Certified Six Sigma Black Belt Exam Assessment 5 — Questions and Answers
Question 1: A team assessing supplier quality uses an attribute agreement analysis. Three appraisers each inspect 30 parts twice. What is the primary metric reported?
- Gauge R&R %Study Variation
- Kappa statistic (Cohen's Kappa) (Correct answer)
- Discrimination ratio
- Cpk for attribute data
Correct answer: Kappa statistic (Cohen's Kappa)
Cohen's Kappa measures agreement between appraisers (and within appraisers vs. reference) beyond chance in attribute measurement system analysis.
Question 2: During a process assessment, a Black Belt discovers that a key input variable (X) explains 64% of the variation in the output (Y). What is the correlation coefficient (r) between X and Y?
- 0.64
- 0.80 (Correct answer)
- 0.41
- 0.51
Correct answer: 0.80
R-squared = 0.64 means r = √0.64 = 0.80; the correlation coefficient is the square root of the coefficient of determination.
Question 3: A Black Belt is assessing whether the variance of a new process is lower than the variance of the existing process. Which hypothesis test is appropriate?
- Two-sample t-test
- F-test (Levene's or Bartlett's test) (Correct answer)
- Z-test for proportions
- Mann-Whitney U test
Correct answer: F-test (Levene's or Bartlett's test)
The F-test (or Levene's/Bartlett's test) is used to compare variances between two populations.
Question 4: In a process assessment, a team identifies 'opportunity' as each solder joint on a circuit board. The board has 200 joints and 8 defects were found across 50 boards. What is the DPMO?
- 800 (Correct answer)
- 8,000
- 800,000
- 80,000
Correct answer: 800
DPMO = (Defects / (Units × Opportunities per unit)) × 1,000,000 = (8 / (50 × 200)) × 1,000,000 = 800 DPMO.
Question 5: Which assessment method evaluates the risk of a process failure by examining 'what can go wrong' before the process is implemented?
- Control chart analysis
- Design FMEA (DFMEA)
- Process FMEA (PFMEA) (Correct answer)
- Fault tree analysis
Correct answer: Process FMEA (PFMEA)
Process FMEA (PFMEA) proactively identifies potential failure modes in a process before implementation and assesses their risk via RPN.
Question 6: A Black Belt assesses process capability using a Ppk of 1.1 and a Cpk of 1.6 for the same process. What does this large gap between Ppk and Cpk suggest?
- The measurement system has high bias
- Significant special cause variation is present in the long-term data (Correct answer)
- The process is centered within specification limits
- Short-term variation exceeds long-term variation
Correct answer: Significant special cause variation is present in the long-term data
A large gap where Cpk >> Ppk indicates that long-term performance (Ppk) is significantly worse than short-term potential (Cpk), suggesting special cause variation over time.
Question 7: A team is conducting a process assessment and finds the average cycle time is 45 minutes with a standard deviation of 8 minutes. The upper spec limit is 60 minutes and lower spec limit is 20 minutes. What is Cpk?
- 0.94
- 1.04
- 0.625 (Correct answer)
- 1.25
Correct answer: 0.625
Cpk = min((USL−mean)/(3σ), (mean−LSL)/(3σ)) = min(15/24, 25/24) = min(0.625, 1.042) = 0.625, indicating the upper spec limit is the binding constraint.
Certified Six Sigma Black Belt Exam Assessment 5
A team assessing supplier quality uses an attribute agreement analysis.
Three appraisers each inspect 30 parts twice.
What is the primary metric reported?