Ong Hong Choon, Alih Ekele
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia.
PLoS One. 2015 Apr 29;10(4):e0125835. doi: 10.1371/journal.pone.0125835. eCollection 2015.
The tendency for experimental and industrial variables to include a certain proportion of outliers has become a rule rather than an exception. These clusters of outliers, if left undetected, have the capability to distort the mean and the covariance matrix of the Hotelling's T2 multivariate control charts constructed to monitor individual quality characteristics. The effect of this distortion is that the control chart constructed from it becomes unreliable as it exhibits masking and swamping, a phenomenon in which an out-of-control process is erroneously declared as an in-control process or an in-control process is erroneously declared as out-of-control process. To handle these problems, this article proposes a control chart that is based on cluster-regression adjustment for retrospective monitoring of individual quality characteristics in a multivariate setting. The performance of the proposed method is investigated through Monte Carlo simulation experiments and historical datasets. Results obtained indicate that the proposed method is an improvement over the state-of-art methods in terms of outlier detection as well as keeping masking and swamping rate under control.
实验变量和工业变量中包含一定比例异常值的趋势已成为一种常态而非例外。这些异常值集群如果未被检测到，就有可能扭曲为监测个体质量特征而构建的霍特林T2多元控制图的均值和协方差矩阵。这种扭曲的影响是，由此构建的控制图变得不可靠，因为它会出现掩盖和淹没现象，即一个失控过程被错误地判定为受控过程，或者一个受控过程被错误地判定为失控过程。为了解决这些问题，本文提出了一种基于聚类回归调整的控制图，用于在多元环境中对个体质量特征进行回顾性监测。通过蒙特卡罗模拟实验和历史数据集对所提方法的性能进行了研究。所得结果表明，所提方法在异常值检测以及控制掩盖和淹没率方面优于现有方法。
