Combined class of distributions with an exponentiated Weibull family for reliability application

IF 2.3 2区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality Technology and Quantitative Management Pub Date : 2022-11-06 DOI:10.1080/16843703.2022.2138111

Minjae Park

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引用次数: 0

Abstract

ABSTRACT We develop a novel class of distributions after the exponentiated Weibull family and vtub-shaped failure rate for systems are considered and compounded together. This combined class of distributions can be applied to reliability applications using the data, and we investigate its properties. We study the mathematical properties of combined distributions including order statistics and estimation by maximum likelihood. In addition, we implement an EM algorithm to determine unknown parameters using maximum likelihood estimates, and maximum entropy characterizations are discussed under appropriate constraints. Using maximum likelihood estimation, we obtain point estimates and interval estimation for parameters. We develop a novel approach to measuring the reliability of multi-component systems as well as a single-component system and illustrate the usefulness of the proposed approach. We apply the approach to real data sets and discuss numeric examples to show the statistical properties of the new compounding class of distributions derived in the paper.

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一类具有指数威布尔族的组合分布在可靠性应用中

在综合考虑指数威布尔族和vtub形故障率的基础上，提出了一类新的分布。这类组合分布可以应用于使用数据的可靠性应用，我们研究了它的性质。研究了组合分布的数学性质，包括序统计量和极大似然估计。此外，我们实现了一种EM算法，利用最大似然估计来确定未知参数，并讨论了在适当约束下的最大熵表征。利用极大似然估计，得到了参数的点估计和区间估计。我们开发了一种新的方法来测量多组件系统以及单组件系统的可靠性，并说明了所提出方法的实用性。我们将该方法应用于实际数据集，并讨论了数值例子来说明本文导出的新复合类分布的统计性质。

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来源期刊

Quality Technology and Quantitative Management ENGINEERING, INDUSTRIAL-OPERATIONS RESEARCH & MANAGEMENT SCIENCE

CiteScore

5.10

自引率

21.40%

发文量

审稿时长

>12 weeks

期刊介绍： Quality Technology and Quantitative Management is an international refereed journal publishing original work in quality, reliability, queuing service systems, applied statistics (including methodology, data analysis, simulation), and their applications in business and industrial management. The journal publishes both theoretical and applied research articles using statistical methods or presenting new results, which solve or have the potential to solve real-world management problems.