Lean Six Sigma Black Belt Certification Control Phase: SPC 2 — Questions and Answers
Question 1: On an X-bar chart, a process shows 8 consecutive points all above the centerline. What does this pattern indicate?
- Natural random variation
- A shift in the process mean (Correct answer)
- Increased process variation
- Measurement system error
Correct answer: A shift in the process mean
Eight consecutive points on the same side of the centerline is a Western Electric run rule indicating a sustained shift in the process mean.
Question 2: Which SPC chart is most appropriate for monitoring the number of defects per unit when the sample size varies?
- c chart
- np chart
- u chart (Correct answer)
- p chart
Correct answer: u chart
The u chart monitors defects per unit and accommodates variable sample sizes, unlike the c chart which requires constant sample size.
Question 3: Process capability index Cpk differs from Cp in that Cpk:
- Measures only spread relative to spec limits
- Accounts for process centering as well as spread (Correct answer)
- Is used only for non-normal data
- Requires a minimum of 25 subgroups
Correct answer: Accounts for process centering as well as spread
Cpk accounts for both process spread and the location of the process mean relative to specification limits, penalizing off-center processes.
Question 4: A control chart shows points within control limits but with a distinct sawtooth pattern alternating high-low-high-low. What is the most likely cause?
- Increased random variation
- Over-adjustment of the process (tampering)
- A gradual process drift
- Two distinct process streams mixed in sampling (Correct answer)
Correct answer: Two distinct process streams mixed in sampling
A consistent alternating pattern often indicates two process streams (e.g., two machines or shifts) being sampled alternately within subgroups.
Question 5: The Average Run Length (ARL) for a Shewhart X-bar chart with 3-sigma limits when the process is in control is approximately:
- 27
- 100
- 370 (Correct answer)
- 500
Correct answer: 370
For a 3-sigma control chart in control, the ARL is approximately 370, meaning a false alarm occurs on average every 370 subgroups.
Question 6: When establishing control limits for a new X-bar and R chart, the standard approach is to collect at least how many rational subgroups?
- 10
- 20-25 (Correct answer)
- 50
- 100
Correct answer: 20-25
A minimum of 20–25 subgroups is the standard recommendation to establish reliable control limits with adequate statistical stability.
Question 7: A process has Cp = 1.5 but Cpk = 0.8. What does this tell you?
- The process spread is too wide for the spec limits
- The process is well centered and capable
- The process has adequate spread but is significantly off-center (Correct answer)
- Both indices indicate a capable process
Correct answer: The process has adequate spread but is significantly off-center
Cp = 1.5 shows the process spread fits within specs, but Cpk = 0.8 reveals the process mean is shifted toward or beyond a spec limit.
Lean Six Sigma Black Belt Certification Control Phase: SPC 2
On an X-bar chart, a process shows 8 consecutive points all above the centerline.
What does this pattern indicate?