Lean Six Sigma Black Belt Certification Control Phase: SPC 5 — Questions and Answers
Question 1: A multivariate control chart (e.g., Hotelling's T² chart) is preferred over separate univariate charts when:
- Only one quality characteristic is critical
- Multiple correlated quality characteristics must be monitored simultaneously (Correct answer)
- The process produces attribute data
- Sample sizes are too small for X-bar charts
Correct answer: Multiple correlated quality characteristics must be monitored simultaneously
Hotelling's T² chart monitors multiple correlated variables together, preventing inflated false alarm rates that occur when running many separate univariate charts.
Question 2: The D4 constant on an R chart for a subgroup size of n=5 is approximately 2.114. This constant is used to calculate:
- The lower control limit of the R chart
- The upper control limit of the R chart (Correct answer)
- The center line of the R chart
- The process standard deviation estimate
Correct answer: The upper control limit of the R chart
UCL_R = D4 × R-bar; for n=5, D4 ≈ 2.114, so the upper control limit is 2.114 times the average range.
Question 3: Pre-control charts differ from standard SPC control charts primarily because they:
- Require a minimum of 25 subgroups to establish limits
- Use specification limits to set zones rather than calculated statistical control limits (Correct answer)
- Monitor only attribute data such as defect counts
- Are based on the CUSUM methodology
Correct answer: Use specification limits to set zones rather than calculated statistical control limits
Pre-control uses zones defined by the specification limits (green = middle half of spec, yellow = outer quarters, red = beyond spec) rather than statistically derived control limits.
Question 4: When transitioning a process from the Improve phase to Control, which action ensures the SPC chart remains relevant long-term?
- Using the original pre-improvement control limits to detect regression
- Recalculating control limits based on the improved process baseline (Correct answer)
- Switching from variables charts to attribute charts after improvement
- Widening control limits to reduce false alarms after changes
Correct answer: Recalculating control limits based on the improved process baseline
After process improvement, new control limits must be calculated from the improved baseline to correctly reflect the new process capability and detect future deviations.
Question 5: Zone C on a Western Electric control chart refers to the region between:
- 0 and 1 sigma from the centerline (Correct answer)
- 1 and 2 sigma from the centerline
- 2 and 3 sigma from the centerline
- Beyond 3 sigma from the centerline
Correct answer: 0 and 1 sigma from the centerline
Zone C is the innermost zone spanning 0 to 1 sigma on each side of the centerline; Zone B is 1–2 sigma, and Zone A is 2–3 sigma.
Question 6: A Six Sigma process has a process sigma level of 6, which corresponds to a defect rate of 3.4 DPMO. This calculation assumes:
- The process is perfectly centered with zero shift
- A 1.5 sigma long-term process shift from the target (Correct answer)
- A Cpk of exactly 2.0 with no centering offset
- Bilateral specification limits with equal distance on both sides
Correct answer: A 1.5 sigma long-term process shift from the target
The 3.4 DPMO figure for a 6-sigma process incorporates the industry-standard assumption of a 1.5-sigma long-term shift in the process mean.
Question 7: Which statement correctly describes the relationship between a process being 'in control' and 'capable'?
- A process in control is always capable of meeting specifications
- A process can be in control but not capable, capable but not in control, both, or neither (Correct answer)
- Capability can only be assessed after a process is in control
- In-control and capable are equivalent terms in SPC
Correct answer: A process can be in control but not capable, capable but not in control, both, or neither
Statistical control (predictability) and capability (meeting specs) are independent: a process can be stable but centered outside specs, or meeting specs but erratically.
Lean Six Sigma Black Belt Certification Control Phase: SPC 5
A multivariate control chart (e.g., Hotelling's T² chart) is preferred over separate univariate charts when: