A New Process Control Chart for Monitoring Short-Range Serially Correlated Data
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.
