• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.199-212
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• 2001

We consider a k-out-of-n system with repair under T-policy. Life time of each component is exponentially distributed with parameter $\lambda$. Server is called to the system after the elapse of T time units since his departure after completion of repair of all failed units in the previous cycle or until accumulation of n-k failed units, whichever occurs first. Service time is assumed to be exponential with rate ${\mu}$. T is also exponentially distributed with parameter ${\alpha}$. System state probabilities in finite time and long run are derived for (i) cold (ii) warm (iii) hot systems. Several characteristics of these systems are obtained. A control problem is also investigated and numerical illustrations are provided. It is proved that the expected profit to the system is concave in ${\alpha}$ and hence global maximum exists.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.105-110
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• 1995

In this paper, we shall convey preservation of some partial orderings and closures of some positive ageing classes under k-out-of-n systems of like components. That is, if the life time of a component A is larger than that of a component B in any of the NBU, DMRL, NBUE, HNBUE, NBUFR and NBUFRA orderings, then a k-out-of-n system formed by i.i.d.. components of type A has larger life time, in that ordering, than that of a similar system consisting of n i.i.d. components type of B. And using these partial orderings, closures of positive aging classes(NBU, DMRL, NBUE, HNBUE, NBUFR and NBUFRA) under the coherent system like components.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.201-206
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• 2004

The linear consecutive-k-out-of-n:F system consists of n components ordered linearly and fails if and only if at least k consecutive components fail. We assume that the failure times of components are independent and identical exponentially distributed. This paper develops a model to calculate the expected cost per unit time of a linear consecutive-k-out-of-n:F system. The optimization problem to find the system structure parameter k to minimize the expected cost per unit time is considered.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.397-397
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• 2000

There exists an increasing need of study for generalized consecutive k-out-of-n systems. This paper demonstrates that a recursive formula for multi-dimensional consecutive k-out-of-n systems can be systematically developed by means of conventional structure function analysis. By taking advantage of notational convenience, the formulae expressed in the same recursive fashion just as the one dimensional consecutive k-out-of-n system. With the aids of the recursive formulae, not only the exact reliability of the system, but also the optimal arrangement of components is obtainable in a straightforward way.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.17 no.30
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• pp.209-214
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• 1994

A consecutive k out of n failure lines with sink-source parts is a system of components in sequence such that the system fails whether some k consecutive components are all fail. Some object, be it a flow, is to be relayed from a source to a sink through a sequence of intermediate stations(components). Now care should be taken as to if the source and the sink are also considered components of the systems, i. e. , whether they serve the same function as the intermediate components (stations). Such systems are different from ordinary consecutive k- out of n failure lines by adding the on source and sink pole[6]. The main properties of the reliability by the optimal redundancy of consecutive k out of n failure lines are presented under this modification.

• Journal of Korean Society for Quality Management
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• v.21 no.1
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• pp.144-151
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• 1993

This Paper shows a special case of the optimization criterion is to make the maximum profit in the system reliability of the k out of n open & close structure. Especially, the number of the optimal k is determined for the profit maximization in system reliability by deriving several properties of the optimal k out of n systems in one of four possible styles(closed & opened).

• International Journal of Reliability and Applications
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• v.2 no.4
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• pp.253-262
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• 2001

A k-out-of-n standby system is considered where all of its components are s-independent and classified either working or cold standby connected with imperfect switches. The probability density function of the life length for this system is established in closed form, when the underlying components have constant failure rates. Also the reliability function of the system is derived. Finally, the reliability functions for one, two and three out of four systems are deduced for perfect or imperfect switches and identical or non-identical constant failure rates for working and standby components.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.3
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• pp.250-260
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• 2004

This study considers a linear connected-(r,s)-out-of-(m,n):F lattice system whose components are ordered like the elements of a linear (m,n )-matrix. We assume that all components are in the state 1 (operating) or 0 (failed) and identical and s-independent. The system fails whenever at least one connected (r,s)-submatrix of failed components occurs. The purpose of this paper is to present an optimization scheme that aims at minimizing the expected cost per unit time. To find the optimal threshold of maintenance intervention, we use a genetic algorithm for the cost optimization procedure. The expected cost per unit time is obtained by Monte Carlo simulation. The sensitivity analysis to the different cost parameters has also been made.

• Journal of Applied Reliability
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• v.17 no.4
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• pp.332-342
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• 2017

Purpose: In this study, the lifetime distribution of a k-out-of-n system with heterogeneous components is suggested as Markov model, and the time-to-failure (TTF) distribution of each component is considered as phase-type distribution (PHD). Furthermore, based on the model, a redundancy allocation problem with a mix of components (RAPMC) is proposed. Methods: The lifetime distribution model for the system is formulated by the structured Markov chain. From the model, the various information on the system lifetime can be ascertained by the matrix-analytic (or-geometric) method. Conclusion: By the generalization of TTF distribution (PHD) and the consideration of heterogeneous components, the lifetime distribution model can delineate many real systems and be exploited for developing system operation policies such as preventive maintenance, warranty. Moreover, the effectiveness of the proposed RAPMC is verified by numerical experiments. That is, under the equivalent design conditions, it presented a system with higher reliability than RAP without component mixing (RAPCM).

• Journal of the Korean Society for Railway
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• v.15 no.1
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• pp.42-47
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• 2012

There are ATC (Automatic Train Control), ATP (Automatic Train Protection), ATS (Automatic Train Stop) and ATO (Automatic Train Operation) etc. in train control systems. As various train control systems are installed according to sections, on-board signaling systems are installed to apply to the section. Hence, operation flexibility of trains is decreased. In other words, when trains are operated in the section where other train control systems are used, the on-board signaling systems are changed. Recently, a study on the combined on-board signaling system has been researched to solve this problem. The combined on-board signaling system consists of ATC, ATP and ATS device. Because the train control systems are vital, it needs to design the combined on-board signaling system by using k out of n system. In this paper, when k out of n system is applied in the combined on-board signaling system, the reliability and loss cost are analyzed by using failure rate in each device. Hence, the ideal number of systems is presented according to the number of outputs.