Reliability Determination of a r-Successive-out-of-n:F System

Kontoleon, J.M.

doi:10.1109/tr.1980.5220921

Cited by 186 publications

(76 citation statements)

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“…For example, when k = n/log 2 n the threshold of the failure subset is located at 1 2 and has width of order 1/log n (for a similar result, see [22]). This model was introduced by Kontoleon [19] to model some problems arising in engineering science, such as oil transportation using pipelines, telecommunication using spacecraft relay stations, transmission of data in a ring network of computers, etc.…”

Section: Examples Of Explicit Threshold Widths and Locationsmentioning

confidence: 99%

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Rossignol

2007

J. Appl. Probab.

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We show that there exist symmetric properties in the discrete n-cube whose threshold widths range asymptotically between 1/ √ n and 1/log n. These properties are built using a combination of failure sets arising in reliability theory. This combination of sets is simply called a product. Some general results on the threshold width of the product of two sets A and B in terms of the threshold locations and widths of A and B are provided.

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Section: Examples Of Explicit Threshold Widths and Locationsmentioning

confidence: 99%

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Rossignol

2007

J. Appl. Probab.

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“…For example, when k = ⌊n/ log 2 n⌋, the threshold of the failure subset is located at 1/2, with a width of order 1/ log n (for a similar result, see Paroissin and Ycart [24]). This model was introduced by Kontoleon [21] to model some problems arising in engineering science, such as oil transportation using pipelines, telecommunication system by spacecraft relay station or transmission of data in a ring of computer ring networks, etc.…”

Section: Example 22 Connectivitymentioning

confidence: 99%

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Rossignol

2007

Journal of Applied Probability

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We investigate the threshold widths of some symmetric properties which range asymptotically between 1/ √ n and 1/ log n. These properties are built using a combination of failure sets arising from reliability theory. This combination of sets is simply called a product. Some general results on the threshold width of the product of two sets A and B in terms of the threshold locations and widths of A and B are provided.

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“…The consecutive k-out-of-n: G systems have attracted the attention of many researchers because of their wide applications: telecommunication, pipelines, distribution of water...etc. From their 1148 appearance in Kontoleon (1980), the reliability and several opened problems related to the binary consecutive k-out-of-n: G systems had been resolved El-Neweihi et al (1978), Ross (1979), Chiang and Niu (1981), Derman et al (1982), Wu and Chen (1994), , Kuo et al (1990). But seen that the multi-state systems are more flexible and reflect many real situations, a generalization of the binary consecutive k-out-of-n to the multi-state consecutive k-out-of-n has been done in ; Hwang and Yao (1989).…”

Section: Introductionmentioning

confidence: 99%

Reliability of Multi-state Consecutive -out-of- Series and Parallel Systems

Bouloudene¹,

Belaloui²

2017

JAS

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Abstract. In this paper, we focus on multi-state complex systems and their reliability. First, we provide a formula which computes the reliability of consecutive k-out-of-n: G systems. Then, we extend the used method to obtain the reliability of consecutive k-out-of-L n : G series and consecutive k-out-of-L n : G parallel systems. In the end, we illustrate all theoretical results by numerical examples.Résumé. Dans ce papier, nous nous intéressons aux systèmes multi-étatsà configurations complexes et leur fiabilité. Nous commençons parétablir une formule qui permet de calculer la fiabilité des systèmes k-consécutifs-sur-n : G. Ensuite, nousétendons la méthode utilisée pour obtenir la fiabilité des systèmes k-consécutifs-sur-L n : G série et k-consécutifs-sur-L n : G parallèle. Enfin, nous illustrons tous les résultats théoriques par des exemples numériques.

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Reliability Determination of a r-Successive-out-of-n:F System

Cited by 186 publications

References 1 publication

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Arbitrary Threshold Widths for Monotone, Symmetric Properties

Reliability of Multi-state Consecutive -out-of- Series and Parallel Systems

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