TY - JOUR

T1 - Analysis of R-out-of-N repairable systems

T2 - The case of phase-type distributions

AU - Barron, Yonit

AU - Frostig, Esther

AU - Levikson, Benny

PY - 2004/3

Y1 - 2004/3

N2 - An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R - 1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

AB - An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R - 1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

KW - Availability

KW - Down time

KW - Markov renewal process

KW - Phase-type distribution

KW - Regenerative point

KW - Semi-regenerative point

KW - Up time

UR - http://www.scopus.com/inward/record.url?scp=1842614214&partnerID=8YFLogxK

U2 - 10.1239/aap/1077134467

DO - 10.1239/aap/1077134467

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AN - SCOPUS:1842614214

SN - 0001-8678

VL - 36

SP - 116

EP - 138

JO - Advances in Applied Probability

JF - Advances in Applied Probability

IS - 1

ER -