Abstract
Most multivariate quality control charts for determining whether the process mean vector is in-control or out-of-control are based on aggregate statistics, such as Hotelling’s . When no correlation is present among the characteristics, monitoring with a statistic reduces to running independent Shewhart charts on the individual variables. When correlations do exist, the is a powerful tool; but has a major drawback, that is, it does not gives any direct information as to what has caused the out-of-control condition, when the statistic indicates an out-of-control process. When the value of a Hotelling’s signals an out-of-control condition, an investigation must be initiated to find out possible causes of the problem by studying not only the individual variables but also the correlations among them. Principal components and factor analysis are two useful tools for studying the correlations. It is proved in this paper that the value of the Hotelling’s based on the original variables is the same as that based on the factor scores, and hence it is reasonable to use a method that is based on the factor scores for determining whether a process is out-of-control or not, and, if any, the factor(s) that had caused the out-of-control condition. We consider the cases with known and unknown population covariance matrix S. The proposed method is easy to implement using S-PLUS package on a personal computer. Finally, we compare our method with several existing methods to illustrate the usefulness of the proposed method.