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

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:

Accepted Answer

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

Answer

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:

Accepted Answer

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

Answer

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:

Accepted Answer

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

Answer

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?

Accepted Answer

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

Answer

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.

Certified Six Sigma Black Belt Exam Practice Test

Certified Six Sigma Black Belt Exam Practice Test

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