Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Design of Experiments (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 degrees of freedom for main effect estimates
- To detect curvature (nonlinearity) in the response surface (Correct answer)
- To reduce the total number of experimental runs required
- To eliminate aliasing between two-factor interactions
Correct answer: To detect curvature (nonlinearity) in the response surface
Center points, where all factors are set at their midpoint (coded as 0), allow the experimenter to test for pure quadratic curvature in the response without committing to a full response surface design. If the average of the center point responses differs significantly from the average of the factorial points, curvature is present.
Question 2: In a 2^k factorial experiment, blocking is used primarily to:
- Increase the precision of interaction effect estimates at the expense of main effects
- Isolate and remove the effect of nuisance variables from the estimate of treatment effects (Correct answer)
- Reduce the total number of experimental runs by aliasing blocks with high-order interactions
- Ensure that all factor combinations appear in each replicate of the experiment
Correct answer: Isolate and remove the effect of nuisance variables from the estimate of treatment effects
Blocking assigns runs to groups (blocks) to account for a known but uncontrollable source of variation (e.g., different batches, operators, or days). By confounding the block effect with a high-order interaction deemed negligible, the experimenter removes nuisance variation from the experimental error, improving sensitivity to factor effects.
Question 3: A Box-Behnken design differs from a Central Composite Design (CCD) in that:
- Box-Behnken designs include axial star points that extend beyond the factorial cube
- Box-Behnken designs never require all factors at their extreme (high/low) levels simultaneously (Correct answer)
- Box-Behnken designs require far more runs than an equivalent CCD for the same number of factors
- Box-Behnken designs can only be used when exactly three factors are under investigation
Correct answer: Box-Behnken designs never require all factors at their extreme (high/low) levels simultaneously
Box-Behnken designs place experimental points at the midpoints of the edges of the factor space, intentionally avoiding vertex (corner) points where all factors are simultaneously at their extreme levels. This makes them advantageous when corner combinations are physically impossible, hazardous, or prohibitively expensive to produce.
Question 4: In a two-factor factorial experiment, a statistically significant AB interaction effect implies that:
- Factors A and B each have large main effects that dominate the response
- The effect of factor A on the response is consistent regardless of the level of factor B
- The effect of one factor on the response changes depending on the level of the other factor (Correct answer)
- Both factors should be removed from the model and the experiment should be redesigned
Correct answer: The effect of one factor on the response changes depending on the level of the other factor
An interaction means the factors do not act independently — the magnitude or even the direction of one factor's effect differs across the levels of the other factor. When a significant interaction is present, main effects alone are insufficient to describe the system, and the interaction term must be included in the model and interpreted carefully.
Question 5: Which of the following best describes the Yates algorithm in factorial design analysis?
- A randomization procedure that assigns factor combinations to experimental runs in a balanced order
- A systematic, column-based arithmetic procedure for computing all factorial effect estimates from data arranged in standard order (Correct answer)
- A graphical technique for identifying which factors are active using a normal probability plot of effects
- A method for constructing a resolution III fractional factorial from a full factorial design
Correct answer: A systematic, column-based arithmetic procedure for computing all factorial effect estimates from data arranged in standard order
The Yates algorithm processes response data listed in Yates standard order through k successive cycles of additions and subtractions. The final column yields the contrast totals for all 2^k factorial effects (main effects and interactions), which are then divided by the appropriate divisor to obtain effect estimates.
Question 6: Plackett-Burman designs are most appropriately used for which of the following objectives?
- Optimizing a response surface by estimating quadratic and interaction terms with high precision
- Screening a large number of factors (up to N-1 factors in N runs) to identify the vital few (Correct answer)
- Estimating all two-factor interactions without any aliasing in a minimal-run experiment
- Blocking a full factorial experiment to control for a known nuisance variable
Correct answer: Screening a large number of factors (up to N-1 factors in N runs) to identify the vital few
Plackett-Burman designs are highly saturated two-level screening designs (e.g., 12, 20, 24 runs) that allow up to N-1 factors to be studied in N runs. They are resolution III designs ideal for the early phase of experimentation when the goal is to separate the vital few factors from the trivial many, with the understanding that two-factor interactions are partially aliased with main effects.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Design of Experiments (DOE) 1
What is the primary purpose of adding center points to a 2^k factorial design?