Vining and Myers ( “ Combining Taguchi and Response Surface Philosophies:

A Dual Response Approach, ” Journal of Quality Technology , 22 , 15 – 22, 1990)

analyze an experiment, which originally appeared in Box and Draper [ 1987 ].

This experiment studied the effect of speed ( x1 ), pressure ( x2 ), and distance

( x3 ) on a printing machine ’ s ability to apply coloring inks on package labels.

The following table summarizes the experimental results.

i x i x2 x3 y i1 y i2 y i3 yi s i 1 − 1 − 1 − 1 34 10 28 24.0 12.5 2 0 − 1 − 1 115 116 130 120.3 8.4 3 1 − 1 − 1 192 186 263 213.7 42.8 4 − 1 0 − 1 82 88 88 86.0 3.7 5 0 0 − 1 44 178 188 136.7 80.4 6 1 0 − 1 322 350 350 340.7 16.2 7 − 1 1 − 1 141 110 86 112.3 27.6 8 0 1 − 1 259 251 259 256.3 4.6 9 1 1 − 1 290 280 245 271.7 23.6 10 − 1 − 1 0 81 81 81 81.0 0.0 11 0 − 1 0 90 122 93 101.7 17.7 12 1 − 1 0 319 376 376 357.0 32.9 13 − 1 0 0 180 180 154 171.3 15.0 14 0 0 0 372 372 372 372.0 0.0 15 1 0 0 541 568 396 501.7 92.5 16 − 1 1 0 288 192 312 264.0 63.5 17 0 1 0 432 336 513 138.9 27 1 1 1 878 991 1161 1010.0 142.5

a. Fit an appropriate modal to each respone and conduct the residual analysis.

b. Use the sample variances as the basis for weighted least - squares estimation of the original data (not the sample means).

c. Vining and Myers suggest fi tting a linear model to an appropriate transformation of the sample variances. Use such a model to develop the appropriate weights and repeat part b.