ASQ Six Sigma Black Belt 3 — Questions and Answers
Question 1: A Black Belt notices that a control chart shows 8 consecutive points on the same side of the centerline. According to Western Electric rules, this indicates:
- Natural process variation
- A special cause of variation (Correct answer)
- A measurement system error only
- The process is in control but capable
Correct answer: A special cause of variation
Eight or more consecutive points on one side of the centerline is a Western Electric run rule indicating a non-random (special cause) pattern.
Question 2: Which type of hypothesis test should be used when comparing the means of two independent groups with unknown and unequal variances?
- Paired t-test
- Welch's t-test (Correct answer)
- One-sample z-test
- F-test
Correct answer: Welch's t-test
Welch's t-test (two-sample t-test with unequal variances) is appropriate when comparing two independent group means with unequal variances.
Question 3: In regression analysis, what does the coefficient of determination (R²) measure?
- The slope of the regression line
- The proportion of variance in Y explained by X (Correct answer)
- Whether the residuals are normally distributed
- The statistical significance of the model
Correct answer: The proportion of variance in Y explained by X
R² represents the proportion of total variation in the response variable explained by the predictor variable(s) in the model.
Question 4: A Six Sigma team wants to prioritize which defect types to address first. Which tool would BEST help visualize the cumulative impact of defect categories?
- Histogram
- Scatter plot
- Pareto chart (Correct answer)
- Box plot
Correct answer: Pareto chart
A Pareto chart ranks defect categories by frequency and overlays a cumulative percentage line, enabling the team to identify the vital few causes.
Question 5: In the context of Lean Six Sigma, what does 'takt time' represent?
- The total time required to complete one unit from start to finish
- The available production time divided by customer demand rate (Correct answer)
- The time a unit spends waiting between process steps
- The cycle time of the bottleneck operation
Correct answer: The available production time divided by customer demand rate
Takt time is the available production time divided by customer demand, setting the pace at which products must be completed to meet demand.
Question 6: Which type of control chart is most appropriate for monitoring the proportion defective when subgroup sizes vary?
- p-chart (Correct answer)
- np-chart
- c-chart
- u-chart
Correct answer: p-chart
The p-chart monitors the proportion (fraction) defective and accommodates variable subgroup sizes, unlike the np-chart which requires constant subgroup size.
Question 7: What is the primary objective of a Gauge R&R (Repeatability and Reproducibility) study?
- To determine whether a process is centered within specification limits
- To quantify how much measurement system variation contributes to total observed variation (Correct answer)
- To calibrate measuring instruments to NIST standards
- To identify outliers in production data
Correct answer: To quantify how much measurement system variation contributes to total observed variation
Gauge R&R separates total measurement variation into repeatability (equipment variation) and reproducibility (appraiser variation) components.
ASQ Six Sigma Black Belt 3
A Black Belt notices that a control chart shows 8 consecutive points on the same side of the centerline.
According to Western Electric rules, this indicates: