基于B样条和聚类分析的非参数轮廓监控方法研究

doi:10.12005/orms.2021.0148

运筹与管理 ›› 2021, Vol. 30 ›› Issue (5): 79-87.DOI: 10.12005/orms.2021.0148

基于B样条和聚类分析的非参数轮廓监控方法研究

聂斌, 叶文静, 刘迪青, 刘晓卉

天津大学管理与经济学部,天津 300072

收稿日期:2019-05-16 出版日期:2021-05-25
通讯作者: 叶文静(1995-),女,福建人,硕士研究生,主要研究方向:统计过程控制、轮廓监控。
作者简介:聂斌(1971-),男,天津人,天津大学副教授,博士,主要研究方向:统计过程控制、实验设计和可靠性工程。
基金资助:
国家自然科学基金面上项目(71672122)

Nonparametric Profile Monitoring Using B-spline and Clustering Analysis

NIE Bin, YE Wen-jing, LIU Di-qing, LIU Xiao-hui

College of Management and Economics, Tianjin University, Tianjin 300072, China

Received:2019-05-16 Online:2021-05-25

摘要/Abstract

摘要： 在轮廓监控中,产品或过程的质量特征可以由一种特定的函数关系表示。如果轮廓的函数形式是已知的,则可以使用参数化方法来监控轮廓。然而,当轮廓形态复杂时,继续使用参数方法则可能导致由于模型设定不准确而无法正确识别异常轮廓的问题。因此本文提出了一种基于非参数回归的新方法以解决制造过程中常见的复杂轮廓监控问题。所提方法将基于非参数回归的B样条与迭代的聚类分析过程相结合,在应用过程中不需要对轮廓的形式进行限制性假设。仿真研究评估了该监控方法在不同变异情况下的性能,并且通过与现有方法的比较分析,验证了该方法的有效性和优越性。最后通过轮廓监控领域的一个经典案例说明了新方法的实际应用效果。

关键词: B样条, K-means, T²统计量, 轮廓监控, 统计过程控制

Abstract: When process or product data follow a particular curve in quality control, profile monitoring is suitable and appropriate for assessing and diagnosing quality status. If the functional form of the profile is known, parametric methods could be used to monitor the profile. However, when the profilehas complex shape, parametric methods may result in the problem that the outliers cannot be correctly detected due to the misspecified model. Therefore, this article proposes a novel approach based on nonparametric regression to monitor the phase I process for complex profiles. This approach combines the B-spline based on nonparametric regression with the modified cluster analysis process, and does not require restrictive assumptions on the form of the profile in the application. Our simulation study analyzes the performance of the proposed approach under different circumstances, and the effectiveness and applicability of the approach are verified by comparison with the existing approaches. Finally, a classic case in the field of profile T² monitoring is used to illustrate the practical application of the novel approach in this article.

Key words: B-spline, K-means, T² statistics, profile monitoring, statistical process control

中图分类号:

C931.1

聂斌, 叶文静, 刘迪青, 刘晓卉. 基于B样条和聚类分析的非参数轮廓监控方法研究[J]. 运筹与管理, 2021, 30(5): 79-87.

NIE Bin, YE Wen-jing, LIU Di-qing, LIU Xiao-hui. Nonparametric Profile Monitoring Using B-spline and Clustering Analysis[J]. Operations Research and Management Science, 2021, 30(5): 79-87.

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基于B样条和聚类分析的非参数轮廓监控方法研究

Nonparametric Profile Monitoring Using B-spline and Clustering Analysis

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