Consider the data set shown in Table 18.5.3, representing the thicknesses of a protective coating.

a. Find the average, X, and the range, R, for each sample.

b.* Find the overall average, X, and the average range, R.

c.* Find the center line for the X chart.

d.* Find the control limits for the X chart.

e. Draw the X chart.

f. Comment on what you see in the X chart. In particular, is this process in control? How do you know?

g. Write a paragraph, as if to your supervisor, summarizing the situation and defending the action you feel is appropriate.

TABLE 18.5.3 Thicknesses of a Protective Coating: 25 Samples of Three Items Each Individual Measurements within Each Sample Sample Identification Number 1251 12.60 12.40 12.44 12.78 12.75 12.53 12.64 12.57 12.70 12.74 12.90 13.05 12.88 13.03 12.96 12.91 12.95 13.17 13.17 12.95 1304 13.12 12.83 13.24 12.70 12.53 12.81 12.57 12.61 12.43 12.51 12.49 12.74 12.87 12.80 12.83 13.00 12.88 12.85 12.88 12.75 13.03 12.81 13.05 13.04 13.25 13.07 13.13 13.18 1257 12.56 12.60 12.61 12.68 12.51 1281 12.95 12.86 12.91 13.132 13.11 13.05 6 10 12 13 T4 15 16 17 18 13.01 12.89 13.17 12.97 12.80 12.95 13.11 1331 13.13 20 25