How to simultaneously reduce /spl alpha/ and /spl beta/ error with SPC? A multivariate process control approach

We describe the multivariate statistical process control approach which uses a weighted average metric as a metric plotted on a control chart. We show that the optimal weighted coefficient is a function of the mean-shift vector and covariance matrix of metrics of interest. The control chart constructed by this optimal weighted average metric will have the highest signal to noise ratio and the lowest /spl alpha/ and /spl beta/ errors. A numerical example using actual data from a fab is also provided.