Abstract Multivariate categorical quality characteristics, whose distribution can be displayed by a contingency table, are routinely encountered in many applications. When most of the cell entries in the contingency table are very small or zeros counts, which is so-called sparse contingency table in the literature, existing methods developed in the literature are often inadequate for use, due to the inaccuracy of the maximum likelihood estimate of its probability distribution, and the inflation of online charting statistics. This paper studies the multivariate statistical process control problem for such sparse contingency table. We integrate the group least absolute shrinkage and selection operator (LASSO) method with the Ridge method to estimate the in-control distribution of a contingency table and propose an efficient EWMA control chart, based on a modified Pearson χ2 statistic, to monitor the changes in it. Numerical results show that our proposed approach has the best overall performance, compared with its competitors. Finally, a real data example is used to demonstrate the effectiveness of the proposed control chart.

中文翻译：

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具有稀疏列联表的多元分类过程的有效制图方案

摘要 多变量分类质量特征的分布可以通过列联表显示，在许多应用中经常遇到。当列联表中的大多数单元格条目非常小或计数为零时，即文献中所谓的稀疏列联表，由于最大似然估计的不准确，文献中开发的现有方法往往不能充分使用其概率分布，以及在线图表统计数据的膨胀。本文研究了这种稀疏列联表的多元统计过程控制问题。我们将组最小绝对收缩和选择算子（LASSO）方法与岭方法相结合，以估计列联表的控制分布并提出有效的 EWMA 控制图，基于修改后的 Pearson χ2 统计量，以监测其中的变化。数值结果表明，与竞争对手相比，我们提出的方法具有最佳的整体性能。最后，一个真实的数据例子被用来证明所提出的控制图的有效性。