8.4. The data shown below constituted the original run preceding that of Table 8.3. As in that table, specifications were 0.1235 to 0.1250 in. with data in 0.0001 in. units below 0.1250 in. and n¼5.

Time July 27 8:00 8:30 9:00 9:30 10:00 11:00 12:30 x-bar 8.0 7.4 6.8 5.4 5.6 4.0 3.4 R 2 3 2 2 3 4 3 Time July 27 1:15 2:30 2:45 3:15 4:00 4:30 x-bar 10.8 11.6 10.4 9.6 9.8 9.4 R 2 3 2 3 2 4 Time July 30 9:00 9:30 10:00 11:00 12:15 12:45 1:15 x-bar 7.4 7.8 7.4 5.4 7.0 5.8 3.8 R 4 4 2 3 2 3 2 Time July 30 1:45 2:15 2:45 3:30 4:00 4:30 x-bar 4.6 4.2 2.8 6.2 5.6 6.2 R 4 4 3 5 4 2 Time July 31 8:00 x-bar 9.4 R 4

(a) Plot the x-bar and R points, check the R chart for control.

Estimate s if justified.

(b) Would the x-bar chart with ordinary limits be in control?

(c) Draw by eye the trend lines for m. Show the minimum and maximum safe process averages, and the slanting control limits for x-bar.

(d) Were the trend lines for m started and ended at about the right level?