Reliability of Combined $k{\hbox{-out-of-}}n$ and Consecutive $k_{c}{\hbox{-out-of-}}n$ Systems of Markov Dependent Components

Demir, Sevcan

doi:10.1109/tr.2009.2026816

Cited by 22 publications

(11 citation statements)

References 10 publications

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“…A similar result given in (6) was obtained by Demir Atalay and Zeybek [8] (see page 628, (14)) under the exchangeability assumption.…”

Section: Distribution Of Runs Arranged In a Circle With Markov-desupporting

confidence: 84%

“…The reliability of the circular system with Markov-dependent components is the first equation at the bottom of the next page, where defined as in (12). Demir [6] considered the reliability of the and systems for the linear sequence of under the Markov dependence assumption, and the results obtained in the (9) (10) (11) last two lemmas of this study accord with the results obtained in that study. Now, let's consider the reliability of the circular and systems.…”

Section: Reliabilities Of Systems With Two Commonsupporting

confidence: 75%

“…Theorem 1: Let be the states of homogeneous Markov-dependent binary trials arranged in a circle, and and denote the longest success run and the total number of successes with respect to the circular sequence of , respectively. Then, see (6). The proof of Theorem 1 is in the Appendix.…”

Section: Distribution Of Runs Arranged In a Circle With Markov-dementioning

confidence: 97%

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Reliability of Circular Systems With Markov Dependencies

Atalay

Zeybek

2014

IEEE Trans. Rel.

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We study the reliabilities of circular and systems. These systems involve two common failure criteria which are more suitable for real world applications. Explicit formulas for the reliabilities of these circular systems are obtained for Markov-dependent components using the distribution theory of runs. The obtained results are also important for the distribution theory of runs. Moreover, the presented formulas consist of combinatorial terms, and therefore enable easier calculations. Some numerical results and the results of a simulation study are presented.

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“…A similar result given in (6) was obtained by Demir Atalay and Zeybek [8] (see page 628, (14)) under the exchangeability assumption.…”

Section: Distribution Of Runs Arranged In a Circle With Markov-desupporting

confidence: 84%

Section: Reliabilities Of Systems With Two Commonsupporting

confidence: 75%

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Reliability of Circular Systems With Markov Dependencies

Atalay

Zeybek

2014

IEEE Trans. Rel.

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“…When , a fact is that at least one of is zero in any of their combinations in (21); otherwise, , and consequently the index of the last matrix :…”

Section: Appendixmentioning

confidence: 99%

“…The Markovdependent components have been studied (see, e.g., [20], and [21]). As exemplified in Papastavridis and Lambiris [20], an oil pipeline system consists of pumps in a row; and if a certain pump fails, then the previous pump carries a greater load to assure a continuous flow of oil, and thus the probability of its failure could increase.…”

mentioning

confidence: 99%

Joint Reliability Importance in a Consecutive- <formula formulatype="inline"><tex Notation="TeX">$k$</tex> </formula>-out-of-<formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula>:F System and an <formula formulatype="inline"><tex Notation="TeX">$m$</tex></formula>-Consecutive- <formula formulatype="inline"><tex Notation="TeX">$k$</tex></formula>-out-of-<formula formulatype="inline"><tex

2015

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The Joint Reliability Importance (JRI) of two components evaluates the interaction effect between the components on system reliability. This paper focuses on the JRI of components in a consecutive--out-of-:F system, and an -consecutive-out-of-:F system, both with Markov-dependent components. We derive the closed-form formulas of the JRI of two components using probability generating functions, and extend the results to the JRI of three and more components. We further provide exact conditional distributions of random variables which are used in probability generating functions for determining the JRI of two components. Our numerical examples and tests demonstrate the use of derived formulas, and provide further insights about the JRI for Markov-dependent components.

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Reliability measures for two-part partition of states for aggregated Markov repairable systems

Cui

Zhang

2012

Ann Oper Res

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Three models for the aggregated stochastic processes based on an underlying continuous-time Markov repairable system are developed in which two-part partition of states is used. Several availability measures such as interval availability, instantaneous availability and steady-state availability are presented. Some of these availabilities are derived by using Laplace transforms, which are more compact and concise. Other reliabilitydistributions for these three models are given as well. Keywords Two-part partition • Aggregation • Repairable systems • Availability measures • Distributions 1 IntroductionRepairable systems have been increasingly studied in the field of reliability (e.g. Altinel et al. 2011 andCancela et al. 2012). For example, Cui and Xie (2001, 2004) considered periodically inspected repairable systems. Cui and Li (2004) described a repairable system in which the number of allowed repairs is finite. Guo et al. (2007) proposed a new general repair model based on the number of repairs. The class of coherent systems composed of random failing repairable components is studied by Kiureghian et al. (2007). And the segregated failures model of availability of fault-tolerant computer systems with severable recovery procedures are presented by Vilkomir et al. (2008). Moreover, Ambani et al. (2010) discussed exponential machines with maintenance-reliability coupling problem. Yu and Cui (2010) studied a two-stage directed network of Markov repairable systems. Peng et al. (2011) considered the reliability and maintenance modeling for multiple dependent competing failure processes, and so forth (e.g. Srinivasan and Subramanian 2006).

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Reliability of Combined $k{\hbox{-out-of-}}n$ and Consecutive $k_{c}{\hbox{-out-of-}}n$ Systems of Markov Dependent Components

Cited by 22 publications

References 10 publications

Reliability of Circular Systems With Markov Dependencies

Reliability of Circular Systems With Markov Dependencies

Reliability measures for two-part partition of states for aggregated Markov repairable systems

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