Lean Six Sigma Black Belt Certification Statistical Process Control (SPC) 4 — Questions and Answers
Question 1: When calculating the process performance index Ppk, which measure of sigma is used?
- Within-subgroup sigma estimated from R-bar/d2
- Overall sample standard deviation of all individual values (Correct answer)
- Sigma from a normal probability plot
- Moving range average divided by d2
Correct answer: Overall sample standard deviation of all individual values
Ppk uses the overall (long-term) standard deviation calculated from all individual data points, capturing both common and special cause variation.
Question 2: A Black Belt wants to detect a 1.5-sigma shift in the process mean quickly. Which chart would be MOST effective?
- Shewhart X-bar chart with subgroup size 5
- CUSUM or EWMA chart (Correct answer)
- c-chart
- Moving range chart
Correct answer: CUSUM or EWMA chart
CUSUM and EWMA charts are specifically designed to detect small to moderate process mean shifts (1–2 sigma) much faster than Shewhart charts.
Question 3: Which assumption is critical for control charts based on the normal distribution to be valid?
- The data must be discrete
- Observations must be independent and identically distributed (Correct answer)
- Subgroup sizes must be at least 30
- The process must be capable (Cpk ≥ 1.33)
Correct answer: Observations must be independent and identically distributed
Control charts assume observations are independent and come from the same distribution; autocorrelation or non-stationarity can cause false signals and misleading limits.
Question 4: On an I-MR chart, the Moving Range chart monitors which source of variation?
- Variation between subgroups
- Consecutive point-to-point variation (short-term variability) (Correct answer)
- Long-term process drift
- Between-operator variability
Correct answer: Consecutive point-to-point variation (short-term variability)
The MR chart tracks the absolute difference between consecutive individual values, capturing short-term, point-to-point process variability.
Question 5: A process engineer discovers that subgroups on an X-bar chart were formed by collecting samples from multiple process streams mixed together. What problem does this cause?
- Increased sensitivity to special causes
- Control limits that are too wide, masking real shifts
- Control limits that are too narrow, causing false alarms (Correct answer)
- No impact on control limit validity
Correct answer: Control limits that are too narrow, causing false alarms
Mixing samples from multiple streams within a subgroup inflates within-subgroup variation, narrowing control limits and producing excessive false alarms (a violation of rational subgrouping).
Question 6: The Average Run Length (ARL) of a control chart at the in-control state is approximately 370 for 3-sigma limits. What does this mean?
- The process will produce 370 defects before triggering an alarm
- On average, a false alarm occurs once every 370 subgroups when the process is in control (Correct answer)
- The process requires 370 data points to establish control limits
- 370 subgroups must be collected before the chart is reliable
Correct answer: On average, a false alarm occurs once every 370 subgroups when the process is in control
ARL₀ ≈ 370 for 3-sigma Shewhart charts means a false alarm (Type I error) is expected approximately once every 370 subgroups when no real shift has occurred.
Question 7: Which control chart would be used to monitor the fraction of nonconforming units when subgroup sizes are unequal?
- np-chart
- c-chart
- p-chart (Correct answer)
- u-chart
Correct answer: p-chart
The p-chart monitors the proportion (fraction) of nonconforming items and accommodates variable subgroup sizes, with control limits recalculated for each subgroup size.
Lean Six Sigma Black Belt Certification Statistical Process Control (SPC) 4
When calculating the process performance index Ppk, which measure of sigma is used?