Bounds for increasing multi-state consecutive k-out-of-r-from-n: F system with equal components probabilities

Radwan, Taha; Habib, A.; Al-Seedy, R.O.; El-Sherbeny, A. S.

doi:10.1016/j.apm.2010.11.059

Cited by 23 publications

(15 citation statements)

References 27 publications

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“…Another interesting future line of work is to study other aspects of consecutive kout-of-n systems when probabilities or dependencies are ill-known, such as for instance importance measures (Zhu et al 2012), multi-state versions of the systems (Radwan et al 2011) or design optimization (Shingyoch et al 2010).…”

Section: Resultsmentioning

confidence: 99%

Reliability Analysis with Ill-Known Probabilities and Dependencies

Destercke

Poss

Sallak

2014

Vulnerability, Uncertainty, and Risk

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In this work, we are interested in estimating the uncertainty that a system will work, given the probabilities that its components will be either failing or working. Usually, this estimation is done by propagating the component uncertainties through a structure function. This problem is well-studied when component probabilities are known and when the component are assumed to be independent. In this paper, we first recall some results obtained when considering that probabilities are unknown and when one either assume component independence or no knowledge about the components dependence. We also explore some structures not studied up to now, such as consecutive k-out-of-n structures.

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Section: Resultsmentioning

confidence: 99%

Reliability Analysis with Ill-Known Probabilities and Dependencies

Destercke

Poss

Sallak

2014

Vulnerability, Uncertainty, and Risk

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“…When • m=1, the increasing MS L(k,1,s,n:F) becomes the increasing MS consecutive-k-out-of-s-from-n: F system. An example of increasing MS consecutive-k-out-of-s-from-n: F system in Ref [19] is examined by our bounds and given in table 1. When • H=1 and m=1, the increasing MS L(k,1,s,n:F) becomes the binary consecutive-k-out-of-s-from-n: F system.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In the last few years, many systems generalized to MS systems, because the MS models give more limberness for modelling the equipment conditions. Such as, MS consecutive k-out-of-n:F system [9,22,24], MS k-out-of-n:F system [1,10,20], MS consecutive k-out-of-r-from-n: F system [8,19] and MS L(k,m,s,n:F) [7]. In this paper, we study MS L(k,m,s,n:F).…”

Section: Introductionmentioning

confidence: 99%

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

Radwan¹

2018

Eksploatacja i Niezawodność – Maintenance and Reliability

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A “multi-state linear k-within-(m,s)-of-(m,n):F lattice system” (MS L(k,m,s,n:F)) comprises of m×n components, which are ordered in m rows and n columns. The state of system and components may be one of the following states: 0, 1, 2, …, H. The state of MS L(k,m,s,n:F) is less than j whenever there is at least one sub-matrix of the size m×s which contains kl or more components that are in state less than l for all j ≤ l ≤ H. This system is a model for many applications, for example, tele communication, radar detection, oil pipeline, mobile communications, inspection procedures and series of microwave towers systems. In this paper, we propose new bounds of increasing MS L(k,m,s,n:F) reliability using second and third orders of Boole-Bonferroni bounds with i.i.d components. The new bounds are examined by previously published numerical examples for some special cases of increasing MS L(k,m,s,n:F). Also, illustration examples of modelling the system and numerical examples of new bounds are presented. Further, comparisons between the results of second and third orders of Boole-Bonferroni bounds are given.

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“…The multi-state consecutive k-out-of-r-from-n: F system was studied by [1,2]. When r = n, we have a multi-state k-out-of-n: F system that was studied in [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

New bounds of increasing multi-state consecutive k-out-of-r-from-n:F system by applying the third order Boole-Bonferroni bounds

Radwan¹

2015

ams

Self Cite

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The multi-state consecutive k-out-of-r-from-n: F system model consists of n linearly ordered components where the system and its components may be in one of the possible states: 0, 1, …, M. Such model can be used in oil pipeline systems, telecommunication systems, and mobile communication systems. Other applications are in the radar detection, in quality control, inspection procedures and in a series of microwave towers. This paper suggests new bounds of multi-state consecutive k-out-of-r-from-n: F system using the third order Boole-Bonferroni bounds when the components have the same state distribution. Further, Comparisons between the existing and suggested bounds are given.

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Bounds for increasing multi-state consecutive k-out-of-r-from-n: F system with equal components probabilities

Cited by 23 publications

References 27 publications

Reliability Analysis with Ill-Known Probabilities and Dependencies

Reliability Analysis with Ill-Known Probabilities and Dependencies

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

New bounds of increasing multi-state consecutive k-out-of-r-from-n:F system by applying the third order Boole-Bonferroni bounds

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