ABSTRACT
We mentioned in Chapter 1 that the statistics involved in multivari ate process control depend on the “origins” of the target values m. The methodology and the applications presented in this chapter are for the case when the target values are assigned externally, i.e. from an external requirement or when a prespecified standard mo has to be met. It should be noted that comparisons with externally specified targets are not usu ally considered in statistical process control since such targets do not account properly for valid process characteristics. However, whenever multivariate prespecified standards are set, multivariate quality control procedures can be used to assess whether the multivariate means of the products equal the external targets mo. The next two chapters deal with cases in which target values are derived and computed internally. We shall distinguish between targets derived from the tested sample itself, and targets which are derived from a “reference” or “base” sample. If we denote by μ, the multivariate mean of the products Y, the statistical analysis in quality control with external targets is equivalent to testing hypotheses of the form
where F “n|_p is the upper 100% percentile of the central F-distribution with (p, «i — p) degrees of freedom. If the value of 7^ exceeds the critical value, we conclude that the derivations between Y and the ex ternal targets mo cannot be explained by random error. In such cases an assignable cause affecting the process is to be suspected.
