AnderSet Laboratories produces rough lenses that will ultimately be ground into precision lenses for use in laboratory equipment. The company has developed the following thickness measures, based on 15 samples of four lenses that were taken when the process was under control:

a. Use these data to calculate X and R and set up the appropriate control charts.

b. Can the process be “under control” in statistical terms but still fail to meet the needs of AnderSet’s customers? Explain, using a numerical example.

c. Suppose AnderSet Laboratories takes some additional samples of the same size, yielding the following results. Plot these samples on the control charts and circle any observations that appear to be out of control.

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MEAN (MICRONS) (n = 4) MINIMUM MAXIMUM 3.989 3.900 3.617 4.206 3.971 4.302 4.062 4.214 4.400 3.890 3.749 3.937 4.036 3.501 4.084 4.134 3.543 4.584 3.037 2.935 3.929 5.082 3.797 5.695 4.255 3.404 2.837 5.246 5.106 6.382 4.197 4.085 4.239 4.312 3.949 4.356 3.989 4.302 4.400 3.617 3.867 3.900 4.170 4.046 4.206 MEAN (MICRONS) (n = 4) MINIMUM MAXIMUM 4.134 4.011 4.612 3.913 3.891 4.474 4.584 4.499 5.145 4.009 3.934 4.891 4.612 4.085 4.983 5.627 5.183 6.080