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 y = xλ, so λ = .5 here; Minitab will identify the best value of λ). Transform the data as suggested, calculate control limits for X̅, R, and S charts, and check for the presence of any out-of-control signals.

2961 6496037231275 31 1221 1328 122 214867627154 13211 1 22 2 1 56 13 2 6 8 37 41 89 25 8 5631683718958 141 2 200 250 300 350 400 400 500 0505050505050 33 4455667788990 700 750 800