The following data on the deviation from target in the parallel orientation is taken from Table 1 of the article cited in Example 16.5. Sometimes a transformation of the data is appropriate, either because of nonnormality or because subgroup variation changes systematically with the subgroup mean. The authors of the cited article suggested a square root transformation for this data (the family of Box-Cox transformations is , so here; Minitab will identify the best value of l). Transform the data as suggested, calculate control limits for , R, and S charts, and check for the presence of any out-of-control signals.

des dim observations 200 14 31 12 250 22 13 9 300 12 22 16 350 11 28 1 X

y 5 x l 5 .5 l n 5 8 des dim observations 400 15 12 36 450 6 31 14 500 13 24 9 550 21 18 16 600 6 16 20 650 8 17 23 700 3 26 17 750 17 12 22 800 41 17 3 850 18 11 21 900 9 15 22 950 25 4 17 1000 8 23 15