CONSECUTIVE k-OUT-OF-n SYSTEMS WITH MAINTENANCE

STAVROS G. PAPASTAVRIDIS AND MARKOS V. KOUTRAS

Department of Mathematics, University of Athens, Panepistemiopolis, 157 84 Athens, Greece

(Received May 24, 1990; revised May 27, 1991)

Abstract. A consecutive k-out-of-n system consists of n linearly or cyclically ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system’s components we prove a limit theorem for the time to first failure of both linear and circular systems.

Key words and phrases: Consecutive k-out-of-n systems, reliability bounds, maintenance, time to failure, Weibull limit theorem.