Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 4 — Questions and Answers
Question 1: Which of the following is TRUE about replication in a DOE?
- Replication and repeated measurements are identical concepts
- Replication involves completely re-running the entire experimental setup for a treatment combination (Correct answer)
- Replication reduces the number of degrees of freedom available for error
- Replication eliminates the need for randomization
Correct answer: Replication involves completely re-running the entire experimental setup for a treatment combination
True replication means independently setting up and running an experimental condition again, which provides an estimate of pure experimental error and increases power.
Question 2: A Yates algorithm in factorial DOE analysis is used to:
- Generate the run order for the experiment
- Systematically calculate effect estimates from experimental data (Correct answer)
- Determine the minimum number of runs needed
- Compute the signal-to-noise ratio for each factor
Correct answer: Systematically calculate effect estimates from experimental data
The Yates algorithm is a systematic computational method for calculating all main effects and interaction effects from a 2^k factorial experiment.
Question 3: In a split-plot design, what distinguishes the 'whole-plot' factor from the 'sub-plot' factor?
- Whole-plot factors have more levels than sub-plot factors
- Whole-plot factors are harder or more expensive to change between runs (Correct answer)
- Sub-plot factors are continuous while whole-plot factors are categorical
- Whole-plot factors must be quantitative
Correct answer: Whole-plot factors are harder or more expensive to change between runs
Whole-plot factors are those that are difficult or costly to change (e.g., oven temperature requiring long reset times), so their levels are held fixed across multiple sub-plot factor combinations.
Question 4: What does the coefficient of determination (R²) indicate in a DOE regression model?
- The probability that the model is statistically significant
- The proportion of total variation in the response explained by the model (Correct answer)
- The number of significant factors in the experiment
- The ratio of model error to total error
Correct answer: The proportion of total variation in the response explained by the model
R² represents the fraction of response variation accounted for by the fitted model; a value close to 1 indicates the model explains most of the observed variation.
Question 5: When a DOE residual plot shows a 'funnel' pattern (increasing spread with fitted values), this indicates:
- The model has too many factors included
- Non-constant variance (heteroscedasticity) in the residuals (Correct answer)
- The experiment was not properly randomized
- Significant curvature in the response surface
Correct answer: Non-constant variance (heteroscedasticity) in the residuals
A funnel-shaped residual plot indicates non-constant variance, suggesting a data transformation (e.g., log or square root) may be needed.
Question 6: In Taguchi's parameter design, 'inner array' factors are:
- Noise factors that the engineer cannot control in production
- Control factors that the engineer can set and control (Correct answer)
- Interaction terms between noise and control factors
- Factors that are fixed at their center points
Correct answer: Control factors that the engineer can set and control
The inner array contains the control factors (those the engineer can set), while the outer array contains noise factors that represent uncontrollable variation in actual use.
Question 7: Which of the following best describes the defining relation of a fractional factorial design?
- The equation used to calculate the predicted response values
- The set of effects that equal the identity (I) and determine the alias structure (Correct answer)
- The relationship between factor levels and coded values
- The formula for computing degrees of freedom
Correct answer: The set of effects that equal the identity (I) and determine the alias structure
The defining relation is the set of generator words (each equal to I) from which all aliases can be derived by multiplying elements of the defining relation together.
Certified Six Sigma Black Belt Exam Design of Experiments (DOE) 4
Which of the following is TRUE about replication in a DOE?