Lean Six Sigma Green Belt Certification DMAIC: Measure Phase Tools 5 — Questions and Answers
Question 1: A Green Belt plots an X-bar chart and notices that all sample means fall within the control limits but 90% cluster tightly near the centerline. What is the most likely cause?
- The process is highly capable
- The subgroup sample size is too small
- The control limits are too wide relative to the actual process variation (Correct answer)
- Common cause variation has been eliminated
Correct answer: The control limits are too wide relative to the actual process variation
When points cluster too closely to the centerline, the control limits were likely calculated from inflated variation estimates, making them too wide to detect real signals.
Question 2: Which formula correctly expresses the relationship between total observed variation, process variation, and measurement system variation?
- σ²_total = σ²_process × σ²_measurement
- σ²_total = σ²_process + σ²_measurement (Correct answer)
- σ²_total = σ²_process − σ²_measurement
- σ²_total = (σ²_process + σ²_measurement) / 2
Correct answer: σ²_total = σ²_process + σ²_measurement
Variances from independent sources are additive; total observed variance equals the sum of process variance and measurement system variance.
Question 3: A practitioner uses an attribute agreement analysis with three appraisers and 50 parts. What is the primary output being evaluated?
- The precision of a continuous measurement gauge
- The consistency of appraisers in classifying parts as pass/fail or by category (Correct answer)
- The number of distinct categories a gauge can detect
- The Cpk of the inspection process
Correct answer: The consistency of appraisers in classifying parts as pass/fail or by category
Attribute agreement analysis evaluates how consistently appraisers agree with each other and with a reference standard when making categorical (attribute) judgments.
Question 4: In a time series plot of daily defect counts, a practitioner observes a consistent upward trend over 20 days. This pattern most likely indicates:
- The process is stable with high common cause variation
- A special cause is systematically affecting the process over time (Correct answer)
- The measurement system has poor repeatability
- The sample size is insufficient
Correct answer: A special cause is systematically affecting the process over time
A sustained directional trend in a time series plot is a non-random pattern that indicates a special cause (e.g., tool wear, material degradation) is systematically shifting the process.
Question 5: When calculating sigma level from a DPMO value, a Green Belt must account for the 1.5-sigma shift convention because:
- All processes naturally drift by exactly 1.5 sigma over time
- It is a standard assumption that long-term process mean shifts by approximately 1.5 sigma from the short-term mean (Correct answer)
- Measurement systems always add 1.5 sigma of error
- The normal distribution table only works with the 1.5 shift applied
Correct answer: It is a standard assumption that long-term process mean shifts by approximately 1.5 sigma from the short-term mean
The 1.5-sigma shift is a convention established by Motorola to account for the typical long-term drift of a process mean relative to its short-term capability.
Question 6: A Green Belt wants to compare the variation between two suppliers' part dimensions. Which graphical tool best allows a direct visual comparison of spread and central tendency for both groups simultaneously?
- Pareto chart
- Scatter diagram
- Box plot (box-and-whisker plot) (Correct answer)
- Run chart
Correct answer: Box plot (box-and-whisker plot)
A box plot displays median, quartiles, and outliers for each group side by side, enabling direct visual comparison of both central tendency and spread between groups.
Question 7: What is the key difference between rational subgrouping and random sampling in the context of control charts?
- Rational subgrouping is used only for attribute data; random sampling for continuous data
- Rational subgrouping groups samples to maximize variation between subgroups while minimizing it within, to detect process shifts (Correct answer)
- Random sampling ensures subgroup sizes are equal across all samples
- Rational subgrouping eliminates the need for control limits
Correct answer: Rational subgrouping groups samples to maximize variation between subgroups while minimizing it within, to detect process shifts
Rational subgrouping deliberately forms subgroups so that within-subgroup variation reflects only common cause variation, making between-subgroup shifts due to special causes more detectable.
Lean Six Sigma Green Belt Certification DMAIC: Measure Phase Tools 5
A Green Belt plots an X-bar chart and notices that all sample means fall within the control limits but 90% cluster tightly near the centerline.
What is the most likely cause?