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I would like to set up control charts for some of our processes. From each run, one wafer is taken and analyzed on five positions of the wafer. How should I interpret this sampling scheme: as one sample (I-MR) or as five samples (Xbar-R)?

Thank you for your question.  It is one that many people have to address with their process applications.   The application you describe does not fit an X-bar and R chart because it isn’t a rational subgroup.

If you think about measuring five points on the same wafer, the variability in those five measurements is just the variability within a given piece.  However if you did use the X-bar and R chart, it would be interpreted as the variability from piece to piece and therefore give you an improper calculation for the control limits on the X-bar chart.

Using the I-MR chart is the better option.  You could enter the average of the 5 points or simply agree to use the value from a given location on the wafer.   It would also be interesting to maintain a separate range chart for the 5 values (independent of the MR chart calculated with the individuals chart).

Monitoring this range chart would show if the variability within the wafer is remaining consistent.

Craig Tickel

Craig is a Senior Consultant at and a Master Black Belt with over 25 years of success working with companies like Procter & Gamble, Johnson & Johnson, General Electric, Starwood Hotels & Resorts and Stepan Company. He’s an expert at helping people learn and apply Lean Six Sigma to achieve their goals.