On ℓ-overlapping Runs of Ones of Length<i>k</i>in Sequences of Independent Binary Random Variables

Makri, Frosso S.; Psillakis, Zaharias M.

doi:10.1080/03610926.2013.788717

Cited by 9 publications

(3 citation statements)

References 62 publications

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“…Third, in case we want we use block codes with smaller code words, but having in mind that they would be less efficient, we can search for codes with relative efficiency between and including η 2 and η 4 . These codes have (m, n) ∈ ∪ i=1 ∆ i , we observe that the next more efficient pairs after (13,24) are, in order of decreasing efficiency, the pairs (7,13), (8,15), (9,17), (10,19), (11,21), (12,23), (1,2) and of course their multiples. Their efficiency η = (m/n)/C, including (13,24), in decreasing order are: 99.98%, 99.38%, 98.44%, 97.71%, 97.14%, 96.68%, 96.30% and 92.29%, respectively.…”

Section: Cfa Of a (D K)-code Capacitymentioning

confidence: 79%

On Run-Length-Constrained Binary Sequences

Psillakis¹

2023

IJIT

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A class of binary sequences, constrained with respect to the length of zero runs, is considered. For such sequences, termed (d, k)-sequences, new combinatorial and computational results are established. Explicit expressions for enumerating (d, k)-sequences of finite length are obtained. Efficient computational procedures for calculating the capacity of a (d, k)-code are given. A simple method for constructing a near-optimal (d, k)-code is proposed. Illustrative numerical examples demonstrate further the theoretical results.

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Section: Cfa Of a (D K)-code Capacitymentioning

confidence: 79%

On Run-Length-Constrained Binary Sequences

Psillakis¹

2023

IJIT

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“…The distribution of the random variable N L(1:n) n;k;l has been named the binomial distribution of order k for l overlapping runs of length k; and introduced and studied by Aki and Hirano [2]. The reliability of Lin/m/Con/k/l/n : F system can be expressed as P fEg = P fN L(1:n) n;k;l < mg: Some recent discussions on this topic are Eryilmaz [9], Eryilmaz and Mahmoud [8], Levitin [26], Makri and Psillakis [29,30] and Makri and Psillakis [31]. For extensive reviews of the runs related literature, we refer to Balakrishnan and Koutras [4], Fu and Lou [13], and Koutras [23].…”

Section: Introductionmentioning

confidence: 99%

Analysis of joint reliability importance in linear m-consecutive-k,l -out-of-n:F system

Kan

Ozkut

2020

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Combinatorial techniques have an important role to compute the joint reliability importance (JRI) of some coherent systems. We obtain combinatorial formula for calculation of the JRI of two components in a generalised version of consecutive type systems consisting of n linearly ordered components such that system fails if and only if (i¤) there are at least m l-overlapping runs of k consecutive failed components (n m(k l) + l; l < k). Overlapping runs mean having common elements which is denoted by l: We concentrate on both s-independent & identical components and exchangeable components. Explicit combinatorial formulae are provided for computing the JRI of the above mentioned cases. For both cases, we also compare the results with linear m-consecutive-k-out-of-n:F system (nonoverlapping case when l = 0). In addition, some numerical and illustrative examples are presented. Acronyms and Notations MRI Marginal Reliability Importance JRI Joint Reliability Importance Lin/m/Con/k/l/n : F Linear m-consecutive-k,l-out-of-n:F n number of components X i the state of component i, i = 1; : : : ; n (X i = 1 if the ith component fails, and X i = 0 if the ith component works) E the event that the system works k minimum number of failed components that may cause system failure z maximum number of failed components such that a system can still work successfully

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“…According to Makri and Psillakis (2013), in order to study formally -overlapping counting in any sequence of 0-1…”

Section: Introductionmentioning

confidence: 99%

Counting Runs of Ones with Overlapping Parts in Binary Strings Ordered Linearly and Circularly

Makri

Psillakis²,

Arapis³

2013

IJSP

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On a binary (0 − 1) string of length n the -overlapping counting scheme of runs of 1 s of a fixed length k is considered. According to this scheme, a run of 1s of length k which is counted may have overlapping part of length at most , 0 ≤ < k ≤ n, with the previous run of 1 s of length k that has been enumerated. The numbers of all -overlapping runs of 1 s of length k in all 2 n binary strings (linearly or circularly ordered) of length n are examined, and simple and easy to compute closed explicit expressions are provided via the probability mass function and the expected value of properly defined random variables. The numbers of binary strings of length n, ordered on a line or on a circle, with a specific number of -overlapping runs of 1s of length k are also provided via closed expressions. The numbers which are studied, are potentially useful in several scientific areas like applied probability, engineering and bioinformatics. The study is illustrated by extensive numerical examples.

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On ℓ-overlapping Runs of Ones of Lengthkin Sequences of Independent Binary Random Variables

Cited by 9 publications

References 62 publications

On Run-Length-Constrained Binary Sequences

On Run-Length-Constrained Binary Sequences

Analysis of joint reliability importance in linear m-consecutive-k,l -out-of-n:F system

Counting Runs of Ones with Overlapping Parts in Binary Strings Ordered Linearly and Circularly

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