Design of Experiments and Quality Engineering Methods
What the exam tests
Design selection, aliasing and resolution, randomization, replication, and sequential strategy from screening to optimization.
Core rules
- A full two-level factorial has 2^k runs and estimates all main effects and interactions. A fractional factorial 2^(k-p) trades resolution for runs.
- Resolution III: main effects clear of each other but aliased with two-factor interactions. Resolution IV: main effects clear of two-factor interactions, but two-factor interactions alias with each other. Resolution V: main effects and two-factor interactions all clear of each other.
- Randomize run order to protect against nuisance drift; block known noise (shift, lot, oven); replicate to obtain pure error; add center points to test for curvature.
- Strategy is sequential: screening (Plackett-Burman, Taguchi arrays) then characterization then optimization with response surface methods (central composite, Box-Behnken). Taguchi separates parameter design (robustness) from tolerance design (tightening specs).
Worked example
A 2^(3-1) design with generator C = AB has four runs and is Resolution III. Effect C is aliased with interaction AB, so a large C effect cannot be attributed to the factor rather than the interaction. The fix is a foldover: run the mirror-image design, which de-aliases C from AB and yields a Resolution IV combined design. Reasoning: adding runs that reverse all signs separates the confounded pair without discarding the first four runs.
Traps that cost marks
Calling a Resolution IV design interaction-safe for two-factor interactions. Pooling effects into error without examining them first. Running trials in convenient rather than random order. Interpreting a main effect when its interaction is significant, which requires a plot of the interaction. Extrapolating outside the tested factor range. Using an R-squared that is high only because the model is overfit.