Handling multivariate problems with univariate control charts
Statistical process control (SPC) is an important ingredient of quality management. SPC has evolved from a technique to a philosophy, and now includes a large number of techniques and methods directed to quality control and quality improvement. Few processes can be controlled through only one parameter. Hence research into multivariate methods applied to SPC has been undertaken already long ago. Hotelling introduced in 1947 the T-2 control chart as a technique for monitoring a multivariate process, and several authors have since elaborated on this. In essence the aim to approach the problem of SPC from a multivariate perspective is to make more efficient use of the data by incorporating the covariances in the model. However, multivariate methods have not gained much popularity. This is due to two important drawbacks: interpretation of out-of-control situations signalled by a multivariate chart is usually difficult and involves further statistical evaluation of the data; and estimation of the process-inherent covariance matrix is sensitive to out-of-control conditions. This paper illustrates some important control chart methods for multivariate problems. A real-world case is analysed by several authors in different ways. From this case and many others we conclude that it is often sufficient to use a few univariate control charts, even though the nature of the process is multivariate. The key argument for this conclusion is that direct interpretation on the shop floor is very important. A brief introduction to the implementation of SPC is given in this paper as well. Copyright (C) 1999 John Wiley & Sons, Ltd.
control charts statistical process control contrasts multivariate analysis principal components