On the mean and extreme distances between failures in Markovian binary sequences

Authors:
Serkan Eryılmaz;Femin Yalçın
Affiliations:
Department of Industrial Engineering, Atilim University, 06836, Incek, Ankara, Turkey;Department of Mathematics, Izmir University of Economics, 35330, Balcova, Izmir, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

This paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented.