Doe: Screening Using Fractional Factorials

Screening Examples:

• The first example follows the printed circuit board study in Brady and Allen (2003).
• Pre-step.Here, let us assume that the result of “thought experiments” based on “entertained assumptions” was the informed choice of the n=8 run design including m=4 factors used in the actual study.
• For ranges, we have L= {low transistor output, screwed, 0.5 turns, current sink} and
• H= {high transistor output, soldered, 1.0 turns, alternative sink}′. The factors each came from different people with the last factor coming from rework line operators.
• In evaluating the cost of poor quality, e.g., low yield, it was relevant to consider costs in addition to the direct cost of rework. This followed in part because production time variability from rework caused the need to quote high lead times to customers, resulting in lost sales.

Example: Consider the Table. What are D, X, X′X, and A? (The DOE and estimated coefficients in a fictional study)

Answer 1: D is the entire matrix in Table 12.6 without the column for the runs. Using X = (1|D) one has