Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Improve Phase: DOE 1

Question 1

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

Accepted Answer

To detect curvature (non-linearity) in the response surface

Answer

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?

Accepted Answer

The number of generators used to define the fraction

Answer

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?

Accepted Answer

To account for the variation caused by known but uncontrollable nuisance factors

Answer

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:

Accepted Answer

Identify which main effects and interactions are statistically significant

Answer

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?

Accepted Answer

Central Composite Design (CCD)

Answer

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.

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Improve Phase: DOE 1