Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers 2 — Questions and Answers
Question 1: A Six Sigma Black Belt notices that all plotted points on an X-bar chart fall within the control limits but seven consecutive points are above the center line. What should be concluded?
- The process is in statistical control
- A special cause of variation is likely present (Correct answer)
- The control limits need to be recalculated
- The sample size is too small
Correct answer: A special cause of variation is likely present
Seven or more consecutive points on one side of the center line indicate a run, which is evidence of a special cause of variation even though no points exceed the control limits.
Question 2: Which control chart is most appropriate for monitoring the number of paint defects found on each automobile body when the inspection area varies from vehicle to vehicle?
- c chart
- p chart
- u chart (Correct answer)
- np chart
Correct answer: u chart
The u chart monitors the number of defects per unit of measure and is used when the area of opportunity (inspection area) is not constant across samples.
Question 3: When calculating the process capability index Cpk, a Black Belt obtains Cpk = 1.0 and Cp = 1.5. What does this indicate about the process?
- The process is perfectly centered between the specification limits
- The process spread is too wide for the specifications
- The process is capable but not centered within the specification limits (Correct answer)
- The specification limits need to be widened
Correct answer: The process is capable but not centered within the specification limits
A Cp of 1.5 shows the process spread fits well within the specifications, but a lower Cpk of 1.0 reveals the process mean has shifted away from the center of the specification range.
Question 4: An EWMA chart is preferred over a Shewhart X-bar chart in which of the following situations?
- When detecting large shifts in the process mean
- When the subgroup size is greater than 10
- When detecting small sustained shifts in the process mean (Correct answer)
- When monitoring attribute data
Correct answer: When detecting small sustained shifts in the process mean
The EWMA (Exponentially Weighted Moving Average) chart is specifically designed to detect small, sustained shifts in the process mean by incorporating weighted historical data into each plotted point.
Question 5: A process has a Pp of 1.33 but a Cp of 0.89. What is the most likely explanation?
- The process has excessive within-subgroup variation
- The long-term performance is better than the short-term capability
- The between-subgroup variation is smaller than the within-subgroup variation
- The process has significant between-subgroup variation that inflates overall variability (Correct answer)
Correct answer: The process has significant between-subgroup variation that inflates overall variability
A Pp greater than Cp is unusual; however, when Cp is lower than Pp it typically indicates the within-subgroup estimate of sigma is larger, but here Pp > Cp means long-term sigma is smaller, which suggests the subgrouping strategy may not be capturing the true short-term variation correctly.
Question 6: On a moving range (MR) chart used with an individuals (I) chart, what is the upper control limit formula when d2 = 1.128 and D4 = 3.267?
- UCL = D4 × R-bar (Correct answer)
- UCL = 3 × MR-bar / d2
- UCL = MR-bar + 3 × d2
- UCL = D4 × MR-bar / d2
Correct answer: UCL = D4 × R-bar
The upper control limit for a moving range chart is calculated as UCL = D4 multiplied by the average moving range (MR-bar), using the D4 constant for a subgroup size of 2.
Certified Six Sigma Black Belt Exam Certified Six Sigma Black Belt Statistical Process Control (SPC) Questions and Answers 2
A Six Sigma Black Belt notices that all plotted points on an X-bar chart fall within the control limits but seven consecutive points are above the center line.
What should be concluded?