Certified Six Sigma Black Belt Measurement System Analysis Questions and Answers — Questions and Answers
Question 1: A Gage R&R study was performed to evaluate a measurement system. The results show that the %Contribution for the total Gage R&R is 25%, with repeatability accounting for 20% and reproducibility for 5%. The part-to-part variation is 75%. What is the most appropriate conclusion and next step?
- The measurement system is unacceptable because the total Gage R&R variation is too high, and the primary issue is with the measurement device itself. (Correct answer)
- The measurement system is acceptable, as the part-to-part variation is the largest source of variation.
- The measurement system is unacceptable, and the primary focus for improvement should be on training the operators.
- The measurement system is marginally acceptable, but the operators are using the gage inconsistently.
Correct answer: The measurement system is unacceptable because the total Gage R&R variation is too high, and the primary issue is with the measurement device itself.
According to AIAG (Automotive Industry Action Group) guidelines, a %Contribution for Gage R&R greater than 9% is considered unacceptable. In this scenario, the 25% total is well above this threshold. Repeatability, or Equipment Variation (EV), represents the variation when the same operator measures the same part multiple times and is associated with the gage itself. Reproducibility, or Appraiser Variation (AV), is the variation when different operators measure the same part. Since repeatability (20%) is the dominant source of measurement error compared to reproducibility (5%), the primary problem lies with the measurement instrument (the gage), not the operators.
Question 2: A Black Belt is conducting a Measurement System Analysis on a new digital scale. They measure a certified 10.00kg standard weight multiple times across the scale's operating range (from 1kg to 50kg). They find that the average measurement for the 10.00kg weight is 10.05kg, but for a 40.00kg standard weight, the average measurement is 40.30kg. This issue, where the magnitude of the error changes across the measurement range, is known as a problem with:
- Stability
- Repeatability
- Linearity (Correct answer)
- Reproducibility
Correct answer: Linearity
Linearity is defined as the change in bias over the operating range of the measurement instrument. The scenario describes a situation where the systematic error (bias) is not constant; it increases as the weight being measured increases. This indicates a linearity problem. Stability relates to how the measurement system performs over time, while repeatability and reproducibility relate to the precision (consistency) of the measurements, not the systematic accuracy across the range.
Question 3: An Attribute Agreement Analysis is being conducted for a visual inspection process where operators classify products as 'Pass' or 'Fail'. Which of the following is the primary goal of this type of study?
- To determine the bias and linearity of the attribute measurement system.
- To calculate the process capability (Cpk) based on the inspection results.
- To assess the consistency of the appraisers' judgments against a standard and against each other. (Correct answer)
- To establish statistical control limits for the number of defects found.
Correct answer: To assess the consistency of the appraisers' judgments against a standard and against each other.
Attribute Agreement Analysis is specifically designed for discrete or attribute data (e.g., pass/fail, go/no-go). Its purpose is to evaluate the quality of an attribute measurement system by assessing how well appraisers agree with themselves (repeatability), with each other (reproducibility), and with a known standard or expert appraisal (accuracy). Bias and linearity are concepts associated with continuous (variable) measurement systems. Process capability and control charts are process analysis tools, not tools for evaluating the measurement system itself.
Question 4: In the context of a Gage R&R study, which of the following best describes 'reproducibility'?
- The variation observed when the same appraiser measures the same part multiple times using the same gage.
- The variation observed when different appraisers measure the same part multiple times using the same gage. (Correct answer)
- The difference between the average of the measurements and the true value of the part.
- The ability of the measurement system to produce the same results over an extended period of time.
Correct answer: The variation observed when different appraisers measure the same part multiple times using the same gage.
Reproducibility, also known as Appraiser Variation (AV), is the variation in the average of the measurements made by different appraisers when measuring the same part. It quantifies the consistency between different people. In contrast, repeatability is the variation from the gage itself when used by a single appraiser, bias is the difference from the true value (accuracy), and stability is the consistency over time.
Question 5: A Six Sigma team analyzes the output of a Gage R&R study and finds that the Number of Distinct Categories (ndc) is 2. What does this value indicate about the measurement system?
- The measurement system has excellent resolution and can distinguish between many different levels of performance.
- The measurement system is only able to divide the process data into two groups, which is inadequate for process control. (Correct answer)
- The study was conducted with only two operators, limiting the validity of the results.
- The measurement system has a significant linearity problem that must be addressed.
Correct answer: The measurement system is only able to divide the process data into two groups, which is inadequate for process control.
The Number of Distinct Categories (ndc) is a metric that indicates the resolution of the measurement system relative to the process variation. An ndc of 2 means the gage can only distinguish between two groups of parts (e.g., 'high' and 'low'). An ndc of less than 5 is generally considered unacceptable for process analysis and control, as the measurement system cannot adequately distinguish between parts within the process spread. An ndc of 5 or more is typically desired.
Question 6: Which of the following describes a measurement system property known as 'stability'?
- The change in bias across the full operating range of the gage.
- The variation due to different operators using the measurement system.
- The consistency of measurements on the same part by the same operator.
- The consistency of the measurement system's bias over time. (Correct answer)
Correct answer: The consistency of the measurement system's bias over time.
Stability, sometimes referred to as drift, is the change in bias over time. It assesses whether the measurement system's accuracy remains consistent over extended periods. A stable system produces the same results when measuring the same master part at different points in time. This is typically evaluated using control charts. The other options describe linearity, reproducibility, and repeatability, respectively.
Certified Six Sigma Black Belt Measurement System Analysis Questions and Answers
A Gage R&R study was performed to evaluate a measurement system.
The results show that the %Contribution for the total Gage R&R is 25%, with repeatability accounting for 20% and reproducibility for 5%.
The part-to-part variation is 75%.
What is the most appropriate conclusion and next step?