Certified Six Sigma Black Belt Exam Assessment 2 — Questions and Answers
Question 1: A Gauge R&R study reveals that %Study Variation for repeatability is 28% and for reproducibility is 19%. What is the overall assessment of this measurement system?
- Acceptable — both components are below 30%
- Marginal — total variation exceeds 30% and requires investigation (Correct answer)
- Unacceptable — reproducibility alone disqualifies the system
- Acceptable — only repeatability is evaluated in Gauge R&R
Correct answer: Marginal — total variation exceeds 30% and requires investigation
When combined %Study Variation (repeatability + reproducibility) exceeds 30%, the measurement system is considered marginal to unacceptable and warrants improvement.
Question 2: Which metric best quantifies the ability of a process to meet customer specifications over the long term, accounting for process shifts?
- Cp
- Cpk
- Pp
- Ppk (Correct answer)
Correct answer: Ppk
Ppk uses overall (long-term) standard deviation and accounts for process centering, making it the best long-term capability index.
Question 3: During an assessment of a transactional process, a team finds a defect rate of 3,400 DPMO. What sigma level does this correspond to?
- 3.0 sigma
- 3.4 sigma
- 4.0 sigma (Correct answer)
- 4.5 sigma
Correct answer: 4.0 sigma
A DPMO of 3,400 corresponds to approximately 4.0 sigma (short-term), accounting for the standard 1.5 sigma shift.
Question 4: A Black Belt is assessing process stability before calculating capability indices. Which tool is most appropriate for this evaluation?
- Histogram
- Control chart (Correct answer)
- Pareto chart
- Scatter diagram
Correct answer: Control chart
Control charts reveal whether a process is in statistical control (stable) over time, which is a prerequisite for valid capability calculations.
Question 5: In a process assessment, the number of defects per unit (DPU) is 0.08. Assuming a Poisson distribution, what is the approximate first-pass yield (FPY)?
- 92.0%
- 92.3% (Correct answer)
- 96.0%
- 99.2%
Correct answer: 92.3%
FPY = e^(−DPU) = e^(−0.08) ≈ 0.923, or approximately 92.3%.
Question 6: A team is assessing which of five potential root causes contributes most to output variation. Which statistical technique should they use?
- Hypothesis testing
- Multi-vari analysis (Correct answer)
- Process FMEA
- Affinity diagram
Correct answer: Multi-vari analysis
Multi-vari analysis is specifically designed to identify and compare sources of variation across families (positional, cyclical, temporal) to find dominant contributors.
Question 7: When assessing process capability for a non-normal distribution, what is the most rigorous approach?
- Increase sample size until the data appear normal
- Apply a Box-Cox transformation or fit an appropriate distribution (Correct answer)
- Use only Cpk regardless of distribution shape
- Divide specification limits by the process standard deviation
Correct answer: Apply a Box-Cox transformation or fit an appropriate distribution
Transforming non-normal data (Box-Cox) or fitting the actual distribution ensures capability indices accurately reflect the true process performance.
Certified Six Sigma Black Belt Exam Assessment 2
A Gauge R&R study reveals that %Study Variation for repeatability is 28% and for reproducibility is 19%.
What is the overall assessment of this measurement system?