Most control charts monitor only one quality characteristic. There are, however, many manufactured
products for which good quality requires meeting specifications in more than one physical
characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate
sample for each characteristic and then create individual univariate control charts which are
independently monitored. This method can result in errors due to not accounting for the effects
of correlation. In order to avoid these errors, an alternate approach to multivariate quality control
problems is proposed and studied here. The original problem is converted into a univariate problem
by using the following transformation:
y=Σ aixi
i
where
αi = weighting coefficient for the ith quality characteristic
Xi = represents the ith quality characteristic
This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs.
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