Effective application of Q(R) charts in low-volume manufacturing

Q charts provide means for statistical process control in low-volume processes and start-up phases of production. Concerns on their performance have led to research into different types of enhancements and much discussion on the appropriateness of these. Driven by the aim to implement control charts in the low-volume production of advanced wafer steppers, we investigate the performance of additional run rules and tightening control limits on the traditional Q chart compared with an exponentially weighted moving average (EWMA). Furthermore, we develop an alternative QR chart based on the mean moving range as estimator of the process standard deviation and consider the economics of low-volume processes by means of a specific cost model. The comparisons are based on the run length distributions after a permanent shift and trend, both with an onset early in the process. Real life examples are given for various important variables in wafer stepper production. It is concluded that the EWMA based on QR statistics provides the best performance throughout. Competing alternatives with almost equal performance are the EWMA of Q statistics and the combination of four tests of special causes (1-of-1, 2-of-3, 4-of-5 and 8-of-8) applied on either the Q or QR chart. Overall, the mean moving range performs better.