Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets

Endharta, Alfonsus Julanto; Yun, Won Young; Ko, Young Myoung

doi:10.1016/j.ress.2018.07.023

Cited by 36 publications

(18 citation statements)

References 45 publications

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“…">7.Circular k ‐ m ‐balanced survivability: The system is up if and only if at least k components are operating, and the system is spatially balanced (i.e., the operational components are uniformly spread); see Endharta et al. (2018). …”

Section: Conceptsmentioning

confidence: 99%

On the reliability estimation of stochastic binary systems

Cancela

Murray

Robledo

et al. 2021

Int Trans Operational Res

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A stochastic binary system (SBS) is a multicomponent on‐off system subject to random independent failures on its components. After potential failures, the state of the subsystem is ruled by a logical function (called structure function) that determines whether the system is operational or not. A SBS serves as a natural generalization of network reliability analysis, where the goal is to find the probability of correct operation of the system (in terms of connectivity, network diameter, or different measures of success). A particular subclass of interest is stochastic monotone binary systems (SMBS), which are characterized by nondecreasing structure. We explore the combinatorics of SBS, which provide building blocks for system reliability estimation, looking at minimal nonoperational subsystems, called mincuts. One key concept to understand the underlying combinatorics of SBS is duality. As methods for exact evaluation take exponential time, we discuss the use of Monte Carlo algorithms. In particular, we discuss the F‐Monte Carlo method for estimating the reliability polynomial for homogeneous SBS, the recursive variance reduction for SMBS, which builds upon the efficient determination of mincuts, and three additional methods that combine in different ways the well‐known techniques of permutation Monte Carlo and splitting. These last three methods are based on a stochastic process called the creation process, a temporal evolution of the SBS which is static by definition. All the methods are compared using different topologies, showing large efficiency gains over the basic Monte Carlo scheme.

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Section: Conceptsmentioning

confidence: 99%

On the reliability estimation of stochastic binary systems

Cancela

Murray

Robledo

et al. 2021

Int Trans Operational Res

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show abstract

“…A k ‐out‐of‐ n pairs:G balanced system contains n pairs of components, and the two components in a pair must be working or shut down at the same time 1 . The reliability evaluation 1 and degradation analysis 2 have been developed for such a system, and different reliability evaluation methods, such as Monte‐Carlo simulation 3 and minimal path sets, 4 have been investigated. Guo and Elsayed 5 extended this first type of system into a two‐dimensional situation and proposed a

( {{k_1},\;{k_2}} )

‐out‐of‐

( {n,\;m} )

pairs:G system.…”

Section: Introductionmentioning

confidence: 99%

A multi‐state k‐out‐of‐n:F balanced system with a rebalancing mechanism

Wang

Zhao

Zuo

2021

Quality & Reliability Eng

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Balanced systems have extensive applications in engineering fields such as new energy storage and aeronautics. The reliability analysis of such systems has been reported in literature. However, most existing studies focus on the binary‐state situation, and research on multi‐state cases and the relevant rebalancing mechanism is still limited. To fill this gap, a multi‐state k‐out‐of‐n:F balanced system with a rebalancing mechanism is studied in this paper. Both components and the system have multiple states, and all the components are required to be working in similar states to ensure that the system operates in a balanced condition. It means that the difference between the maximum and minimum component states should not exceed a threshold. Otherwise, the system is out of balance and should be rebalanced by identifying the components whose states are too high and adjusting them into lower states. A continuous‐time Markov process is used to describe the component operation process and relevant reliability indices are derived accordingly. An age maintenance strategy is also proposed and an optimization model is constructed to obtain the optimal results. Finally, numerical examples based on a product line balancing problem are presented to demonstrate the application of the proposed model.

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“…Systems that arise from the “balance” have attracted a great deal of attention in reliability theory. Researchers have started to study the balanced system in 2016, progress has been made in the research field of reliability modeling and application of balanced system by extending the concept of system balance, considering different system structures and adopting different reliability modeling methods, the main contributions are in Hua and Elsayed, 1,2 Cui et al, 3 Cui et al, 4 Endharta et al, 5 and Fang and Cui. 6 New definitions and new models for balanced systems were proposed based on some practical background, and the related reliability indexes were derived by using various approaches, such as the aggregated stochastic process, the k -out-of- n : F system, the order statistics technique, and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…As for the balanced system structure studied in the previous paper, it mainly focused on five kinds: k -out-of- n pairs: G balanced systems, 1,2 circular k -out-of- n : G balanced systems, 5 k -out-of- n : F balanced systems with m sectors, 3 multi-dimension ( k 1 , k 2 ) -out-of- ( n , m ) : G balanced systems, 7 and sectors in series balanced systems. 4 In this paper, a new balanced system structure, a consecutive k -out-of- m : F system with a symmetry line, is developed.…”

Section: Introductionmentioning

confidence: 99%

Reliability evaluation of consecutive k-out-of-m: F balanced systems with a symmetry line

Chen

Cui

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Based on some real backgrounds, a new balanced system structure, a consecutive k-out-of- m: F system with a symmetry line, is proposed in this paper. Considering different state numbers of a subsector, the new balanced system is analyzed under two situations respectively: the subsector with binary-state and the subsector with multi-state, while the multi-state balanced systems have not been studied in the previous research. Besides, two models are developed in terms of assumptions for the two situations, respectively. For this system, several methods, such as the finite Markov chain imbedding approach, the order statistics technique and the phase-type distributions, are used on the models. In addition to system reliability formulas, the means and variances of the system lifetimes under two models for different situations are given. Finally, numerical examples are presented to illustrate the results obtained in this paper.

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Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets

Cited by 36 publications

References 45 publications

On the reliability estimation of stochastic binary systems

On the reliability estimation of stochastic binary systems

A multi‐state k‐out‐of‐n:F balanced system with a rebalancing mechanism

Reliability evaluation of consecutive k-out-of-m: F balanced systems with a symmetry line

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