An article in the IEEE Transactions on Components, Hybrids, and Manufacturing Technology (1992, Vol. 15) described an experiment for aligning optical chips onto circuit boards. The method involves placing solder bumps onto the bottom of the chip. The experiment used three solder bump sizes and three alignment methods. The response variable is alignment accuracy (in micrometers). The data are as follows:

(a) Is there any indication that either solder bump size or alignment method affects the alignment accuracy? Is there any evidence of interaction between these factors? Use a = 0.05.

(b) What recommendations would you make about this process?

(c) Analyze the residuals from this experiment. Comment on model adequacy.

Alignment Method Solder Bump Size (diameter in mm) 2 3 4.60 1.55 1.05 75 4.53 1.45 1.00 1.72 0.82 2.33 130 2.44 1.76 0.95 2.36 4.95 2.73 260 4.55 2.60 2.46