Generalized multi-state k-out-of-n:G systems

Huang, Jian; Zuo, Ming J.; Wu, Yanhong

doi:10.1109/24.855543

Cited by 157 publications

(96 citation statements)

References 6 publications

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“…When • m=1 and s = n, the increasing MS L(k,1,n,n:F) becomes the increasing MS k-out-of-n:F system. An example of MS kout-of-n:F system in Ref [10] is examined using formula (18) …”

Section: Numerical Resultsmentioning

confidence: 99%

“…In the last few years, many systems generalized to MS systems, because the MS models give more limberness for modelling the equipment conditions. Such as, MS consecutive k-out-of-n:F system [9,22,24], MS k-out-of-n:F system [1,10,20], MS consecutive k-out-of-r-from-n: F system [8,19] and MS L(k,m,s,n:F) [7]. In this paper, we study MS L(k,m,s,n:F).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

Radwan¹

2018

Eksploatacja i Niezawodność – Maintenance and Reliability

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A “multi-state linear k-within-(m,s)-of-(m,n):F lattice system” (MS L(k,m,s,n:F)) comprises of m×n components, which are ordered in m rows and n columns. The state of system and components may be one of the following states: 0, 1, 2, …, H. The state of MS L(k,m,s,n:F) is less than j whenever there is at least one sub-matrix of the size m×s which contains kl or more components that are in state less than l for all j ≤ l ≤ H. This system is a model for many applications, for example, tele communication, radar detection, oil pipeline, mobile communications, inspection procedures and series of microwave towers systems. In this paper, we propose new bounds of increasing MS L(k,m,s,n:F) reliability using second and third orders of Boole-Bonferroni bounds with i.i.d components. The new bounds are examined by previously published numerical examples for some special cases of increasing MS L(k,m,s,n:F). Also, illustration examples of modelling the system and numerical examples of new bounds are presented. Further, comparisons between the results of second and third orders of Boole-Bonferroni bounds are given.

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“…When • m=1 and s = n, the increasing MS L(k,1,n,n:F) becomes the increasing MS k-out-of-n:F system. An example of MS kout-of-n:F system in Ref [10] is examined using formula (18) …”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

Radwan¹

2018

Eksploatacja i Niezawodność – Maintenance and Reliability

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“…Instead, these systems can be described as multi-state systems (MSS) [5]. A multi-state k-out-of-n: G system and a multi-state k-out-of-n: F system model were investigated in References [6,7].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analysis of Multi-State Weighted k-Out-of-n Systems Applied to Transmission Lines

et al. 2017

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Multi-state weighted k-out-of-n systems are widely applied in various scenarios, such as multiple line (power/oil transmission line) transmission systems where the capability of fault tolerance is desirable. However, the complex operating environment and the dynamic features of load demands influence the evaluation of system reliability. In this paper, a stochastic multiple-valued (SMV) approach is proposed to efficiently predict the reliability of two models of systems with non-repairable components and dynamically repairable components. The weights/performances and reliabilities of multi-state components (MSCs) are represented by stochastic sequences consisting of a fixed number of multi-state values with the positions being randomly permutated. Using stochastic sequences with L multiple values, linear computational complexities with parameters n and L are required by the SMV approach to compute the reliability of different multi-state k-out-of-n systems at a reasonable accuracy, compared to the complexities of universal generating functions (UGF) and fuzzy universal generating functions (FUGF) that increase exponentially with the value of n. The analysis of two benchmarks shows that the proposed SMV approach is more efficient than the analysis using UGF or FUGF.

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“…But, usually they are binary systems or systems consisting of binary components [1], [3], [7], while the multi-state systems are less analyzed. Analysis of multi-state systems is mainly based on expressing the reliability of the system using the reliability for certain level of the components without the consideration of the time as a dimension in the working process of the system [6] and [7]. In these papers only the influence of the structure of the system on its reliability is considered.…”

Section: Introductionmentioning

confidence: 99%

Multi-state Systems with Graduate Failure and Equal Transition Intensities

Mihova¹,

Popeska²

2009

MedJM

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We consider unrecoverable homogeneous multi-state systems with graduate failures, where each component can work at M + 1 linearly ordered levels of performance. The underlying process of failure for each component is a homogeneous Markov process such that the level of performance of one component can change only for one level lower than the observed one, and the failures are independent for different components. We derive the probability distribution of the random vector X, representing the state of the system at the moment of failure and use it for testing the hypothesis of equal transition intensities. Under the assumption that these intensities are equal, we derive the method of moments estimators for probabilities of failure in a given state vector and the intensity of failure. At the end we calculate the reliability function for such systems.

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Generalized multi-state k-out-of-n:G systems

Cited by 157 publications

References 6 publications

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

On System Reliability of Increasing multi-state linear k-within-(m,s)-of-(m,n):F lattice system

Approximate Analysis of Multi-State Weighted k-Out-of-n Systems Applied to Transmission Lines

Multi-state Systems with Graduate Failure and Equal Transition Intensities

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