The thickness of a printed circuit board is an important quality parameter. Data on board thickness (in inches) are given in Table 5E.1 for 25 samples of three boards each.

a. Set up x̅ and R control charts. Is the process in statistical control?

b. Estimate the process standard deviation.

c. What are the limits that you would expect to contain nearly all the process measurements?

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Sample Number x 0.0629 0.0636 0.0640 0.0630 0.0631 0.0622 0.0628 0.0631 0.0633 0.0634 0.0630 0.0631 0.0619 0.0628 0.0630 0.0613 0.0629 0.0634 0.0630 0.0639 0.0625 0.0628 0.0627 0.0622 0.0623 0.0626 0.0633 0.0631 0.0631 0.0633 0.0635 0.0630 0.0638 0.0623 0.0630 0.0630 0.0635 0.0631 0.0630 0.0645 0.0640 0.0631 0.0619 0.0644 0.0632 0.0631 0.0627 0.0630 0.0616 0.0623 0.0631 0.0630 0.0630 0.0626 0.0636 0.0631 0.0629 0.0640 0.0635 0.0629 0.0628 0.0625 0.0616 0.0615 0.0625 0.0619 0.0630 0.0632 0.0630 0.0635 0.0629 0.0635 0.0623 0.0629 0.0630 10 12 13 14 15 16 17 18 19 20 21 23 24 25