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Some Charting Methodologies in MSPC.

机译：MSPC中的某些制图方法。

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摘要

We consider statistical process control (SPC) for phase II monitoring of the process mean when process measurements are multivariate. In cases when the direction of a potential mean shift is known, Healy (1987) generalized the univariate cumulative sum (CUSUM) chart to multivariate cases, using the likelihood ratio inferences, and the generalized CUSUM chart was shown to be efficient. Other existing multivariate control charts usually do not use any prior information about the potential mean shift, making them less efficient in cases when such prior information is available. We first suggest a multivariate CUSUM chart for applications in which the mean shift direction is not completely known but it follows a prior distribution. This chart can be regarded as a compromise of Healy's CUSUM chart and other existing multivariate control charts, in terms of proper accommodation of prior information about the potential shift. Numerical studies show that it performs well in cases when such prior information is available.;Conventional multivariate SPC charts, such as the Crosier's CUSUM and the multivariate EWMA charts, can only give signals of mean shift, and they cannot tell us which components of the response have shifted and what type of shift (e.g., upward or downward shift) has occurred. We second propose a CUSUM chart based on the maximum and minimum of the process response components, which is labeled as the MM-CUSUM chart and which reduces the dimension of the monitoring problem to 2. Since the maximum of the response components is sensitive to upward mean shifts, and the minimum is sensitive to downward mean shifts, this chart can not only give a signal of mean shift but also tell us whether the shift is upward or downward. By tracking the frequency of each component being the maximum or the minimum across all time points, we can further determine the likelihood of each component being shifted. In cases when the process response components have a lower or upper bound, which is common in practice (e.g., the economic indices are always non-negative), the MM-CUSUM chart would be especially efficient.
机译：当过程测量值是多变量时，我们将统计过程控制（SPC）用于过程平均值的第二阶段监视。在已知潜在均值移动方向的情况下，Healy（1987）使用似然比推论将单变量累积总和（CUSUM）图推广到多变量情况，并且表明广义CUSUM图是有效的。其他现有的多元控制图通常不使用有关潜在均值漂移的任何先验信息，从而在此类先验信息可用的情况下使它们的效率降低。我们首先为应用提供一个多元CUSUM图表，在该应用中平均移动方向尚不完全清楚，但遵循先验分布。就适当地容纳有关潜在变动的先验信息而言，该图表可以视为Healy CUSUM图表和其他现有的多元控制图的折衷。数值研究表明，在可以获得此类先验信息的情况下，该方法性能良好。传统的多元SPC图表（例如Crosier的CUSUM和多元EWMA图表）只能给出均值漂移信号，而不能告诉我们变量的哪些成分响应已经转移，发生了什么类型的转移（例如，向上或向下转移）。我们第二次基于过程响应组件的最大值和最小值提出一个CUSUM图表，该图表被标记为MM-CUSUM图表，并且将监视问题的范围减小到2。由于响应组件的最大值对向上敏感均值漂移，最小值对均值漂移很敏感，此图不仅可以给出均值漂移的信号，还可以告诉我们该变化是向上还是向下。通过跟踪所有时间点上每个分量的频率为最大值或最小值，我们可以进一步确定每个分量发生偏移的可能性。在过程响应组件具有下限或上限的情况下（这在实践中很常见）（例如，经济指标始终为非负数），MM-CUSUM图将特别有效。

著录项

  • 作者

    Liu, Wei.;

  • 作者单位

    University of Minnesota.;

  • 授予单位 University of Minnesota.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 145 p.
  • 总页数 145
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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