Certified Six Sigma Black Belt Design of Experiments (DOE) Questions and Answers Flashcards
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What is the defining relation used to determine the alias structure of a fractional factorial design?
Answer: The set of generators and their generalized interactions that equal the identity column
The defining relation consists of all words formed by the generators and their products set equal to I, which determines every alias pair in the design.
In a Plackett-Burman design with 12 runs, what is the maximum number of factors that can be studied?
Answer: 11
Plackett-Burman designs allow screening of up to N-1 factors in N runs, so a 12-run design screens up to 11 factors.
A team uses a central composite design (CCD) and finds significant lack of fit. What is the most appropriate next step?
Answer: Consider adding higher-order terms or transforming the response variable
Significant lack of fit means the current model does not adequately describe the data, so augmenting with higher-order terms or applying a transformation is warranted.
Which principle ensures that the effect of an uncontrolled nuisance variable is spread evenly across all treatment combinations in a DOE?
Answer: Randomization
Randomization distributes the influence of unknown and uncontrolled nuisance variables evenly across all experimental runs, preventing systematic bias.
In a split-plot experiment, why are some factors called 'hard-to-change'?
Answer: Resetting them for every run is impractical or very costly
Hard-to-change factors are applied at the whole-plot level because resetting them between every run would be prohibitively expensive or time-consuming.
What does the term 'rotatability' mean in the context of a response surface design?
Answer: The prediction variance is the same at all points equidistant from the design center
A rotatable design ensures that the variance of the predicted response depends only on the distance from the center, not on the direction, providing uniform precision.