One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I in terms of the probability of signal criterion. This assessment is carried out in the absence and presence of outliers. We show that, in both phases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

翻译：监测当今产品质量的重大挑战之一是质量特性的高度维度。本文讨论高维过程的第一阶段分析,在一段时间内收集的样品数量有限的情况下,通过个别观察对高维过程进行分析。使用新的图表统计,我们在第一阶段提出了可靠的参数估计程序。这一稳健的程序在参数估计方面是有效的,因为数据中存在外部线或污染。为参数估计提出了一致的估测标准,通过模拟得出并评估了有限的抽样校正系数。我们从信号标准的概率的角度评估了第一阶段拟议方法的统计性能。这一评估是在没有外部线和存在外部线的情况下进行的。我们表明,在这两个阶段,拟议的控制图计划有效地检测了进程中的各种变化。此外,我们提出了两个真实世界的例子,以说明我们拟议方法的适用性。