Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 3 — Questions and Answers
Question 1: When analyzing a DOE, a significant interaction between two factors means:
- Both factors individually have large main effects
- The effect of one factor depends on the level of the other factor (Correct answer)
- The factors are correlated in the data collection phase
- The experiment must be repeated with more replicates
Correct answer: The effect of one factor depends on the level of the other factor
A significant interaction means the effect of Factor A on the response changes depending on which level of Factor B is set, so factors cannot be interpreted independently.
Question 2: What is the signal-to-noise (S/N) ratio in Taguchi methods primarily used to measure?
- The ratio of between-group variance to within-group variance
- The robustness of a product or process response to noise factors (Correct answer)
- The correlation between control factors and response variables
- The efficiency of a fractional factorial design
Correct answer: The robustness of a product or process response to noise factors
Taguchi's S/N ratio quantifies how much variation (noise) exists relative to the mean signal, with higher S/N indicating more robust performance.
Question 3: In a 2^(4-1) fractional factorial experiment, how many runs are required?
- 4
- 8 (Correct answer)
- 16
- 32
Correct answer: 8
A 2^(4-1) design is a half-fraction of a full 2^4 = 16 run design, so it requires 2^(4-1) = 2^3 = 8 runs.
Question 4: Which DOE term describes the difference in response between the high and low levels of a factor, averaged across all other factor combinations?
- Interaction effect
- Main effect (Correct answer)
- Residual
- Contrast
Correct answer: Main effect
The main effect of a factor is the average change in response when moving from the low level to the high level, averaged over all levels of other factors.
Question 5: A normal probability plot of effects in a factorial experiment is used to:
- Check if experimental runs follow a normal distribution
- Identify which effects are statistically significant versus noise (Correct answer)
- Determine the optimal factor settings
- Validate the blocking structure of the design
Correct answer: Identify which effects are statistically significant versus noise
On a normal probability plot, insignificant effects fall on a straight line (noise), while significant effects deviate noticeably from the line.
Question 6: What is the purpose of blocking in a designed experiment?
- To increase the number of factors that can be studied
- To reduce the effect of a known nuisance variable on the comparison of treatments (Correct answer)
- To eliminate the need for randomization
- To create a fractional factorial design
Correct answer: To reduce the effect of a known nuisance variable on the comparison of treatments
Blocking groups experimental runs by a known nuisance variable (e.g., batches, days, machines) so its effect can be removed from the error term.
Question 7: In response surface methodology, a Box-Behnken design differs from a Central Composite Design primarily because it:
- Requires fewer factors to implement
- Does not include corner points of the factor space (Correct answer)
- Cannot estimate quadratic effects
- Uses only two levels for each factor
Correct answer: Does not include corner points of the factor space
Box-Behnken designs avoid the extreme corner combinations of all factors at their highest or lowest levels simultaneously, which can be impractical or dangerous.
Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 3
When analyzing a DOE, a significant interaction between two factors means: