Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 2 — Questions and Answers
Question 1: In a 2^k factorial design, what does the 'k' represent?
- The number of replicates
- The number of factors (Correct answer)
- The number of levels per factor
- The number of center points
Correct answer: The number of factors
In a 2^k factorial design, k is the number of factors and 2 represents the number of levels (high and low) for each factor.
Question 2: Which type of DOE design is most appropriate when the experimenter suspects curvature in the response surface?
- Full factorial design
- Plackett-Burman design
- Central Composite Design (CCD) (Correct answer)
- Latin square design
Correct answer: Central Composite Design (CCD)
Central Composite Design (CCD) includes axial (star) points that allow estimation of quadratic effects and detection of curvature.
Question 3: What is the primary purpose of randomization in a designed experiment?
- To reduce the number of runs required
- To guard against lurking variables and time-related effects (Correct answer)
- To ensure all factor combinations are tested
- To minimize the number of factors studied
Correct answer: To guard against lurking variables and time-related effects
Randomization distributes the effects of unknown nuisance variables across all experimental runs, preventing systematic bias.
Question 4: In a fractional factorial design, a resolution III design means:
- Main effects are confounded with each other
- Main effects are confounded with 2-factor interactions (Correct answer)
- 2-factor interactions are confounded with each other
- All effects can be estimated independently
Correct answer: Main effects are confounded with 2-factor interactions
In a resolution III design, main effects are aliased (confounded) with 2-factor interactions, so they cannot be separately estimated.
Question 5: A Plackett-Burman design is best used for:
- Optimizing a process with 2-3 factors
- Screening many factors to identify the vital few (Correct answer)
- Modeling quadratic relationships between factors
- Analyzing split-plot experiments
Correct answer: Screening many factors to identify the vital few
Plackett-Burman designs are highly efficient screening designs that study many factors in relatively few runs to identify significant main effects.
Question 6: What is the alias structure in a fractional factorial design?
- The list of factor levels used in each run
- The relationship showing which effects are confounded with each other (Correct answer)
- The coded values assigned to factor levels
- The error terms in the ANOVA table
Correct answer: The relationship showing which effects are confounded with each other
The alias structure defines which effects are indistinguishable from each other due to the fraction chosen in the experimental design.
Question 7: In DOE, what is a 'center point' used for?
- To set factor levels at their nominal values for all factors simultaneously
- To estimate pure error and check for curvature without additional factor combinations (Correct answer)
- To define the centerline of a control chart
- To randomize the run order of an experiment
Correct answer: To estimate pure error and check for curvature without additional factor combinations
Center points are runs at the midpoint of all factor ranges; they provide an estimate of pure experimental error and can detect curvature in the response.
Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 2
In a 2^k factorial design, what does the 'k' represent?