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Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart

机译：使用基于小波的无分布CUSUM图表监视非线性轮廓

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摘要

WDFTC is a wavelet-based distribution-free CUSUM chart for detecting shifts in the mean of a profile with noisy components. Exploiting a discrete wavelet transform (DWT) of the mean in-control profile, WDFTC selects a reduced-dimension vector of the associated DWT components from which the mean in-control profile can be approximated with minimal weighted relative reconstruction error. Based on randomly sampled Phase I (in-control) profiles, the covariance matrix of the corresponding reduced-dimension DWT vectors is estimated using a matrix-regularisation method; then the DWT vectors are aggregated (batched) so that the non-overlapping batch means of the reduced-dimension DWT vectors have manageable covariances. To monitor shifts in the mean profile during Phase II operation, WDFTC computes a Hotelling's T~2-type statistic from successive non-overlapping batch means and applies a CUSUM procedure to those statistics, where the associated control limits are evaluated analytically from the Phase I data. Experimentation with several normal and non-normal test processes revealed that WDFTC was competitive with existing profile-monitoring schemes.
机译：WDFTC是基于小波的无分布CUSUM图表，用于检测带有噪声成分的配置文件平均值的变化。利用平均控制内轮廓的离散小波变换（DWT），WDFTC选择相关DWT组件的降维矢量，从中可以用最小的加权相对重建误差来近似平均控制内轮廓。基于随机采样的I相（在控制中）配置文件，使用矩阵正则化方法估算相应的降维DWT向量的协方差矩阵；然后对DWT向量进行汇总（批处理），以使降维DWT向量的不重叠批均值具有可管理的协方差。为了监视第二阶段操作期间平均轮廓的变化，WDFTC从连续的非重叠批均值计算出Hotelling的T〜2型统计量，并对这些统计量应用CUSUM程序，其中从第一阶段分析地评估相关的控制极限数据。对几种正常和非正常测试过程的实验表明，WDFTC与现有的配置文件监视方案相比具有竞争力。

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  • 来源
    《International Journal of Production Research》 |2012年第24期|6574-6594|共21页
  • 作者

    Joongsup (Jay) Lee; Youngmi Hur; Seong-Hee Kim; James R. Wilson;

  • 作者单位

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;

    Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218-2682, USA;

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;

    Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    SPC; quality control; statistical methods; profile; CUSUM chart; wavelet transform;

    机译：SPC;质量控制;统计方法;轮廓;CUSUM图表;小波变换;

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