Multivariate Quality Control Chart for Autocorrelated Processes

Abstract

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996 Theodossiou, PT . 1993. Predicting shifts in the mean of multivariate time series process: an application in predicting business failures. Journal of the American Statistical Association, 88(422): 441–447. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.