Mixture Representations for Three-State Systems With Three-State Components

Eryılmaz, Serkan

doi:10.1109/tr.2015.2404896

Cited by 9 publications

(7 citation statements)

References 21 publications

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“…The following proposition shows that this result actually still holds for the probability signature whenever the joint relative quality function is invariant under the operation of set complement. This is the case for instance when the numbers q(A, B) are given by (8).…”

Section: Proof We Havementioning

confidence: 99%

“…Note that the system components considered in this paper have two states only. Of course it is natural to also investigate multistate systems made up of multistate components (see, e.g., [1,3,7,8,[12][13][14]16]). We believe that our algebraic approach can be extended to this general case to investigate the concept of signature.…”

Section: Now Recall From Proposition 24 Thatmentioning

confidence: 99%

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Joint signature of two or more systems with applications to multistate systems made up of two-state components

Marichal

Mathonet

Navarro

et al. 2017

European Journal of Operational Research

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The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the k-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order n whose (k, l)-entry is the probability that the k-th failure causes the first system to fail and the l-th failure causes the second system to fail. This concept was successfully used to derive a signaturebased decomposition of the joint reliability of the two systems. In the first part of this paper we provide an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. We also provide and discuss a necessary and sufficient condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. In the second part of this paper we show how our results can be efficiently applied to the investigation of the reliability and signature of multistate systems made up of two-state components. The key observation is that the structure function of such a multistate system can always be additively decomposed into a sum of classical structure functions. Considering a multistate system then reduces to considering simultaneously several two-state systems.

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Section: Proof We Havementioning

confidence: 99%

Section: Now Recall From Proposition 24 Thatmentioning

confidence: 99%

Joint signature of two or more systems with applications to multistate systems made up of two-state components

Marichal

Mathonet

Navarro

et al. 2017

European Journal of Operational Research

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“…The Laplace transform is defined as R Ã sys (s) = Ð + ' 0 e Àst R sys (t)dt. Due to the linear property and convolution theorem of Laplace transform, we obtain equation (15). By taking inverse Laplace transform, the approximation of the system reliability is derived…”

Section: Reviews On the Fmciamentioning

confidence: 99%

“…They obtained the survival function of such a system model. Furthermore, Eryilmaz 15 proposed that the survival function of a three-state system with a general structure can be represented as a mixture of the survival functions of the three-state k -out-of- n :G systems.…”

Section: Introductionmentioning

confidence: 99%

An approximation method for evaluating the reliability of a dynamic k-out-of-n:F system subjected to cyclic alternating operation conditions

Lin

Cui

Coit

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part O:

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This article extends the finite Markov chain imbedding approach to evaluate the system reliability of a dynamic k-out-ofn:F system operating under two cyclic alternating conditions, and this article presents a method to obtain the optimal replacement interval of the system according to age-based replacement policy. In terms of the ''dynamic k-out-of-n:F'' model, we regard the system as two distinct k-out-of-n:F systems with different values of k while the system is operating under each condition. We apply the proposed model to analyze the reliability of a wireless sensor network, whose sensors switching into sleep state to save energy and shifting into listen state to detect the information alternatively. We also obtain the optimal replacement interval to redeploy the wireless sensor networks.

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“…Da et al (2014) computed the signature reliability and minimal signature of k -out-of- n systems on the basis of their modules. Eryilmaz (2015) evaluated the signature reliability for mixture of more than one state of the systems with dependent components and determined the expected lifetime and reliability of the k -out-of- n system. Franko and Tütüncü (2016) determined the reliability of weighted k -out-of- n system using signature of components importance.…”

Section: Introductionmentioning

confidence: 99%

Computations of the signature reliability of the coherent system

Kumar

Singh

2017

IJQRM

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Purpose The purpose of this paper is to compute the signature reliability of the coherent systems. Design/methodology/approach The considered k-out-of-n coherent system consists of n number of elements connected in series. With the help of these systems, the authors have evaluated a mathematical structure using universal generating function. Findings Using the universal generating function technique, the authors evaluate tail signature, Barlow-Proschan index, expected lifetime and expected cost. Originality/value In this paper, the authors have developed a coherent systems based on the universal generating function technique.

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Mixture Representations for Three-State Systems With Three-State Components

Cited by 9 publications

References 21 publications

Joint signature of two or more systems with applications to multistate systems made up of two-state components

Joint signature of two or more systems with applications to multistate systems made up of two-state components

An approximation method for evaluating the reliability of a dynamic k-out-of-n:F system subjected to cyclic alternating operation conditions

Computations of the signature reliability of the coherent system

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