k-out-of-n reliability system are assumed to be situated in a random environment such that shocks generated by the environment will cause failure with probability p to one randomly chosen component. Explicit formulas for k = 2 and 3 are derived for generating functions and expectations and variances for the system time to failure. An equivalene between linear and circular systems is derived.