利用贝叶斯因子监测高斯过程均值的两种贝叶斯方法

IF 2.2 3区工程技术 Q3 ENGINEERING, INDUSTRIAL

Quality and Reliability Engineering International Pub Date : 2024-05-04 DOI:10.1002/qre.3567

Yaxin Tan, Amitava Mukherjee, Jiujun Zhang

{"title":"利用贝叶斯因子监测高斯过程均值的两种贝叶斯方法","authors":"Yaxin Tan, Amitava Mukherjee, Jiujun Zhang","doi":"10.1002/qre.3567","DOIUrl":null,"url":null,"abstract":"This paper develops two novel process monitoring schemes for the mean of a Gaussian process: the Bayes factor (BF) and the improved Bayes factor (IBF) schemes. Conjugate priors are used to construct the plotting statistics. The performance of the proposed schemes is evaluated in terms of average run length (ARL), standard deviation of run length (SDRL), and several percentiles, and these performance metrics across different hyper‐parameters and various sample sizes are evaluated via Monte Carlo simulations. Both zero‐state and steady‐state out‐of‐control (OOC) performances are investigated comprehensively. The simulation results show that the IBF scheme outperforms the existing Bayesian exponentially weighted moving average (EWMA) schemes under different loss functions in zero‐state. In steady‐state conditions, the IBF scheme outperforms for small shifts. Finally, we present two examples to illustrate the practical application of the proposed schemes.","PeriodicalId":56088,"journal":{"name":"Quality and Reliability Engineering International","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two Bayesian approaches of monitoring mean of Gaussian process using Bayes factor\",\"authors\":\"Yaxin Tan, Amitava Mukherjee, Jiujun Zhang\",\"doi\":\"10.1002/qre.3567\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper develops two novel process monitoring schemes for the mean of a Gaussian process: the Bayes factor (BF) and the improved Bayes factor (IBF) schemes. Conjugate priors are used to construct the plotting statistics. The performance of the proposed schemes is evaluated in terms of average run length (ARL), standard deviation of run length (SDRL), and several percentiles, and these performance metrics across different hyper‐parameters and various sample sizes are evaluated via Monte Carlo simulations. Both zero‐state and steady‐state out‐of‐control (OOC) performances are investigated comprehensively. The simulation results show that the IBF scheme outperforms the existing Bayesian exponentially weighted moving average (EWMA) schemes under different loss functions in zero‐state. In steady‐state conditions, the IBF scheme outperforms for small shifts. Finally, we present two examples to illustrate the practical application of the proposed schemes.\",\"PeriodicalId\":56088,\"journal\":{\"name\":\"Quality and Reliability Engineering International\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quality and Reliability Engineering International\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/qre.3567\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, INDUSTRIAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quality and Reliability Engineering International","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/qre.3567","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}

引用次数: 0

摘要

本文针对高斯过程的均值开发了两种新型过程监测方案：贝叶斯因子（BF）和改进贝叶斯因子（IBF）方案。共轭先验用于构建绘图统计。通过蒙特卡洛模拟评估了不同超参数和不同样本量下的这些性能指标。对零状态和稳态失控（OOC）性能进行了全面研究。仿真结果表明，在零状态下的不同损失函数条件下，IBF 方案优于现有的贝叶斯指数加权移动平均（EWMA）方案。在稳态条件下，IBF 方案在小幅移动时的表现优于现有方案。最后，我们举了两个例子来说明所提方案的实际应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Two Bayesian approaches of monitoring mean of Gaussian process using Bayes factor

This paper develops two novel process monitoring schemes for the mean of a Gaussian process: the Bayes factor (BF) and the improved Bayes factor (IBF) schemes. Conjugate priors are used to construct the plotting statistics. The performance of the proposed schemes is evaluated in terms of average run length (ARL), standard deviation of run length (SDRL), and several percentiles, and these performance metrics across different hyper‐parameters and various sample sizes are evaluated via Monte Carlo simulations. Both zero‐state and steady‐state out‐of‐control (OOC) performances are investigated comprehensively. The simulation results show that the IBF scheme outperforms the existing Bayesian exponentially weighted moving average (EWMA) schemes under different loss functions in zero‐state. In steady‐state conditions, the IBF scheme outperforms for small shifts. Finally, we present two examples to illustrate the practical application of the proposed schemes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quality and Reliability Engineering International 管理科学-工程：工业

CiteScore

4.90

自引率

21.70%

发文量

181

审稿时长

6 months

期刊介绍： Quality and Reliability Engineering International is a journal devoted to practical engineering aspects of quality and reliability. A refereed technical journal published eight times per year, it covers the development and practical application of existing theoretical methods, research and industrial practices. Articles in the journal will be concerned with case studies, tutorial-type reviews and also with applications of new or well-known theory to the solution of actual quality and reliability problems in engineering. Papers describing the use of mathematical and statistical tools to solve real life industrial problems are encouraged, provided that the emphasis is placed on practical applications and demonstrated case studies. The scope of the journal is intended to include components, physics of failure, equipment and systems from the fields of electronic, electrical, mechanical and systems engineering. The areas of communications, aerospace, automotive, railways, shipboard equipment, control engineering and consumer products are all covered by the journal. Quality and reliability of hardware as well as software are covered. Papers on software engineering and its impact on product quality and reliability are encouraged. The journal will also cover the management of quality and reliability in the engineering industry. Special issues on a variety of key topics are published every year and contribute to the enhancement of Quality and Reliability Engineering International as a major reference in its field.