Since the pioneering works by Nomikos and MacGregor, the Batch Multivariate Statistical Process Control (BMSPC) methodology has been extensively revised, and a sheer number of alternative monitoring approaches have been suggested. The different approaches vary in the batch data alignment, the pre‐processing approach, the data arrangement, and/or the type of model used, from two‐way to three‐way and from linear to nonlinear. One of the most accepted pre‐processing schemes, referred to as the trajectory centering and scaling (TCS), is based on the normalization to zero mean and unit variance around the average trajectory. However, the main drawback of TCS is the inherent increase of the level of uncertainty in the estimation of model parameters. In this work, we illustrate how to improve parameter estimation while maintaining the good properties of this pre‐processing approach. This enhancement is achieved with the new pre‐processing approach we call PARAMO, which uses more observations than TCS to estimate the pre‐processing parameters. We show that this improvement favorably impacts the performance of the monitoring system. The results of this research work affect a large amount of the monitoring approaches proposed to date, and we advocate that the pre‐processing procedure proposed here should be generally applied in BMSPC.

中文翻译：

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PARAMO：批处理多变量统计过程控制中的增强数据预处理

自从 Nomikos 和 MacGregor 的开创性工作以来，批量多变量统计过程控制 (BMSPC) 方法已得到广泛修订，并提出了大量替代监测方法。不同的方法在批处理数据对齐、预处理方法、数据排列和/或使用的模型类型方面有所不同，从双向到三向，从线性到非线性。最被接受的预处理方案之一，称为轨迹居中和缩放 (TCS)，它基于对平均轨迹周围的零均值和单位方差的归一化。然而，TCS 的主要缺点是模型参数估计中不确定性水平的固有增加。在这项工作中，我们说明了如何在保持这种预处理方法的良好特性的同时改进参数估计。这种增强是通过我们称为 PARAMO 的新预处理方法实现的，它使用比 TCS 更多的观察来估计预处理参数。我们表明，这种改进对监控系统的性能产生了有利的影响。这项研究工作的结果影响了迄今为止提出的大量监测方法，我们主张这里提出的预处理程序应该普遍应用于 BMSPC。