Efficient analysis of multi-state k-out-of-n systems

Mo, Yuchang; Xing, Liudong; Amari, Suprasad V.; Dugan, J.B.

doi:10.1016/j.ress.2014.09.006

Cited by 80 publications

(48 citation statements)

References 17 publications

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“…Both entities reduce the resulting expansion tree (which is exponential in size) to a rooted acyclic graph that is both canonical and hopefully compact or subexponential. The reduction rules [21] require (a) complete sum expressions are identical. These expressions are shellable and allow the introduction of PRE expressions of the same number of terms.…”

Section: The Sfgs Of S Ands Are Essentially Robddsmentioning

confidence: 99%

Novel representations for a coherent threshold reliability system: a tale of eight signal flow graphs

Rushdi¹,

Alturki²

2018

Turk J Elec Eng & Comp Sci

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Abstract:A threshold system is a reliability system whose success/failure is a threshold switching function in the successes/failures of its components. A coherent system (CS) is one that is causal, monotone, and with relevant components. The coherent threshold system (CTS), typically called the weighted k-out-of-n system, is consequently described by strictly positive weights and threshold. This paper presents recursive relations as well as boundary conditions for eight entities pertaining to a CTS. These are (a) expressions of monoform literals as well as disjoint or probabilityready expressions for either system success or failure, and (b) all-additive formulas as well as inclusion-exclusion ones for either system reliability or unreliability. These entities are obtained according to the best policy of implementing the Boole-Shannon expansion with respect to a higher-weight component before it is made with respect to a lower-weight one. With this best policy, the success and failure expressions with monoform literals are both minimal and shellable.Each of the eight entities considered is represented by an acyclic (loopless) signal flow graph (SFG). The SFG for system success or failure is isomorphic to a reduced ordered binary decision diagram, which is the optimal data structure for a Boolean function. The interrelations between the SFGs demonstrate optimal procedures for implementing (a) the probability (real) transform of a Boolean function, (b) inversion or complementation of a Boolean function, and (c) disjointing or orthogonalization of a sum-of-products expression of a Boolean function. The SFGs discussed herein for a CT can be extended to a general coherent system. They reduce to elegant symmetric regular graphs for the special case of a partially redundant system (k-out-of-n system).

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Section: The Sfgs Of S Ands Are Essentially Robddsmentioning

confidence: 99%

Novel representations for a coherent threshold reliability system: a tale of eight signal flow graphs

Rushdi¹,

Alturki²

2018

Turk J Elec Eng & Comp Sci

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“…where the initial parameters are For C2, its differential equations are: dp t dt p t u p t dp t dt p For C3, we can also get its state differential equations dp t dt p t u p t dp t dt p t , (27) where the initial conditions are (25), (26) and (27).…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The widespread recognition of MSS is that it has been defined as having different performance levels and/or some failure modes with corresponding effects on the system's entire performance. Many researchers have made various contributions for the MSS reliability evaluation and modeling theory recently [13,23,8,9,27,40]. The commonly adopted methods have five basic approaches, such as, an extension of binary theory to MSS cases, the stochastic process approach, the universal generating function (UGF), the Monte-Carlo simulation and recursive algorithm etc [14,45,22,19,2,20,37].…”

Section: Introductionmentioning

confidence: 99%

A combined method for reliability analysis of multi-state system of minor-repairable components

Qin

Niu

Liu

2016

EiN

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“…The assumptions the assumptions of above approaches may not conform to most real-life systems. 11 Dynamic models: Markov model 12,13 ; dynamic fault tree [14][15][16] ; Petri net 17,18 ; Bayesian network 6,19,20 ; multivalued decision diagram 21,22 ; universal generating functions [23][24][25] ; and stochastic process approach 26,27 The problem of combinatorial explosion is intractable. Some of them have been criticized for the high computational complexity.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Reliability assessment of complex electromechanical systems: A network perspective

Lin

Wang

Jia

et al. 2018

Quality & Reliability Eng

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The network theory is widely applied to improve the reliability of a complex electromechanical system. In this application, system reliability assessment with network theory has been paid a great deal of attention. Because of instrument malfunctions, staff omissions, imperfect inspection strategies, and complex structures, field failure data are often subject to interval censoring, making the holistic reliability assessment becomes a difficult task. Most traditional methods assume reliability of critical components or partial reliability as system reliability, which may cause a large bias in system reliability estimation. This paper proposes a novel method to evaluate and predict the system reliability of a complex electromechanical system subject to the insufficient fault data problem from a network perspective. First, the system modeling based on network theory is developed to describe the topology of a holistic system. Second, interval-valued intuitionistic hesitant fuzzy number is proposed in order to solve insufficient data for single component. Then, a new measurecomprehensive reliability-that can reflect the reliability of nodes in combination with functional properties and topological properties, which are formulated by failure data and network model, respectively, is constructed for system reliability assessment. Subsequently, an improved system reliability model based on percolation theory is given in terms of comprehensive reliability of nodes. Finally, to verify the effectiveness of the proposed method, a simulation and a real case study for traction system are implemented.

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Efficient analysis of multi-state k-out-of-n systems

Cited by 80 publications

References 17 publications

Novel representations for a coherent threshold reliability system: a tale of eight signal flow graphs

Novel representations for a coherent threshold reliability system: a tale of eight signal flow graphs

A combined method for reliability analysis of multi-state system of minor-repairable components

Reliability assessment of complex electromechanical systems: A network perspective

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