Reliability properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e859" altimg="si632.svg"><mml:mi>k</mml:mi></mml:math>-out-of-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e864" altimg="si631.svg"><mml:mi>n</mml:mi></mml:math> systems with one cold standby unit

Dembińska, Anna; Nikolov, Nikolay; Stoimenova, Eugenia

doi:10.1016/j.cam.2020.113289

Cited by 23 publications

(5 citation statements)

References 25 publications

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“…A study on the reliability evaluation of a k-out-of-n: F system supported by a multi-state protective device in a shock environment was published in Xian et al [26]. Dembinska et al [3] investigated the k-out-of-n system's reliability characteristics with a single cold standby unit. They primarily focused on the situation in which the system runs in discrete time.…”

Section: Introductionmentioning

confidence: 99%

“…Cekay [2] focused on the reliability of k-out-of-n systems that are created to carry out a certain task that consists of numerous separate phases. Eryilmaz and Devrim [3,4] investigated reliability and ideal replacement strategy for a k-out-of-n system subject to random shocks. Gao et al [5] suggested the ideal of an uncertain weighted k-out-of-n system and added an unknown variable to the weighted k-out-of-n system.…”

Section: Introductionmentioning

confidence: 99%

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Performance Modeling and Estimation of Serial System Exhibiting k-out-of-n: G Scheme with Controller Failure

2023

jjmie

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The k-out-of-n system is a widely used concept in various fields. The significance of this system lies in its ability to ensure reliability, safety, and continuity of operation in various settings, including home appliances, military equipment, communication networks, and manufacturing systems. The system consists of two subsystems, each of which employs the kout-of-n: G scheme. Our aim is to estimate the performance of a system that implements a k-out-of-n: G scheme with a controller using Copula's properties. This system is susceptible to two types of failures; partial and complete failures. If the system fails partially, it is repaired using General repair techniques while completely failed state is repaired using Copula repair techniques. The system is investigated using supplementary variable techniques and the Laplace transformation to obtain explicit expressions for availability, reliability, mean time to failure (MTTF), sensitivity, and expected profit functions, all of which are numerically validated. The outcomes/results are displayed in tables and figures, enabling us to draw the appropriate conclusions and offer recommendations. On the basis of numerical results, the conclusions were drawn. The findings of this study will aid maintenance managers in determining the appropriate time and technique for a system's maintenance.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Performance Modeling and Estimation of Serial System Exhibiting k-out-of-n: G Scheme with Controller Failure

2023

jjmie

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“…Nezakati and Razmkhah 16 studied

m

‐out‐of‐

n

systems having one cold standby component under the condition that the performance of the components is getting worse over time. Dembińska et al 17 focused on the reliability characteristics of an

m

‐out‐of‐

n

system with a single cold standby component in the case when the lifetime of the system is a discrete random variable. Pakdaman and Ahmadi 18 investigated the reliability properties of the

m

‐out‐of‐

n

:G system in the stress‐strength setting with three different types of standby components, that is, cold, warm, and hot standby.…”

Section: Introductionmentioning

confidence: 99%

Optimal standby activation in m‐out‐of‐n systems: A preventive approach

Behboudi

Borzadaran

Asadi

2022

Appl Stoch Models Bus & Ind

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This article investigates an optimal preventive standby activation policy for an m$$ m $$‐out‐of‐n$$ n $$ redundant system. We assume that for such a system, which starts operating at time t=0$$ t=0 $$, a standby component will be activated at either the failure time of the system or at a predetermined time τ$$ \tau $$, whichever occurs first. We first obtain the system reliability function under this switching policy as a function of τ$$ \tau $$. Then, we investigate the optimal switching time τ$$ \tau $$ so that the mean time to failure of the system is maximized. The results indicate that the existence of an optimal value of τ$$ \tau $$ depends on the lifetime of the standby redundancy and its virtual age in the standby state. Some illustrative examples are presented to examine the theoretical outcomes.

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“…However, the discrete models occur very often, for example, when the system performs a task repetitively and its components have certain probabilities of breakdown upon each cycle or when the component lifetimes represent the numbers of turn-on and switch-off up to failures. Reliability properties of coherent systems composed of components with discrete lifetimes have been investigated by Weiss (1962), Young (1970), Tank and Eryilmaz (2015), Dembińska (2018), Dembińska et al (2021), Davies and Dembińska (2019) and Dembińska and Goroncy (2020). Dembińska and Jasiński (2020) studied maximum likelihood estimation based on discrete component lifetimes of a k-out-of-n system.…”

Section: Introductionmentioning

confidence: 99%

The number of failed components in a coherent working system when the lifetimes are discretely distributed

Jasiński

2021

Metrika

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In this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

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Reliability properties of k-out-of-n systems with one cold standby unit

Cited by 23 publications

References 25 publications

Performance Modeling and Estimation of Serial System Exhibiting k-out-of-n: G Scheme with Controller Failure

Performance Modeling and Estimation of Serial System Exhibiting k-out-of-n: G Scheme with Controller Failure

Optimal standby activation in m‐out‐of‐n systems: A preventive approach

The number of failed components in a coherent working system when the lifetimes are discretely distributed

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