Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Design of Experiments (DOE) Questions and Answers 2 — Questions and Answers
Question 1: In a 2^k factorial design, what does the term 'confounding' refer to?
- Aliasing a higher-order interaction with a block effect (Correct answer)
- Randomizing the run order within each block
- Replicating center points to estimate curvature
- Adding noise factors to the experimental layout
Correct answer: Aliasing a higher-order interaction with a block effect
Confounding deliberately aliases a high-order interaction effect with the block effect so the experiment can be run in fewer blocks.
Question 2: A Six Sigma Black Belt runs a 2^4 full factorial with two replicates. How many total experimental runs are required?
- 32 (Correct answer)
- 16
- 24
- 48
Correct answer: 32
A 2^4 design has 16 runs, and two replicates yield 16 × 2 = 32 total runs.
Question 3: Which of the following is the primary advantage of using a fractional factorial design over a full factorial?
- It reduces the number of runs while still estimating main effects (Correct answer)
- It eliminates the need for randomization
- It guarantees detection of all interaction effects
- It removes the requirement for replication
Correct answer: It reduces the number of runs while still estimating main effects
Fractional factorials sacrifice information on higher-order interactions to significantly reduce the total number of experimental runs.
Question 4: What is the resolution of a 2^(5-2) fractional factorial design with generators I=ABCD and I=BCE?
- Resolution III (Correct answer)
- Resolution IV
- Resolution V
- Resolution II
Correct answer: Resolution III
The generators produce a word-length of three (BCE), making it a Resolution III design where main effects are aliased with two-factor interactions.
Question 5: In a Response Surface Methodology (RSM) study, what is the purpose of adding axial (star) points to a factorial design?
- To allow estimation of quadratic (second-order) effects (Correct answer)
- To increase the number of blocks in the experiment
- To reduce the total number of runs needed
- To eliminate multicollinearity among factors
Correct answer: To allow estimation of quadratic (second-order) effects
Axial points extend the factorial design so that curved, second-order relationships between factors and the response can be modeled.
Question 6: A Black Belt notices that the residual plot from a DOE shows a funnel shape with increasing spread. What assumption is most likely violated?
- Constant variance (homoscedasticity) (Correct answer)
- Normality of residuals
- Independence of observations
- Linearity of the model
Correct answer: Constant variance (homoscedasticity)
A funnel-shaped residual plot indicates that variance increases with the predicted value, violating the constant variance assumption.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Design of Experiments (DOE) Questions and Answers 2
In a 2^k factorial design, what does the term 'confounding' refer to?