Certified Six Sigma Black Belt Exam General 3 — Questions and Answers
Question 1: A process has a Cpk of 0.75. Which statement best describes this process?
- The process is centered and capable
- The process is incapable and likely producing defects (Correct answer)
- The process exceeds Six Sigma quality
- The process is in statistical control
Correct answer: The process is incapable and likely producing defects
A Cpk below 1.0 indicates the process is not capable of consistently meeting specifications, meaning defects are likely being produced.
Question 2: What distinguishes a Special Cause variation from Common Cause variation on a control chart?
- Special cause is always larger in magnitude
- Special cause appears as non-random patterns or points outside control limits (Correct answer)
- Common cause requires immediate corrective action
- Special cause is inherent to the process design
Correct answer: Special cause appears as non-random patterns or points outside control limits
Special cause variation is indicated by signals such as points outside control limits, runs, or trends — patterns that are statistically unlikely in a stable process.
Question 3: Which Design of Experiments (DOE) design allows a Black Belt to study main effects and two-factor interactions with a minimum number of runs?
- Full factorial design
- Response surface methodology
- Fractional factorial design (Correct answer)
- One-factor-at-a-time (OFAT) design
Correct answer: Fractional factorial design
Fractional factorial designs study a carefully selected subset of factor combinations, efficiently estimating main effects and two-factor interactions with fewer runs.
Question 4: In a Gage R&R study, what does 'reproducibility' specifically measure?
- Variation due to the measurement instrument itself
- Variation between different operators measuring the same parts (Correct answer)
- Total measurement system variation
- Part-to-part variation
Correct answer: Variation between different operators measuring the same parts
Reproducibility captures the variation attributable to different appraisers (operators) measuring the same items under the same conditions.
Question 5: A Black Belt wants to compare the means of three process configurations simultaneously. Which statistical test is most appropriate?
- Paired t-test
- Two-sample t-test
- One-way ANOVA (Correct answer)
- Chi-square test
Correct answer: One-way ANOVA
One-way ANOVA tests whether the means of three or more groups are statistically equal, avoiding the inflated Type I error risk of multiple t-tests.
Question 6: What is the relationship between Type I error (α) and Type II error (β) when sample size is held constant?
- Decreasing α automatically decreases β
- Decreasing α increases β (they move inversely) (Correct answer)
- α and β are independent of each other
- Both errors decrease together as α decreases
Correct answer: Decreasing α increases β (they move inversely)
With fixed sample size, making the significance level stricter (smaller α) makes it harder to reject H₀, increasing the probability of failing to detect a real effect (β).
Question 7: Which lean concept describes the total time from when a customer request is received to when the product or service is delivered?
- Cycle time
- Takt time
- Lead time (Correct answer)
- Throughput time
Correct answer: Lead time
Lead time spans the entire customer experience from order placement to delivery, encompassing both value-added and non-value-added activities.
Certified Six Sigma Black Belt Exam General 3
A process has a Cpk of 0.75.
Which statement best describes this process?