A universal generating function approach for the analysis of multi-state systems with dependent elements

Levitin, Gregory

doi:10.1016/j.ress.2003.12.002

Cited by 171 publications

(67 citation statements)

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“…Universal generating function is an intuitively simple, efficient expression, and operational tool for discrete random variable, proposed by Professor Ushakov in 1986 [23], and was then applied to reliability assessment of multi-state systems [24][25][26][27]. In the UGF theory, a discrete random variable is expressed in polynomial form, and the polynomial operator is defined according to the operational rule of the variables.…”

Section: Probabilistic Production Simulation Based On Universal Genermentioning

confidence: 99%

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Universal Generating Function Based Probabilistic Production Simulation Approach Considering Wind Speed Correlation

Zhou

Wang

et al. 2017

Energies

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Due to the volatile and correlated nature of wind speed, a high share of wind power penetration poses challenges to power system production simulation. Existing power system probabilistic production simulation approaches are in short of considering the time-varying characteristics of wind power and load, as well as the correlation between wind speeds at the same time, which brings about some problems in planning and analysis for the power system with high wind power penetration. Based on universal generating function (UGF), this paper proposes a novel probabilistic production simulation approach considering wind speed correlation. UGF is utilized to develop the chronological models of wind power that characterizes wind speed correlation simultaneously, as well as the chronological models of conventional generation sources and load. The supply and demand are matched chronologically to not only obtain generation schedules, but also reliability indices both at each simulation interval and the whole period. The proposed approach has been tested on the improved IEEE-RTS 79 test system and is compared with the Monte Carlo approach and the sequence operation theory approach. The results verified the proposed approach with the merits of computation simplicity and accuracy.

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Section: Probabilistic Production Simulation Based On Universal Genermentioning

confidence: 99%

“…In this section, UGF algorithm for dependent random variables is adopted [24,25]. Wind farms are divided into groups, and the UGF model of each group is developed while considering correlation.…”

Section: Modeling Wind Farm Outputs Considering Correlationmentioning

confidence: 99%

Universal Generating Function Based Probabilistic Production Simulation Approach Considering Wind Speed Correlation

Zhou

Wang

et al. 2017

Energies

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“…It is widely adopted in reliability analyses because of its efficiency. It is particularly useful in the reliability analysis of systems with multi-states and large numbers of components [12,18,19]. In the traditional UGF method, the UGF of a component i over state space G i is written as a z-transformation polynomial:…”

Section: An Afp-searching Algorithm Based On a Modified Ugfmentioning

confidence: 99%

“…Thus, we can calculate R e (k,n,t) in the transformed scale by (25), (26) or (27), and the system failure rate α i can be obtained by (18), (19) and (21) with h 0 (t′)=1. Therefore, unless otherwise specified, only the TFR models with an exponential failure time baseline distribution are discussed in this paper.…”

Section: R K N T T T Kmentioning

confidence: 99%

Reliability analysis and optimization of equal load-sharing k-out-of-n phased-mission systems

Chen¹,

He²,

Wei³

2015

Eksploatacja i Niezawodnosc - Maintenance and Reliability

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Reliability analysis and optimization of equal load-shaRing k-out-of-n phased-mission systems analiza niezawodności oRaz optymalizacja systemów fazowych typu "k z n" o Równym podziale obciążenia elementów składowychThere are many studies on k-out-of-n systems, load-sharing systems (LSS) Słowa kluczowe: Właściwa ścieżka uszkodzeń (AFP), algorytm genetyczny (GA), system fazowy (o zadaniach okresowych) (PMS), Model manipulowanej intensywności uszkodzeń (TFR), Uniwersalna funkcja tworząca (UGF).

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“…Levitin [8][9][10] have extensively applied the universal generating function UGF method to solve reliability problems of multi-state systems and showed its effectiveness. UGF method was first proposed by Ushakov [30,31] as a stochastic evaluation method of multistate systems, and is thought to be effective especially for a system hierarchically composed of physical modules like series-parallel or parallel-series systems, which is practically well observed for a system treating flow of oil, gas, job shop and so on.…”

Section: Introductionmentioning

confidence: 99%

Decomposition of a Multi-State System by Series Systems

Ohi

2016

JORSJ

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In the theory and engineering of reliability, it is one of the important issues for reliability researchers to develop effective evaluation methods of reliability performance of systems. For the case of a binary state system, using the minimal-path or minimal-cut sets of the system, an effective method is given by decomposing a structure function into series or parallel systems. For multi-state systems with partially ordered state spaces, however, sufficient examinations of the decomposition and related subjects have not been given. In this paper, following the definition of a series system of Ohi [28], we show a necessary and sufficient condition for a multi-state system to be a series system, which denotes that a system is series system if and only if the serialisation at system's and component's levels are equivalent with each other and then presenting the series-decomposition, we show the relationship among the stochastic bounds which is given by the decomposition. Furthermore, some examinations about the pattern of maximal state vectors of a series system are given. In this paper, we omit the discussions about the parallel system, since it is ordered set theoretically dual of the series system.

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A universal generating function approach for the analysis of multi-state systems with dependent elements

Cited by 171 publications

References 0 publications

Universal Generating Function Based Probabilistic Production Simulation Approach Considering Wind Speed Correlation

Universal Generating Function Based Probabilistic Production Simulation Approach Considering Wind Speed Correlation

Reliability analysis and optimization of equal load-sharing k-out-of-n phased-mission systems

Decomposition of a Multi-State System by Series Systems

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