Lean Six Sigma Black Belt Certification Statistical Process Control (SPC) 5 — Questions and Answers
Question 1: A Black Belt observes that the R-chart shows statistical control, but the X-bar chart shows several out-of-control points. What is the correct interpretation?
- The process variability has increased
- The process mean has shifted while variability remains stable (Correct answer)
- The control limits are incorrectly calculated
- Both charts must be in control before analysis is valid
Correct answer: The process mean has shifted while variability remains stable
An in-control R-chart with out-of-control X-bar points indicates that process spread is stable but the process mean has shifted, a classic sign of a location-type special cause.
Question 2: Which of the following best describes 'rational subgrouping'?
- Selecting the largest possible subgroup size to improve sensitivity
- Forming subgroups so within-subgroup variation represents only common cause variation (Correct answer)
- Randomizing the order of measurement to eliminate bias
- Selecting subgroups that span the full specification range
Correct answer: Forming subgroups so within-subgroup variation represents only common cause variation
Rational subgrouping means forming subgroups so that variation within each subgroup reflects only natural, common cause variation, making between-subgroup shifts detectable.
Question 3: What sigma level corresponds to a defect rate of approximately 3.4 DPMO in the Motorola/Six Sigma convention?
- 3 sigma
- 4 sigma
- 5 sigma
- 6 sigma (Correct answer)
Correct answer: 6 sigma
In the Six Sigma convention, a 6-sigma process yields 3.4 DPMO, accounting for the standard 1.5-sigma long-term mean shift assumption.
Question 4: A Levey-Jennings chart is most commonly used in which industry application of SPC?
- Automotive manufacturing torque monitoring
- Clinical laboratory quality control (Correct answer)
- Software defect tracking
- Chemical batch yield monitoring
Correct answer: Clinical laboratory quality control
Levey-Jennings charts are a standard SPC tool in clinical laboratories for monitoring analytical quality control materials and detecting assay drift.
Question 5: When a process exhibits autocorrelation, using standard Shewhart control charts will most likely result in:
- Control limits that are too wide, causing missed signals
- Control limits that are too narrow, causing excessive false alarms (Correct answer)
- Improved detection of small process shifts
- No change in chart performance
Correct answer: Control limits that are too narrow, causing excessive false alarms
Positive autocorrelation reduces the estimated within-subgroup variability, leading to artificially narrow control limits and inflated false alarm rates on Shewhart charts.
Question 6: Which statistic is plotted on a median chart (X-tilde chart) instead of the subgroup average?
- The geometric mean of the subgroup
- The middle value of the ranked subgroup observations (Correct answer)
- The range divided by d2
- The subgroup standard deviation
Correct answer: The middle value of the ranked subgroup observations
The median chart plots the middle (median) value of each subgroup, offering a simpler calculation that is also robust to outliers compared to the mean.
Question 7: In Phase I SPC analysis, what is the primary objective?
- Monitor future production in real time
- Establish baseline control limits from historical data after removing assignable causes (Correct answer)
- Calculate Cpk to certify the process
- Train operators on chart interpretation
Correct answer: Establish baseline control limits from historical data after removing assignable causes
Phase I SPC involves retrospective analysis of historical data to identify and remove special causes, establishing stable baseline control limits for future monitoring (Phase II).
Lean Six Sigma Black Belt Certification Statistical Process Control (SPC) 5
A Black Belt observes that the R-chart shows statistical control, but the X-bar chart shows several out-of-control points.
What is the correct interpretation?