Multivariate Process Control with Autocorrelated Data

As sensor and computer technology continues to improve, it becomes a normal occurrence that we confront with high dimensional data sets. As in many areas of industrial statistics, this brings forth various challenges in statistical process control and monitoring. This new high dimensional data often exhibit not only cross-­‐correlation among the quality characteristics of interest but also serial dependence as a consequence of high sampling frequency and system dynamics. In practice, the most common method of monitoring multivariate data is through what is called the Hotelling’s T2 statistic. For high dimensional data with excessive amount of cross correlation, practitioners are often recommended to use latent structures methods such as Principal Component Analysis to summarize the data in only a few linear combinations of the original variables that capture most of the variation in the data. In this paper, we discuss the effect of autocorrelation (when it is ignored) on multivariate control charts based on these methods and provide some practical suggestions and remedies to overcome this problem.