A closed-form equation for steady-state availability of cold standby repairable <i>k</i>-out-of-<i>n</i>

Yaghoubi, Afshin; Niaki, Seyed Taghi Akhavan; Rostamzadeh, Hadi

doi:10.1108/ijqrm-08-2018-0212

Cited by 7 publications

(4 citation statements)

References 26 publications

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“…These units can replace any failing components flexibly based on the timing of the damage, thereby extending the mean time to failure (MTTF) of the system. Yaghoubi et al [5] applied Markov's method to derive the reliability of an (n − k) series standby system, using an exponential distribution to model faults and failures. This approach also led to a closed-form expression for the steady-state reliability of a system with (n − k) cold spares and k parts operating in parallel.…”

Section: Introductionmentioning

confidence: 99%

Reliability and Residual Life of Cold Standby Systems

Liu,

Ai,

2024

Mathematics

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In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.

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Section: Introductionmentioning

confidence: 99%

Reliability and Residual Life of Cold Standby Systems

Liu,

Ai,

2024

Mathematics

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“…Yaghoubi et al [ 11 ] introduced quantitative tools using the Markov method and improved the quality of the oil product line. The Markov model applications also include battery production systems [ 12 ], machine tool modeling [ 13 ], k-out-of-n systems [ 14 , 15 ], reconfigurable production systems [ 16 ], maintenance policy [ 17 ], re-entrant production systems [ 18 ], primary care [ 19 ], rolling bearing monitoring [ 20 ], industrial network models [ 21 ], assembly assistance systems [ 22 ], laser-based manufacturing process [ 23 ], and the steel production process [ 24 , 25 ].…”

Section: Introductionmentioning

confidence: 99%

A Novel Analytical Modeling Approach for Quality Propagation of Transient Analysis of Serial Production Systems

Liu

et al. 2022

Sensors

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Production system modeling (PSM) for quality propagation involves mapping the principles between components and systems. While most existing studies focus on the steady-state analysis, the transient quality analysis remains largely unexplored. It is of significance to fully understand quality propagation, especially during transients, to shorten product changeover time, decrease quality loss, and improve quality. In this paper, a novel analytical PSM approach is established based on the Markov model, to explore product quality propagation for transient analysis of serial multi-stage production systems. The cascade property for quality propagation among correlated sequential stages was investigated, taking into account both the status of the current stage and the quality of the outputs from upstream stages. Closed-form formulae to evaluate transient quality performances of multi-stage systems were formulated, including the dynamics of system quality, settling time, and quality loss. An iterative procedure utilizing the aggregation technique is presented to approximate transient quality performance with computational efficiency and high accuracy. Moreover, system theoretic properties of quality measures were analyzed and the quality bottleneck identification method was investigated. In the case study, the modeling error was 0.36% and the calculation could clearly track system dynamics; quality bottleneck was identified to decrease the quality loss and facilitate continuous improvement. The experimental results illustrate the applicability of the proposed PSM approach.

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“…The units in the cold standby state are passive and unpowered; as long as they are put in this condition, they will not be damaged. Therefore, a cold standby component is protected from any tension, and as long as it is in this state, its failure rate is assumed to be zero (Wang et al ., 2021; Yaghoubi et al ., 2020; Akhavan Niaki and Yaghoubi, 2021).…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of a two-unit‏ ‏standby system under Marshall–Olkin dependency

Yaghoubi

Niaki

2022

IJQRM

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PurposeOne of the common approaches to improve systems reliability is using standby redundancy. Although many works are available in the literature on the applications of standby redundancy, the system components are assumed to be independent of each other. But, in reality, the system components can be dependent on one another, causing the failure of each component to affect the failure rate of the remaining active components. In this paper, a standby two-unit system is considered, assuming a dependency between the switch and its associated active component.Design/methodology/approachThis paper assumes that the failures between the switch and its associated active component follow the Marshall–Olkin exponential bivariate exponential distribution. Then, the reliability analysis of the system is done using the continuous-time Markov chain method.FindingsThe derived equations application to determine the system steady-state availability, system reliability and sensitivity analysis on the mean time to failure is demonstrated using a numerical illustration.Originality/valueAll previous models assumed independency between the switch and the associated active unit in the standby redundancy approach. In this paper, the switch and its associated component are assumed to be dependent on each other.

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A closed-form equation for steady-state availability of cold standby repairable k-out-of-n

Cited by 7 publications

References 26 publications

Reliability and Residual Life of Cold Standby Systems

Reliability and Residual Life of Cold Standby Systems

A Novel Analytical Modeling Approach for Quality Propagation of Transient Analysis of Serial Production Systems

Reliability analysis of a two-unit‏ ‏standby system under Marshall–Olkin dependency

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