Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC Questions and Answers 2 — Questions and Answers
Question 1: A process has an X-bar chart with UCL = 50.5, CL = 50.0, and LCL = 49.5. If a single point plots at 50.7, what is the correct interpretation?
- The process is in statistical control
- The process has a special cause variation (Correct answer)
- The point is within specification limits so no action is needed
- The control limits need to be recalculated
Correct answer: The process has a special cause variation
Any point plotting beyond a control limit signals a special cause of variation requiring investigation.
Question 2: Which Western Electric rule is violated when two out of three consecutive points fall in Zone A on the same side of the center line?
- Rule 1 — point beyond 3 sigma
- Rule 2 — two of three in Zone A (Correct answer)
- Rule 3 — four of five in Zone B or beyond
- Rule 4 — eight consecutive points on one side
Correct answer: Rule 2 — two of three in Zone A
Western Electric Rule 2 triggers when two out of three consecutive points fall in Zone A (between 2σ and 3σ) on the same side.
Question 3: When should a Black Belt choose an Individuals and Moving Range (I-MR) chart over an X-bar and R chart?
- When the sample size is greater than 10
- When data is collected in rational subgroups of 5
- When only one measurement per time period is available (Correct answer)
- When the data follows a Poisson distribution
Correct answer: When only one measurement per time period is available
I-MR charts are used when subgrouping is not possible and only individual measurements are available per sampling period.
Question 4: What is the primary purpose of calculating process capability index Cpk rather than Cp?
- Cpk measures long-term variation while Cp measures short-term
- Cpk accounts for process centering relative to specification limits (Correct answer)
- Cpk uses control chart limits instead of specification limits
- Cpk is only applicable to non-normal data
Correct answer: Cpk accounts for process centering relative to specification limits
Cpk accounts for both process spread and how well the process is centered between the specification limits.
Question 5: On a p-chart monitoring the fraction defective, what distribution is used to calculate the control limits?
- Normal distribution
- Binomial distribution (Correct answer)
- Poisson distribution
- Exponential distribution
Correct answer: Binomial distribution
The p-chart is based on the binomial distribution since it tracks the proportion of nonconforming units in a sample.
Question 6: A u-chart is preferred over a c-chart when which condition exists?
- The number of defects per unit follows a normal distribution
- The sample size varies from subgroup to subgroup (Correct answer)
- Only one type of defect is being tracked
- The process is already in statistical control
Correct answer: The sample size varies from subgroup to subgroup
A u-chart tracks defects per unit and accommodates varying sample sizes, while a c-chart requires constant sample sizes.
Lean Six Sigma Black Belt Certification Lean Six Sigma Black Belt Control Phase: SPC Questions and Answers 2
A process has an X-bar chart with UCL = 50.5, CL = 50.0, and LCL = 49.5.
If a single point plots at 50.7, what is the correct interpretation?