The thickness of a metal part is an important quality parameter. Data on thickness (in inches) are given in the following table, for 25 samples of five parts each.

(a) Using all the data, find trial control limits for X and R charts, construct the chart, and plot the data. Is the process in statistical control?

(b) Use the trial control limits from part (a) to identify out-of- control points. If necessary, revise your control limits assuming that any samples that plot outside the control limits can be eliminated.

(c) Repeat parts (a) and (b) for XÌ… and S charts.

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Sample Number 0.0629 0.0636 0.0640 0.0635 0.0640 2 0.0630 0.0631 0.0622 0.0625 0.0627 3 0.0628 0.0631 0.0633 0.0633 0.0630 4 0.0634 0.0630 0.0631 0.0632 0.0633 5 0.0619 0.0628 0.0630 0.0619 0.0625 0.0613 0.0629 0.0634 0.0625 0.0628 0.0630 0.0639 0.0625 0.0629 0.0627 0.0628 0.0627 0.0622 0.0625 0.0627 0.0623 0.0626 0.0633 0.0630 0.0624 9. 10 0.0631 0.0631 0.0633 0.0631 0.0630 11 0.0635 0.0630 0.0638 0.0635 0.0633 12 0.0623 0.0630 0.0630 0.0627 0.0629 0.0635 0.0631 0.0630 0.0630 0.0630 13 14 0.0645 0.0640 0.0631 0.0640 0.0642 15 0.0619 0.0644 0.0632 0.0622 0.0635 16 0.0631 0.0627 0.0630 0.0628 0.0629 17 0.0616 0.0623 0.0631 0.0620 0.0625 18 0.0630 0.0630 0.0626 0.0629 0.0628 19 0.0636 0.0631 0.0629 0.0635 0.0634 20 0.0640 0.0635 0.0629 0.0635 0.0634 0.0628 21 0.0625 0.0616 0.0620 0.0623 22 0.0615 0.0625 0.0619 0.0619 0.0622 0.0630 23 0.0630 0.0632 0.0630 0.0631 24 0.0635 0.0629 0.0635 0.0631 0.0633 25 0.0623 0.0629 0.0630 0.0626 0.0628