Defining the Problem (1). Engineers for a manufacturer of power tools for home use were tr...

Defining the Problem (1). Engineers for a manufacturer of power tools for home use were trying to design an electric drill that did not heat up under strenuous use. The three key design factors were insulation thickness, quality of the wire used in the motor, and size of the vents in the body of the drill.

Collecting Data (2). The engineers had learned a little about off-line quality control, so they designed an experiment that varied these design factors. They created 10 drills using each combination of the three design factors, split them into two lots, and tested the lots under two (supposedly equivalent) torture tests. The temperature of each drill was measured at the end of each test; for each lot, the mean temperature and the logarithm of the variance of temperatures were computed. The engineers wanted to minimize both the mean and the logarithm of the variance.

For this experiment, there are three key design factors:

IT is the insulating thickness of the drill (IT = 2, 3, 4, 5, or 6)

QW is the quality of wire used in the motor (QW = 6, 7, or 8)

VS is the size of the vent in the body of the drill (VS = 10, 11, or 12)

There are 5 × 3 × 3 = 45 different combinations of these design factors. For each combination of factors, 10 drills were made and divided into two lots of five drills. Each drill was subjected to a torture test and the temperature recorded at the end of the test. Avtem represents the average temperature for the five drills of a lot for a given combination of the design factors. The 90 measurements are given here (5 × 3 × 3 × 2 lots = 90). Also included in the data set are

logv = logarithm of the variance of temperatures for a given combination of factors and lot

and I2, Q2, and V2, which are squared terms for the three design factors computed as (design factor ‒ mean design factor)2