Hazard Rate Order Between Parallel Systems With Multiple Types of Scaled Components

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Khaled Masoumifard, Abedin Haidari, Nuria Torrado
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引用次数: 0

Abstract

This study delves into the comparison of two parallel systems, each composed of multiple component types following the scale models with a shared baseline distribution. Under some assumptions imposed on the baseline distribution, it is shown that a restricted version of the p $$ p $$ -larger order between the scale parameter vectors implies the hazard rate order between the system lifetimes, provided that the allocation vectors of the two systems are the same. Additionally, we explore scenarios where one system embodies heterogeneous scale parameters, whereas the other adopts homogeneous ones, examining the hazard rate order between their lifetimes. For the case when the scale vectors of the two systems are the same, it is shown under some assumptions on the baseline distribution that the weak supermajorization order between the allocation vectors results in the reversed hazard rate order between the system lifetimes. Under more restrictions on the allocation vectors, an extension of this result to the likelihood ratio order is also established. Our discussion also highlights the fulfillment of these assumptions by well-known lifetime distributions such as Feller-Pareto, generalized gamma, power-generalized Weibull, exponentiated Weibull, and half-normal distributions. The findings of this work contribute to addressing gaps in the understanding of stochastic orderings between parallel systems and further refine prior research in this domain. Furthermore, the results provide a foundation for practical applications, such as optimizing resource allocation and reliability assessment in engineering and operational contexts.

具有多种比例元件的并联系统间的危险率顺序
本研究深入研究了两个并行系统的比较,每个系统由多个组件类型组成,遵循具有共享基线分布的比例模型。在对基线分布施加一些假设的情况下,如果两个系统的分配向量相同,则尺度参数向量之间的p $$ p $$ -较大阶数的限制版本意味着系统生命周期之间的危险率阶数。此外,我们探讨了一个系统包含异质尺度参数,而另一个系统采用同质尺度参数的情况,检查了它们的生命周期之间的危险率顺序。对于两个系统的尺度向量相同的情况,在基线分布的某些假设下,分配向量之间的弱超多数顺序导致系统生命周期之间的危险率顺序相反。在对分配向量有更多限制的情况下,将这一结果推广到似然比阶。我们的讨论还强调了众所周知的寿命分布(如Feller-Pareto、广义伽马、幂广义威布尔、指数威布尔和半正态分布)对这些假设的满足。这项工作的发现有助于解决并行系统之间随机排序的理解差距,并进一步完善该领域的先前研究。此外,研究结果为工程和操作环境中的资源优化分配和可靠性评估等实际应用提供了基础。
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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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