A Multivariate Sign EWMA Control Chart
A Multivariate Sign EWMA Control Chart
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DOI：
10.1198/tech.2010.09095
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发表时间：
2011-02
期刊：
影响因子：
2.5
通讯作者：
Changliang Zou;F. Tsung
中科院分区：
文献类型：
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作者：
Changliang Zou;F. Tsung
在统计过程控制（SPC）中，当对底层过程分布缺乏或了解有限时，特别是当过程测量是多变量时，非参数控制图非常有用。本文提出了一种新的多变量SPC方法监测位置参数。它是基于适应一个强大的多元符号测试在线顺序监测。加权版本的符号检验是用来制定图表统计量，通过将指数加权移动平均控制（EWMA）计划，这导致在一个非参数对应的经典的多元EWMA（MEWMA）。它是仿射不变的，并且在广泛的一类人口模型上具有严格的分布自由性质。也就是说，当使用为多元正态分布设计的相同控制限时，受控（IC）运行长度分布可以达到（或始终非常接近）标称值。此外，当过程分布来自椭圆方向类时，IC平均游程长度可以通过一维马尔可夫链模型计算。该控制图还具有一些其他有利的功能：计算速度快，计算量与MEWMA图相似;它很容易实现，因为只需要指定多元中位数和相关的变换矩阵（估计）来自监测前的历史数据;它在检测过程偏移，特别是当过程分布是重尾或偏斜时的小或中等偏移方面也是非常有效的。两个制造业的实际数据例子表明，它在应用中表现得很好。这篇文章在网上有补充材料。
Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameters. It is based on adapting a powerful multivariate sign test to online sequential monitoring. The weighted version of the sign test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). It is affine-invariant and has a strictly distribution-free property over a broad class of population models. That is, the in-control (IC) run length distribution can attain (or is always very close to) the nominal one when using the same control limit designed for a multivariate normal distribution. Moreover, when the process distribution comes from the elliptical direction class, the IC average run length can be calculated via a one-dimensional Markov chain model. This control chart possesses some other favorable features: it is fast to compute with a similar computational effort to the MEWMA chart; it is easy to implement because only the multivariate median and the associated transformation matrix need to be specified (estimated) from the historical data before monitoring; it is also very efficient in detecting process shifts, particularly small or moderate shifts when the process distribution is heavy tailed or skewed. Two real-data examples from manufacturing show that it performs quite well in applications. This article has supplementary material online.