Certified Six Sigma Black Belt Exam Measurement System Analysis (MSA) 3 — Questions and Answers
Question 1: Which MSA characteristic describes the change in bias across the operating range of the measurement device?
- Stability
- Repeatability
- Linearity (Correct answer)
- Discrimination
Correct answer: Linearity
Linearity assesses whether bias is consistent (or changes) across the full range of expected measurements, often evaluated via regression of bias vs. reference value.
Question 2: In attribute MSA, 'Kappa' is used to evaluate which of the following?
- The resolution of the measurement device
- Agreement between appraisers accounting for chance agreement (Correct answer)
- The proportion of parts correctly classified
- The total variation contributed by the gauge
Correct answer: Agreement between appraisers accounting for chance agreement
Cohen's Kappa statistic measures inter-rater agreement while correcting for the agreement that would occur by chance alone.
Question 3: A gauge is measured against a reference standard repeatedly over 30 days, and the average measurement drifts upward over time. This indicates a problem with:
- Bias
- Linearity
- Stability (Correct answer)
- Repeatability
Correct answer: Stability
Stability (or temporal stability) refers to the change in bias of a measurement system over time under consistent conditions.
Question 4: When the Number of Distinct Categories (NDC) equals 2, the measurement system can effectively be used for:
- SPC control charts requiring fine discrimination
- Sorting parts into two groups only (pass/fail) (Correct answer)
- Detecting ±1.5σ process shifts reliably
- Capability studies requiring Cp > 1.33
Correct answer: Sorting parts into two groups only (pass/fail)
An NDC of 2 means the gauge can only distinguish between two groups, making it suitable for binary classification (go/no-go) but not for process control.
Question 5: In a crossed Gauge R&R design, every operator measures every part. The alternative design where each operator measures only a unique subset of parts is called:
- Nested Gauge R&R (Correct answer)
- Destructive testing Gauge R&R
- Sequential Gauge R&R
- Balanced incomplete block Gauge R&R
Correct answer: Nested Gauge R&R
A nested (or hierarchical) Gauge R&R design is used when the same part cannot be measured by multiple operators, such as in destructive testing scenarios.
Question 6: Which formula correctly expresses %Repeatability as a percentage of total Gauge R&R variation?
- σ_repeatability / σ_total × 100
- σ²_repeatability / σ²_GRR × 100 (Correct answer)
- σ_repeatability / σ_part × 100
- σ²_repeatability / σ²_total × 100
Correct answer: σ²_repeatability / σ²_GRR × 100
When partitioning variance components, %Repeatability is calculated as the ratio of repeatability variance to total Gauge R&R variance, expressed as a percentage.
Question 7: An MSA study is run with 3 operators, 10 parts, and 2 replications. How many total measurements are taken?
- 30
- 20
- 60 (Correct answer)
- 15
Correct answer: 60
Total measurements = operators × parts × replications = 3 × 10 × 2 = 60.
Certified Six Sigma Black Belt Exam Measurement System Analysis (MSA) 3
Which MSA characteristic describes the change in bias across the operating range of the measurement device?