Some advancements in the analysis of two-unit parallel redundant systems

Linton, Darrell G.

doi:10.1016/0026-2714(76)90140-2

Cited by 31 publications

(3 citation statements)

References 6 publications

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“…In 1955, Cox [1] first proposed the "supplementary variable technique (SVT)" and established the M/G/1 queuing system. Gaver [2] was the first to apply this technique for reliability models, and subsequently, other authors followed this line of research, such as Linton [3], Gupta and Gupta [4], Shi and Li [5], Chung [6], Oliveira et al [7], Zhang and Wu [8], Shakuntla et al [9], Singh et al [10], Ke et al [11], Shekhar et al [12], Gao and Wang [13].…”

Section: Introductionmentioning

confidence: 99%

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

Kasim,

Yumaier

2024

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This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C0−semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system.

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Section: Introductionmentioning

confidence: 99%

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

Kasim,

Yumaier

2024

Axioms

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“…Among them we can highlight the supplementary variable technique, introduced in 1955 by Cox [1], due to the fact that this technique outperforms imbedded Markov chains in the steady-state case. The supplementary variable technique was firstly applied in Gaver [2]; subsequently, other authors, such as Linton [3], Goel et al [4], Gupta and Sharma [5], Shi and Li [6], Chung [7], Yuan [8], Dhillon and Cheng [9], Ram et al [10], Zhang and Wang [11], Ke et al [12], followed this line of research.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a complex system under preemptive repeat repair discipline

Kasim

Gupur

2020

Bound Value Probl

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This paper considers a two-unit complex system, in which one of the components has priority with preemptive repeat repair disciplines, described by partial differential equations with integral boundary conditions. First, we prove that the system has a unique nonnegative time-dependent solution by using the strong continuous semigroup theory of linear operators. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution by means of the spectral properties of the corresponding operator. We also provide the asymptotic behavior of some time-dependent reliability indices, a numerical illustration showing the effects of various parameters on the system, and the validity of the theoretical analysis.

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“…[7,8,12] and the phase method, e.g. [11]. The resulting set of transient differential equations are then solved by a LT technique.…”

Section: Introductionmentioning

confidence: 99%

On Gaver’s Parallel System

Vanderperre

Yadavalli

Makhanov³

2012

The South African Journal of Industrial Engineering

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Gaver's parallel system (and its variants) has received considerable attention in the literature. The Laplace-transform (LT) of the survival function, corresponding to the underlying systems, has been derived by various (alternative) methods. Unfortunately, little-to-no attention has been paid to invert the corresponding transform. First, we present a general reliability analysis of Gaver's basic parallel system (valid for an arbitrary repair time distribution). Then, we formulate some general hints to obtain the numerical inverse. Finally, we propose a tangible methodology to derive the exact inverse in some particular but important cases of non-rotational transforms. OPSOMMINGGaver se parallelsisteem (en variante daarvan) is reeds dikwels behandel in die literatuur. Die Laplacetransformasie van die oorlewingsfunksie van die onderliggende sisteme is reeds afgelei op verskillende uiteenlopende wyses. Ongelukkigerwys is min aandag gegee aan die ooreenstemmende inverse transformasie. Ten aanvang word 'n algemene betroubaarheidsontleding van Gaver se basiese parallelsisteem voorgehou (geldig vir 'n arbitrêre hersteltyd-verdeling). Dit word gevolg deur wenke vir bepaling van die numeriese inverse. Ten slotte word 'n tasbare metodologie vir die afleiding van die presiese inverse vir sekere belangrike nie-rotasionele transformasies voorgestel.

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Some advancements in the analysis of two-unit parallel redundant systems

Cited by 31 publications

References 6 publications

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

C0–Semigroups Approach to the Reliability Model Based on Robot-Safety System

Dynamic analysis of a complex system under preemptive repeat repair discipline

On Gaver’s Parallel System

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