Reliability analysis of a three unit warm standby redundant system with repair

Srinivasan, S. K.; Subramanian, R.

doi:10.1007/s10479-006-7384-z

Cited by 35 publications

(17 citation statements)

References 11 publications

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“…By the preceding conclusion, the numbers of possible solutions for (25) and (26) are C 2 N i +2 , C 1 N i +1 , respectively, so the maximum number of PEPA components that need to be considered for (19) and (20) is…”

Section: A Groups Of System Componentsmentioning

confidence: 75%

“…In cases of nonexponential distributions, supplementary variable techniques [17]- [22] and PH distribution techniques [23], [24] can be used. Moreover, warm standby systems with s-identical components can be solved by developing iterative equations for state probabilities by event decomposition [25], [26]. However, the state-based approach suffers from the state space explosion problem and difficulty in generating the transition rate matrix when the number of components becomes moderately large.…”

Section: A Related Workmentioning

confidence: 99%

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Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Xiao-yue

Hillston

Feng

2017

IEEE Trans. Syst. Man Cybern, Syst.

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Developing analytical availability models for k-outof-n:G warm standby repairable systems with many nonidentical components is tedious and error-prone, requiring specification of the generator matrix of a high dimensional Markov chain. Using the performance evaluation process algebra (PEPA) as an intermediary, this paper gives a new modeling approach for availability evaluation of such systems with r repair facilities. The components of the system are classified into n different groups that consist of statistically identical components following exponential time-to-failure and repair time distributions. A library of PEPA components and their actions are defined for system component groups, repair facilities, repair queue, and system dynamics. To capture the dependency of system states on components, a signaling mechanism is realized by actions with suitably high rates. A compilation tool is provided to automatically generate the PEPA model from a brief specification of the system, using the library components. This provides input for the PEPA analysis tool and is amenable to availability analysis. Examples are used to illustrate the proposed modeling method. Modeling with PEPA provides an efficient way to deal with availability evaluation of systems considered with many groups of repairable components.

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Section: A Groups Of System Componentsmentioning

confidence: 75%

Section: A Related Workmentioning

confidence: 99%

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Xiao-yue

Hillston

Feng

2017

IEEE Trans. Syst. Man Cybern, Syst.

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“…Therefore, repairable system is not only a kind of important system discussed in reliability theory but also one of the main objects studied in reliability mathematics. Many authors have worked in this field, including system modelling (see [9,12,22]), and model analysis (see [5 -7,14,15]) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The spectral analysis ofkout ofN:Gredundant system

Wen-long¹,

He²

2013

Journal of Difference Equations and Applications

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In this paper, k out of N: G redundant system with repair facilities and multiple critical and non-critical errors is investigated. Firstly, we formulate the problem into a suitable Banach space. Then we carry out a detailed spectral analysis of the system operator. Based on the spectral analysis and C 0 semigroup theory, we prove the linear stability and the exponential stability of the system. As a consequence, we get that its dynamic solutions converge exponentially to the steady-state solution. Finally, we derive some reliability indices of the system.

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“…The need of obtaining highly reliable system has been more and more important with the development of the modern technology. The high degree of reliability is usually achieved by introducing redundancy and service facility or repairman [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a new kind n-unit series repairable system

Guo

Gao

et al. 2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution. C 0 -semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.

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Reliability analysis of a three unit warm standby redundant system with repair

Cited by 35 publications

References 11 publications

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

The spectral analysis ofkout ofN:Gredundant system

Stability analysis of a new kind n-unit series repairable system

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