Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 5 — Questions and Answers
Question 1: In a 2^3 full factorial experiment with two replicates, how many total runs are performed?
- 8
- 16 (Correct answer)
- 24
- 32
Correct answer: 16
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?
- To add center points to detect curvature
- To de-alias main effects from 2-factor interactions by reversing all signs in the original design (Correct answer)
- To convert a screening design into a response surface design
- To add additional factor levels to the experiment
Correct answer: To de-alias main effects from 2-factor interactions by reversing all signs in the original design
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?
- R²
- Adjusted R² (Correct answer)
- Predicted R²
- Lack-of-fit p-value
Correct answer: Adjusted R²
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:
- Whether the chosen factor levels are appropriate
- Whether the fitted model adequately describes the true relationship between factors and response (Correct answer)
- Whether the residuals are normally distributed
- Whether interactions are present in the experiment
Correct answer: Whether the fitted model adequately describes the true relationship between factors and response
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:
- Checking the normality of residuals
- Visualizing how two factors jointly affect the response and finding optimal regions (Correct answer)
- Estimating the main effect of a single factor
- Determining the statistical significance of factor interactions
Correct answer: Visualizing how two factors jointly affect the response and finding optimal regions
Contour plots display lines of equal response values across two factor dimensions, helping identify optimal factor combinations and the shape of the response surface.
Question 6: In a DMAIC project, DOE is most commonly conducted during which phase?
- Define
- Measure
- Analyze
- Improve (Correct answer)
Correct answer: Improve
DOE is a key tool in the Improve phase, used to actively manipulate process inputs to optimize the response output after critical factors have been identified in Analyze.
Question 7: What is the difference between a 'saturated' design and a 'resolution III' fractional factorial design?
- They are the same concept described with different terminology
- A saturated design has no degrees of freedom to estimate error, while resolution III simply aliases main effects with 2FIs (Correct answer)
- A saturated design can estimate all 2-factor interactions, but resolution III cannot
- Resolution III designs require more runs than saturated designs
Correct answer: A saturated design has no degrees of freedom to estimate error, while resolution III simply aliases main effects with 2FIs
A saturated design uses all degrees of freedom for estimating effects (leaving none for error), whereas resolution III refers to the specific aliasing pattern regardless of saturation.
Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 5
In a 2^3 full factorial experiment with two replicates, how many total runs are performed?