An Efficient Formula for Generalized Multi-State $k$ -Out-of- $n$ : G System Reliability

Radwan, Taha; Alrawashdeh, Mufda Jameel; Ghanem, Sewelam

doi:10.1109/access.2019.2908864

Cited by 10 publications

(5 citation statements)

References 25 publications

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“…As we will see in the Tables 4-7, the execution time is small, which demonstrates the effectiveness of the proposed bounds. Using our new bounds, we obtained the same results of all published examples of increasing MS C(k,r,n:F) [22] when the components are i.i.d., binary C(k,r,n:F) when H =1 [5], and generalized multi-state k-out-of-n: G system [16] when r=n. All of these systems are special cases of our bounds.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…So that, some recent papers concerned generalization many models to the case where the components are non i.i.d. For example, the generalized multi-state k-out-of-n: G system [16], the phased mission parallel systems [26], and the traditional linear consecutive system [27]. In this paper, we will give a description of MS C(k,r,n:F) and some practical examples in section II.…”

Section: Introductionmentioning

confidence: 99%

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New Bounds for All Types of Multi-state Consecutive $k$ -Out-of-$r$ -From-$n$ : F System Reliability

Radwan

2019

IEEE Access

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The state of MS C(k, r, n:F) is less than j if any r consecutive components contains k l or more, for all j ≤ l ≤ H. This system is a model for a large number of applications. The existing methods for systemreliability evaluation are suitable for some special cases only. In this paper, we suggest bounds for MS C(k, r, n:F) reliability. These bounds are suitable for all system types whether in case of equal or unequal components probabilities. The suggested bounds are examined by previously published examples, when available. Also, illustration examples for the new bounds and system modelling are presented. Furthermore, we studied the cases that make the proposed bounds are sharp.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Bounds for All Types of Multi-state Consecutive $k$ -Out-of-$r$ -From-$n$ : F System Reliability

Radwan

2019

IEEE Access

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“…The conditional probability theory was adapted into the reliability evaluation of a multi-state system. 7 Eryilmaz 8 applied the universal generating function technique (UGF) to consider randomness when measuring the reliability of wind power system. A state transition dependency-based reliability evaluation model was proposed.…”

Section: Introductionmentioning

confidence: 99%

Redundancy optimization for multi-state series-parallel systems using ordinal optimization-based-genetic algorithm

Ding

Zeng

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Multi-state series-parallel systems (MSSPSs) are widely-used for representing engineering systems. In real-life cases, engineers need to design an optimal MSSPS structure by combining different versions and number of redundant components. The objective of the design is to ensure reliability requirements using the least costs, which could be formulated as a redundancy optimization problem under reliability constraints. The genetic algorithm is one of the most frequently used method for solving redundancy optimization problems. In traditional genetic algorithms, the population size needs to be determined based on the experience of the modeler. Often, this ends up creating a large number of unnecessary samples. As a result, the computational burden can be huge, especially for large-scale MSSPS structures. To solve these problems, this paper proposes an optimal structure designing method named as redundancy ordinal optimization. The universal generating function technique is applied to evaluate the reliabilities of the MSSPSs. Based on the reliabilities, an ordinal optimization algorithm is adapted to update the parent populations and the stopping criterion of genetic algorithm, so that the unnecessary structure designs can be eliminated. Numerical examples show that the proposed method improves the computational efficiency while remaining satisfactorily accurate.

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“…A review of the most recent works on the reliability study of repairable k -out-of-n systems showed that these studies either focus on non-time-dependent reliability characteristics [5,17,23,28] or are based on assumptions of exponential [29] or PH-type distributions [4,20] of the repair time of the system's components. The latter contain models that can easily be reduced to Markov processes with a discrete set of states.…”

Section: Introductionmentioning

confidence: 99%

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

Rykov

Kozyrev

Filimonov³

et al. 2020

Prob. Eng. Inf. Sci.

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The reliability study of k-out-of-n systems is of interest both from theoretical and practical points of view. Applications of such models can be seen in many real-world phenomena, including telecommunication, transmission, transportation, manufacturing, and services. A probabilistic study of a real-world k-out-of-n system often helps to develop an optimal strategy for maintaining high system-level reliability. There are many investigations devoted to the reliability-centric analysis of such systems. We consider a mathematical model of a repairable k-out-of-n system that works until k of its n components have failed. During the system's life cycle, its components are repaired with the help of a single repair facility. It is supposed that the components' lifetimes have an exponential distribution and their repair times have a general distribution. The proposed model is intended to be applied to the description of operation of unmanned rotorcraft high-altitude platforms and to be validated with the help of an experimental prototype. For the considered system, we propose an algorithm for calculation of the reliability function, and for special cases, k = 2 and k = 3, its closed-form representation is given. A numerical investigation is performed for special cases. The obtained results are a first step toward the sensitivity analysis of reliability characteristics of k-out-of-n systems to the shape of the repair time distributions of their components.

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An Efficient Formula for Generalized Multi-State $k$ -Out-of- $n$ : G System Reliability

Cited by 10 publications

References 25 publications

New Bounds for All Types of Multi-state Consecutive $k$ -Out-of-$r$ -From-$n$ : F System Reliability

New Bounds for All Types of Multi-state Consecutive $k$ -Out-of-$r$ -From-$n$ : F System Reliability

Redundancy optimization for multi-state series-parallel systems using ordinal optimization-based-genetic algorithm

ON RELIABILITY FUNCTION OF A K-OUT-OF-N SYSTEM WITH GENERAL REPAIR TIME DISTRIBUTION

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