| 多元统计过程控制方法的平方预测误差分析 |
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| 引用本文： | 冯雄峰,阳宪惠,徐用懋. 多元统计过程控制方法的平方预测误差分析[J]. 清华大学学报(自然科学版), 1999, 39(7): 274 |
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| 作者姓名： | 冯雄峰 阳宪惠 徐用懋 |
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| 作者单位： | 清华大学,自动化系,北京,100084 |
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| 基金项目： | 国家“八六三”高技术研究课题 |
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| 摘 要： | 作为多元统计过程控制方法中的常用统计量，平方预测误差（ Ｓ Ｐ Ｅ）的变化规律有待深入研究。介绍了主元分析建模方法，推导了 Ｓ Ｐ Ｅ均值公式，分析了 Ｓ Ｐ Ｅ均值和过程变量均值向量、协方差矩阵之间的解析关系，用来自 ３ 阶液位系统的仿真数据验证了分析的结果。给出了 Ｓ Ｐ Ｅ随过程变量均值向量、协方差矩阵变化而变化的若干规律，说明了这些规律在生产过程监控应用中的意义。
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| 关 键 词： | 多元统计过程控制 平方预测误差 主元分析 过程监控 |
| 修稿时间： | 1998-05-30 |
Squared prediction error analysis of multivariate statistical process control |
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| FENG Xiongfeng,YANG Xianhui,XU Yongmao. Squared prediction error analysis of multivariate statistical process control[J]. Journal of Tsinghua University(Science and Technology), 1999, 39(7): 274 |
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| Authors: | FENG Xiongfeng YANG Xianhui XU Yongmao |
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| Abstract: | Squared prediction error (SPE) statistic is frequently used in multivariate statistical process control and its law of variation needs further investigating. The modelling method of principal component analysis (PCA) is introduced. The mean equation of SPE is developed. The analytical relationships of SPE mean and process variables mean and covariance matrix are analyzed. Simulation data from a 3rd order level system are used to validate the results obtained. Some laws of variation of the SPE mean under the variation of mean and covariance matrix of process variables are given. The significance of the laws in the application of process monitoring is explained. |
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| Keywords: | multivariate statistical process control squared prediction error (SPE) principal component analysis process monitoring |
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