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CONSECUTIVE *k*-OUT-OF-*n* SYSTEMS WITH MAINTENANCE

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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.

**Source**
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