A limit theorem for the reliability of a consecutive-k-out-of-n system
- 1 March 1987
- journal article
- letter
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 19 (03) , 746-748
- https://doi.org/10.1017/s0001867800016864
Abstract
A consecutive-k-out-of-n system consists of n identical and linearly ordered components. The system will fail if and only if at least k consecutive components fail. Let Tn be the system&s lifetime. Then, under very general conditions we prove that there is a positive constant a, so that the distribution of the random variable n (1/ka) Tn converges to a Weibull distribution, as n→∞Keywords
This publication has 2 references indexed in Scilit:
- Bounds for Reliability of Large Consecutive-K-out-of-N:F Systems with Unequal Component ReliabilityIEEE Transactions on Reliability, 1986
- A rearrangement inequality for the longest run, with an application to network reliabilityJournal of Applied Probability, 1985