Abstract–Statistical process control (SPC) charts are critically important for quality control and management in manufacturing industries, environmental monitoring, disease surveillance, and many other applications. Conventional SPC charts are designed for cases when process observations are independent at different observation times. In practice, however, serial data correlation almost always exists in sequential data. It has been well demonstrated in the literature that control charts designed for independent data are unstable for monitoring serially correlated data. Thus, it is important to develop control charts specifically for monitoring serially correlated data. To this end, there is some existing discussion in the SPC literature. Most existing methods are based on parametric time series modeling and residual monitoring, where the data are often assumed to be normally distributed. In applications, however, the assumed parametric time series model with a given order and the normality assumption are often invalid, resulting in unstable process monitoring. Although there is some nice discussion on robust design of such residual monitoring control charts, the suggested designs can only handle certain special cases well. In this article, we try to make another effort by proposing a novel control chart that makes use of the restarting mechanism of a CUSUM chart and the related spring length concept. Our proposed chart uses observations within the spring length of the current time point and ignores all history data that are beyond the spring length. It does not require any parametric time series model and/or a parametric process distribution. It only requires the assumption that process observation at a given time point is associated with nearby observations and independent of observations that are far away in observation times, which should be reasonable for many applications. Numerical studies show that it performs well in different cases.

中文翻译：

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用于监测短程序列相关数据的新过程控制图

摘要 - 统计过程控制 (SPC) 图表对于制造行业的质量控制和管理、环境监测、疾病监测和许多其他应用至关重要。传统的 SPC 图是为过程观察在不同观察时间独立的情况设计的。然而，在实践中，串行数据相关性几乎总是存在于顺序数据中。文献中已经很好地证明，为独立数据设计的控制图对于监测序列相关数据是不稳定的。因此，开发专门用于监控串行相关数据的控制图非常重要。为此，SPC 文献中有一些现有的讨论。大多数现有方法基于参数化时间序列建模和残差监测，其中数据通常被假定为正态分布。然而，在应用中，给定阶次的假设参数时间序列模型和正态性假设往往是无效的，导致过程监控不稳定。尽管对此类残差监控控制图的稳健设计有一些很好的讨论，但建议的设计只能很好地处理某些特殊情况。在本文中，我们尝试通过提出一种利用 CUSUM 图的重新启动机制和相关弹簧长度概念的新型控制图来做出另一项努力。我们提议的图表使用当前时间点弹簧长度内的观测值，并忽略超出弹簧长度的所有历史数据。它不需要任何参数时间序列模型和/或参数过程分布。它只需要假设在给定时间点的过程观察与附近的观察相关并且与观察时间很远的观察无关，这对于许多应用来说应该是合理的。数值研究表明，它在不同情况下表现良好。