Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Design of Experiments (DOE) 1

Question 1

What is the primary purpose of adding center points to a 2^k factorial design?

Accepted Answer

To detect curvature (nonlinearity) in the response surface

Answer

To increase the degrees of freedom for main effect estimates

Answer

To reduce the total number of experimental runs required

Answer

To eliminate aliasing between two-factor interactions

Question 2

In a 2^k factorial experiment, blocking is used primarily to:

Accepted Answer

Isolate and remove the effect of nuisance variables from the estimate of treatment effects

Answer

Increase the precision of interaction effect estimates at the expense of main effects

Answer

Reduce the total number of experimental runs by aliasing blocks with high-order interactions

Answer

Ensure that all factor combinations appear in each replicate of the experiment

Question 3

A Box-Behnken design differs from a Central Composite Design (CCD) in that:

Accepted Answer

Box-Behnken designs never require all factors at their extreme (high/low) levels simultaneously

Answer

Box-Behnken designs include axial star points that extend beyond the factorial cube

Answer

Box-Behnken designs require far more runs than an equivalent CCD for the same number of factors

Answer

Box-Behnken designs can only be used when exactly three factors are under investigation

Question 4

In a two-factor factorial experiment, a statistically significant AB interaction effect implies that:

Accepted Answer

The effect of one factor on the response changes depending on the level of the other factor

Answer

Factors A and B each have large main effects that dominate the response

Answer

The effect of factor A on the response is consistent regardless of the level of factor B

Answer

Both factors should be removed from the model and the experiment should be redesigned

Question 5

Which of the following best describes the Yates algorithm in factorial design analysis?

Accepted Answer

A systematic, column-based arithmetic procedure for computing all factorial effect estimates from data arranged in standard order

Answer

A randomization procedure that assigns factor combinations to experimental runs in a balanced order

Answer

A graphical technique for identifying which factors are active using a normal probability plot of effects

Answer

A method for constructing a resolution III fractional factorial from a full factorial design

Question 6

Plackett-Burman designs are most appropriately used for which of the following objectives?

Accepted Answer

Screening a large number of factors (up to N-1 factors in N runs) to identify the vital few

Answer

Optimizing a response surface by estimating quadratic and interaction terms with high precision

Answer

Estimating all two-factor interactions without any aliasing in a minimal-run experiment

Answer

Blocking a full factorial experiment to control for a known nuisance variable