The data in Table 17.9 consist of 30 subgroups of measurements that specify the location of a "tube hole" in an air conditioner compressor shell. Each subgroup contains the tube hole dimension measurement for five consecutive compressor shells selected from the production line. The first 15 subgroups were observed on March 21, and the second 15 subgroups were observed on March 22. As indicated in Table 17.9, the die press used in the hole punching operation was changed after subgroup 5 was observed, and a die repair was made after subgroup 25 was observed.
TABLE 17.9
30 Subgroups of Tube Hole Location Dimensions for Air Conditioner Compressor Shells

b. Set up and R charts for the 15 subgroups that were observed on March 21 (do not use any of the March 22 data). Do these x and R charts show statistical control?
c. Using the control limits you computed by using the 15 subgroups observed on March 21, set up and R charts for all 30 subgroups. That is. add the subgroup means and ranges for March 22 to your X and R charts, but use the limits you computed from the March 21 data.
d. Do the and R charts obtained in part c show statistical control? Explain.
e. Does it appear that changing to die press #628 is an assignable cause? Explain. (The die press is the machine that is used to punch the tube hole.)
f. Does it appear that making a die repair is an assignable cause? Explain.

Tube Hole Location Measurements 5 Mean, x Range, R Subgroup 13 14.8 19 17.2 17.0 17.6 16 15.2 22 176 15 13 7 13 13.4 16 15 15 19 17 March 21 17 20 15 16 15 18 20 6 15 16 Changed to5 Die Press 13 20 17 #628 Here 14 15.2 13 14 18 19 12 16 3 5 15.0 13 14.2 19 14 2 13 10 17 22 5 14 6 16.8 15.4 10 19 17 1 15 17 15 12 15.2 16.4 16 16.0 18 15.2 17 15.6 15 17 17 14 13 17 14 15 16 18 10 14 16 15 19 19 16 17 20 22 25 17 16 March 22 18 12 15 17 19 18 17 19 19 18 16 18.0 20.8 17.8 18.8 15.4 20 21 18 19 20 9 18 17 16 15 23 24 13 16 15 16 7 7 16.2 16.4 20 13 16 Die Repair25 25 23 2 24 21 22.8 26 27 28 29 Made Here 25 21 26 29 25 26 24 25 22 22 26 21 2725 25 23.0 23 25.8 27 24.0 26 25.0