Geodesic
An estimation method for the reliability of "consecutive-k-out-of-n system"
Serdica Mathematical Journal, Tome 38 (2012) no. 4, pp. 633-644.

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This paper is concerned with consecutive-k-out-of-n system in which all the components have the same q lifetime probability, so, it's possible to estimate q from a sample by using the maximum likelihood principle. In the reliability formula of the consecutive-k-out-of-n system appears the term q^k. The goal in this work is to propose a direct estimation of q^k to avoid the accumulated errors owed to the power. More precisely, we establish a new method based on the Markov chains to calculate and estimate the reliability of the system.
Keywords: Consecutive-k-out-of-n System, Likelihood Estimation, Markov Chains 
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     title = {An estimation method for the reliability of "consecutive-k-out-of-n system"},
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Ksir, Brahim; Bouhadjar, Slimane. An estimation method for the reliability of "consecutive-k-out-of-n system". Serdica Mathematical Journal, Tome 38 (2012) no. 4, pp. 633-644. http://geodesic.mathdoc.fr/item/SMJ2_2012_38_4_a4/