On optimal grouping and stochastic comparisons for heterogeneous items

Hazra, Nil Kamal; Finkelstein, Maxim; Hwan, Ji

doi:10.1016/j.jmva.2017.06.006

Cited by 26 publications

(18 citation statements)

References 4 publications

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“…Recently, Hazra et al (2017) dealt with the problem of random assembling through the viewpoint of 'optimal grouping of components'. In their framework, it was assumed that there are m clusters of components, and all components in the same cluster have independent and identically distributed lifetimes, while components coming from different clusters could have different lifetime distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Following the notation in Hazra et al (2017), we denote the two-stage sampling model as M m n (d | , p, q), where q is the component reliabilities of the m clusters, p is the sampling probabilities, and…”

Section: Introductionmentioning

confidence: 99%

“…The model with d = 1 and m = n is called 'mixing at the system level', whereas the model with d = m = n is called 'mixing at the component level'. Focusing on series and parallel systems constructed from admissible two-stage sampling models, Hazra et al (2017) investigated how the variation of selecting strategy and sampling probabilities p have an impact on the reliability of the resulting series and parallel systems. However, not much is known for coherent systems having a more general structure, such as the k-out-of-n system.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we aim to further probe into the effects of different two-stage sampling strategies on the reliability of k-out-of-n systems. We will tackle this problem through a static and classic viewpoint, instead of the dynamic one focusing on stochastic behavior as the time varies employed in Hazra et al (2017). Overall, we generalize the work of Hazra et al (2017) to a more general k-out-of-n framework.…”

Section: Introductionmentioning

confidence: 99%

“…We will tackle this problem through a static and classic viewpoint, instead of the dynamic one focusing on stochastic behavior as the time varies employed in Hazra et al (2017). Overall, we generalize the work of Hazra et al (2017) to a more general k-out-of-n framework. Specifically, we fix the component reliabilities and study how the corresponding system reliability changes under different two-stage sampling models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Reliability analysis of k-out-of-n systems based on a grouping of components

2019

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In this paper we treat a two-stage grouping procedure of building a k-out-of-n system from several clusters of components. We use a static framework in which the component reliabilities are fixed. Under such a framework, we address the impact of the selecting strategies, the sampling probabilities, and the component reliabilities on the constructed system’s reliability. An interesting finding is that the level of component reliabilities could be identified as a decisive factor in determining how the selecting strategies and the component reliabilities affect the system reliability. The new results generalize and extend those established earlier in the literature such as Di Crescenzo and Pellerey (2011), Hazra and Nanda (2014), Navarro, Pellerey, and Di Crescenzo (2015), and Hazra, Finkelstein, and Cha (2017). Several Monte Carlo simulation experiments are provided to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reliability analysis of k-out-of-n systems based on a grouping of components

2019

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Stochastic comparisons of coherent systems with active redundancy at the component or system levels and component lifetimes following the accelerated life model

Panja,

Kundu,

Pradhan

2023

Appl Stoch Models Bus & Ind

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An effective way to increase system reliability is to use redundancies (spares) into the systems either in component level or in system level. In this prospect, it is a significant issue that which set of available spares providing better system reliability in some stochastic sense. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provide better system reliability than that of the system with another set of redundancy, with respect some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model. The results obtained help us to design more reliable systems by allocating appropriate redundant components from the set of available options for the same. Various examples satisfying the sufficient conditions of the theoretical results are provided. Some results are illustrated with real‐world data.

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On optimal allocation of redundancies in random weighted k$$ k $$‐out‐of‐n$$ n $$ systems

Sahoo,

Hazra

2024

Appl Stoch Models Bus & Ind

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Random weighted ‐out‐of‐ systems are very useful in modeling the lifetimes of systems, wherein the success or failure of a system depends not only on its current operational status, but also on the contributions made by its components. In this paper, we consider random weighted ‐out‐of‐ systems with redundant components drawn randomly from a mixed population consisting of different subpopulations/substocks. We study different optimal allocation policies of active redundancies and minimal repair components in a random weighted ‐out‐of‐ system. Moreover, we investigate how the heterogeneity of subpopulations of items impacts the lifetime of a random weighted ‐out‐of‐ system. We also present some simulational results and a real data analysis for illustrative purpose.

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On optimal grouping and stochastic comparisons for heterogeneous items

Cited by 26 publications

References 4 publications

Reliability analysis of k-out-of-n systems based on a grouping of components

Reliability analysis of k-out-of-n systems based on a grouping of components

Stochastic comparisons of coherent systems with active redundancy at the component or system levels and component lifetimes following the accelerated life model

On optimal allocation of redundancies in random weighted k$$ k $$‐out‐of‐n$$ n $$ systems

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