Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Improve Phase: DOE 1 — Questions and Answers
Question 1: What is the primary purpose of adding center points to a 2^k factorial design?
- To increase the number of factor levels from two to three
- To detect curvature (non-linearity) in the response surface (Correct answer)
- To replace the need for replication at corner points
- To reduce the total number of experimental runs required
Correct answer: To detect curvature (non-linearity) in the response surface
Center points are run at the midpoint of each factor's range. If the average response at center points differs significantly from the average of the factorial points, it indicates pure quadratic curvature — signaling that a first-order model is insufficient and a higher-order (response surface) model may be needed.
Question 2: In a 2^(k-p) fractional factorial design, what does the value 'p' represent?
- The resolution level of the design
- The number of generators used to define the fraction (Correct answer)
- The total number of confounded main effects
- The minimum number of runs required for significance
Correct answer: The number of generators used to define the fraction
In the notation 2^(k-p), 'k' is the total number of factors and 'p' is the number of generators (defining relations) used to create the fraction. Each generator halves the number of runs, so a 2^(k-p) design has 2^k / 2^p = 2^(k-p) runs.
Question 3: What is the primary purpose of blocking in a designed experiment?
- To increase the total number of factors that can be studied simultaneously
- To account for the variation caused by known but uncontrollable nuisance factors (Correct answer)
- To eliminate the need for randomization within the experiment
- To maximize the number of two-factor interaction estimates
Correct answer: To account for the variation caused by known but uncontrollable nuisance factors
Blocking isolates the effect of a known nuisance variable (such as different operators, batches, or days) by grouping experimental runs so that its variation is separated from the treatment effects. This reduces experimental error and improves the precision of factor effect estimates.
Question 4: In a 2^k factorial experiment, a normal probability plot of the estimated effects is used to:
- Verify that factor levels were set correctly during the experiment
- Identify which main effects and interactions are statistically significant (Correct answer)
- Calculate the exact p-value for each factor
- Determine the optimal combination of factor settings
Correct answer: Identify which main effects and interactions are statistically significant
Effects that are negligible tend to be normally distributed around zero and fall along a straight line on the normal probability plot. Effects that are large and statistically significant appear as outliers — they fall noticeably off the line — making this plot a powerful visual tool for screening significant effects without requiring a formal ANOVA.
Question 5: In Response Surface Methodology (RSM), which design is most commonly used to estimate a full second-order (quadratic) model?
- 2^k full factorial design
- Plackett-Burman screening design
- Central Composite Design (CCD) (Correct answer)
- Resolution III fractional factorial design
Correct answer: Central Composite Design (CCD)
A Central Composite Design adds axial (star) points and center points to a 2^k factorial core, providing the data needed to estimate all linear, quadratic, and two-factor interaction terms in a second-order model. This makes it the standard design for optimization in RSM after a region of interest has been identified.
Question 6: In the method of steepest ascent, what is the experimenter trying to accomplish?
- Estimate the alias structure of a fractional factorial design
- Move systematically from the current experimental region toward the optimum response (Correct answer)
- Calculate the signal-to-noise ratio for each factor combination
- Determine the defining relation of a 2^(k-p) design
Correct answer: Move systematically from the current experimental region toward the optimum response
After fitting a first-order model to screening data, the method of steepest ascent uses the estimated coefficients to define a path of experimentation that moves in the direction of the greatest increase in the predicted response. Experiments are run along this path until no further improvement is observed, at which point a higher-order (RSM) design is applied.
Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Improve Phase: DOE 1
What is the primary purpose of adding center points to a 2^k factorial design?