Even if large historical dataset could be available for monitoring key quality features of a process via multivariate control charts, previous knowledge may not be enough to reliably identify or adopt a unique model for all the variables. When no specific parametric model turns out to be appropriate, some alternative solutions should be adopted and exploiting non‐parametric methods to build a control chart appears a reasonable choice. Among the possible non‐parametric statistical techniques, data depth functions are gaining a growing interest in multivariate quality control. Within the literature, several notions of depth are effective for this purpose, even in the case of deviation from the normality assumption. However, the use of the L^p depth for constructing non‐parametric multivariate control charts has been surprisingly neglected so far. Hence, the goal of this work is to investigate the behavior the L^p depth in the statistical process control and to compare its performances to those of the Mahalanobis depth, which is often adopted to build depth‐based control charts.

中文翻译：

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基于Lp深度的多元过程控制图

即使大型历史数据集可用于通过多变量控制图监视过程的关键质量特征，但先前的知识可能不足以可靠地识别或采用所有变量的唯一模型。如果没有合适的参数模型，则应采用一些替代解决方案，而利用非参数方法来构建控制图似乎是一个合理的选择。在可能的非参数统计技术中，数据深度函数对多元质量控制越来越感兴趣。在文献中，即使在偏离正态性假设的情况下，深度的几个概念也可以有效地达到此目的。但是，使用L ^p到目前为止，构建非参数多元控制图的深度令人惊讶地被忽略了。因此，这项工作的目的是研究统计过程控制中L ^p深度的行为，并将其性能与Mahalanobis深度的性能进行比较，而Mahalanobis深度通常用于构建基于深度的控制图。