The most commonly used type of statistical process control (SPC) employs single variable (univariate) control charts that record the values of process product variables and indicate when a given process or product variable is outside some predetermined limit. This approach however is not practical when the number of process variables becomes very large (e.g. greater than 20), or when the process variable interact, such as in a chemical manufacturing process. Techniques for monitoring a process having a large number of process variables or where the process variables interact are known as multivariate quality control techniques. Applications of multivariate quality control are generally aimed at detecting two major sources of process and/or product variability. They are: (1) sensor inaccuracies or failures; and (2) raw material and/or manufacturing process changes that result in shifts in the dynamics that are driving the process. One form of multivariate analysis is known as Principal Component Analysis (PCA). See Wise, B. M., Ricker, N. L., Veltkamp, D. F. and Kowalski, B. R. (1990), "A theoretical basis for the use of principal components models for monitoring multivariate processes", Process Control and Quality, 1, 4151 ). Wise et. al. have shown that both sensor failures and process changes can be detected via multivariate analysis. Wise et al have specifically shown that an arbitrary dynamic linear time invariant state-space model can always be transformed so that the states are directly related to the PCA scores. In addition, they emphasized that multivariate analysis is most effective when the process has significantly more measurements than states (a situation that frequently occurs)., and that for a given dynamic process, either an increase in the measurements or an increase in the sampling period will usually make multivariate analysis appropriate for identifying when a process is out of control. PCA is generally used when controlling manufacturing processes using process data alone.
Another multivariate technique called Partial Least Squares (PLS) is employed when both process and product data are used to control the process. See Stone, M. and Brooks, R. J. (1990). "Continuum Regression: Cross-validated Sequentially Constructed Prediction Embracing Ordinary Least Squares, Partial Least Squares and Principal Components Regression", Journal of the Royal Statistical Society B, 52, 237-269.
Conventional multivariate analysis techniques involve forming and analyzing a small set (e.g. two) surrogate variables that represent the state of the process and by their values indicate when the process is in or out of control. Although it has been possible to effectively identify when a process is out of control using these multivariate analysis techniques, it is often difficult to determine the source of the problem, particularly as the number of process variable increases.