12.10. In an article (“Let’s All Beware the Latin Square,”

Quality Engineering, Vol. 1, 1989, pp. 453–465), J. S. Hunter illustrates some of the problems associated with 3k!p fractional factorial designs. Factor A is the amount of ethanol added to a standard fuel, and factor B represents the air/fuel ratio.

The response variable is carbon monoxide (CO) emission in g/m3. The design is as follows,

Notice that we have used the notation system of 0, 1, and 2 to represent the low, medium, and high levels for the factors. We have also used a “geometric notation” of !1, 0, and %1. Each run in the design is replicated twice.

Transcribed Image Text:

Design A B x2 Observations y 012012112 0 -1 66 62 0 0 78 81 0 +1 90 94 1 -1 0 72 67 1 0 0 80 S 81 1 +1 0 75 78 222 2 -1 +1 68 66 0 +1 66 69 2 +1 +1 60 58