Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 2 — Questions and Answers
Question 1: A process engineer notices that a control chart shows 8 consecutive points on one side of the centerline. What does this pattern indicate?
- Random common cause variation
- A special cause shift in the process mean (Correct answer)
- Measurement system error only
- Normal process behavior within control limits
Correct answer: A special cause shift in the process mean
Eight consecutive points on one side of the centerline is a Western Electric Rule violation indicating a special cause—likely a sustained shift in the process mean.
Question 2: Which measure best describes the spread of the middle 50% of a data distribution?
- Standard deviation
- Range
- Interquartile range (IQR) (Correct answer)
- Variance
Correct answer: Interquartile range (IQR)
The interquartile range (IQR) is the difference between the 75th and 25th percentiles, capturing the spread of the central 50% of data.
Question 3: In regression analysis, what does a residual represent?
- The slope of the regression line
- The difference between observed and predicted values (Correct answer)
- The correlation coefficient squared
- The intercept of the regression equation
Correct answer: The difference between observed and predicted values
A residual is the difference between an observed data value and the value predicted by the regression model.
Question 4: A Black Belt wants to compare the variance of two independent processes. Which statistical test is most appropriate?
- Paired t-test
- F-test (Levene's or Bartlett's test) (Correct answer)
- Chi-square goodness-of-fit
- One-sample Z-test
Correct answer: F-test (Levene's or Bartlett's test)
The F-test (or Levene's/Bartlett's test) is used to compare the variances of two or more independent populations.
Question 5: What is the primary purpose of a multi-vari chart in the Measure phase?
- To display process capability indices
- To identify the largest source of variation among positional, cyclical, and temporal families (Correct answer)
- To confirm normality of the data
- To display the cumulative defect frequency
Correct answer: To identify the largest source of variation among positional, cyclical, and temporal families
A multi-vari chart graphically separates and compares positional, cyclical, and temporal sources of variation to identify the dominant family.
Question 6: When a process has a Cpk of 0.85, what does this indicate?
- The process is centered and capable
- The process is not capable of consistently meeting specifications (Correct answer)
- The process has zero defects per million opportunities
- The process mean equals the specification midpoint
Correct answer: The process is not capable of consistently meeting specifications
A Cpk below 1.00 indicates the process is not capable, meaning a significant portion of output falls outside specification limits.
Question 7: Which type of data requires a p-chart for monitoring in statistical process control?
- Continuous measurement data
- Proportion defective with variable subgroup sizes (Correct answer)
- Count of defects per unit
- Individual measurements with no subgrouping
Correct answer: Proportion defective with variable subgroup sizes
The p-chart monitors the proportion of defective items in subgroups and accommodates variable subgroup sizes.
Lean Six Sigma Black Belt Certification Measure Phase: Data Analysis 2
A process engineer notices that a control chart shows 8 consecutive points on one side of the centerline.
What does this pattern indicate?