串并联系统的冗余分配:一种基于copula的方法

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Ravi Kumar, T. V. Rao, Sameen Naqvi
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引用次数: 0

摘要

为系统分配冗余组件是提高系统寿命的常用方法。本研究通过假设冗余和组件是相关的,探讨了具有两个组件的串联和并联系统中冗余的最优分配。也就是说,我们在组件水平上对两个冗余的情况下的串联(并联)系统进行随机比较。具体来说,我们研究了三种情况下的随机比较:(i)组件(和冗余)具有依赖的寿命,但彼此独立,组件(冗余)在两个生成的系统中具有相同的边际分布;(ii)组件(和冗余)具有依赖的寿命并且彼此独立,但组件(冗余)的边际分布在两个生成的系统中是不同的;(3)组件和冗余是相互依赖的,两个生成系统中组件(冗余)的边际是相同的。在本研究中,我们使用copula的概念对相关性进行建模,并使用广义扭曲分布函数进行所需的随机比较。此外,我们通过各种实例和反例来证明我们的发现。最后,我们提供了一个基于模拟的研究和一个真实的数据分析来说明我们的发现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Redundancy Allocation for Series and Parallel Systems: A Copula-Based Approach

The allocation of redundant components to a system is a common method for enhancing the system's lifetime. This study explores the optimal allocation of redundancies in series and parallel systems with two components by assuming components and redundancies are dependent. That is, we perform the stochastic comparisons of the series (parallel) systems in the case of two redundancies at the component level. Specifically, we examine the stochastic comparisons across three scenarios: (i) components (and redundancies) have dependent lifetimes but are independent of each other, and components (redundancies) have identical marginal distributions in the two generated systems; (ii) components (and redundancies) have dependent lifetimes and are independent of each other, but the marginal distributions of components (redundancies) are different in the two generated system; and (iii) components and redundancies are interdependent and the marginals of the components (redundancies) in the two generated systems are same. In this study, we model the dependency using the concept of copula and perform the desired stochastic comparisons using generalized distorted distribution functions. Furthermore, we demonstrate our findings through various examples and counterexamples. Finally, we provide a simulation-based study and a real data analysis to illustrate our findings.

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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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