Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 5

Question 1

In a 2^3 full factorial experiment with two replicates, how many total runs are performed?

Accepted Answer

16

Answer

A 2^3 full factorial has 8 treatment combinations; with two complete replicates, the total number of runs is 8 × 2 = 16.

Question 2

What is the purpose of 'fold-over' in fractional factorial experiments?

Accepted Answer

To de-alias main effects from 2-factor interactions by reversing all signs in the original design

Answer

Folding over reverses the signs of all factor columns in the original design and combining it with the original eliminates the confounding of main effects with 2-factor interactions.

Question 3

Which metric is typically used to evaluate the quality of a DOE model while penalizing for adding unnecessary terms?

Accepted Answer

Adjusted R²

Answer

Adjusted R² is R² corrected for the number of terms in the model, so it decreases when adding non-significant terms, discouraging model over-fitting.

Question 4

In DOE analysis, the 'lack of fit' F-test is used to determine:

Accepted Answer

Whether the fitted model adequately describes the true relationship between factors and response

Answer

The lack-of-fit test compares pure error (from replicates) to model error; a significant result indicates the model form is inadequate for the data.

Question 5

A contour plot in Response Surface Methodology (RSM) is most useful for:

Accepted Answer

Visualizing how two factors jointly affect the response and finding optimal regions

Answer

Contour plots display lines of equal response values across two factor dimensions, helping identify optimal factor combinations and the shape of the response surface.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 5