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- W79654052 abstract "Consider a sequence of n two state (success-failure) trials. A success run of length k is a sequence of k consecutive successes proceeded and succeeded by failures or nothing. In this thesis the random variable N(n,k) denoting the number of success runs of length k in n binary trials is studied. The exact distribution of N(n,k) is given, via combinatorial analysis, recursive relations and using the Markov chain imbedding technique. The study is carried out for independent but not identically distributed binary sequences. Further, the random variable M(n,k)denoting the number of success runs of length at least k in n binary trials is also studied. A consecutive-k-out-of-n : F system is a system which consists of n components ordered on a line, which fails if and only if at least k consecutive components fail. Such systems have been used to model telecommunication, oil pipeline systems e.t.c. An m-consecutive-k -out-of-n : F system consists of n components ordered on a line, which fails if and only if there are at least m non-overlapping runs of k consecutive failed components. The reliability of the above mentioned systems is related to the cumulative distribution function of the random variable N(n,k) . Exact formulae for the reliability is given by means of binomial and multinomial coefficients, via recursive relations and using the Markov chain imbedding technique. The study is accomplished for systems with independent and Markov dependent components. Finally, numerical examples are given for comparison of the various used methods and to illustrate the theoretical results." @default.
- W79654052 created "2016-06-24" @default.
- W79654052 creator A5075850288 @default.
- W79654052 date "2007-11-12" @default.
- W79654052 modified "2023-09-27" @default.
- W79654052 title "Αριθμός ροών επιτυχιών και αξιοπιστία συνεχόμενων συστημάτων αποτυχίας" @default.
- W79654052 hasPublicationYear "2007" @default.
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