Lesson 7: Trusting the measurement (Measurement System Analysis and Gage R&R)

Every conclusion a Six Sigma project draws rests on measured data. If the measurement system producing that data cannot be trusted, nothing built on top of it can be trusted either, no matter how sophisticated the analysis gets later. Measurement System Analysis, MSA, is the discipline of verifying that a measurement system itself is fit for purpose before the data it produces is used to make decisions.

Precision and accuracy

These two words are used casually as synonyms in everyday speech but mean different things in MSA. Accuracy is how close a measurement is to the true, correct value. Precision is how close repeated measurements of the same thing are to each other, regardless of whether they are close to the true value. A measurement system can be precise but inaccurate, consistently returning the same wrong number, or accurate but imprecise, averaging out to the right number while individual readings scatter widely. A useful measurement system needs both.

Bias, linearity, and stability

Three specific properties of a measurement system are evaluated separately:

• Bias: the difference between the average of repeated measurements and the item's known, true, or reference value. A gage that consistently reads 2 grams heavy on a known 100-gram reference weight has a bias of 2 grams.
• Linearity: whether that bias stays consistent across the full range the gage is used over. A gage that is accurate at the low end of its range but increasingly biased at the high end has a linearity problem, and a single bias check at one point on the scale would miss it entirely.
• Stability: whether the gage's bias and variation stay constant over time, checked by periodically re-measuring the same reference item and watching for drift. A gage that was accurate when it was calibrated six months ago but has since drifted has a stability problem, which is why gages are recalibrated on a schedule rather than checked once and trusted indefinitely.

Gage Repeatability and Reproducibility (Gage R&R)

A Gage R&R study is the standard method for quantifying how much of a measurement system's total observed variation comes from the measurement system itself, as opposed to genuine variation in the parts being measured. It separates measurement variation into two components:

• Repeatability, sometimes called equipment variation: the variation seen when the same appraiser measures the same part multiple times with the same gage. High repeatability variation points to a problem with the equipment itself.
• Reproducibility, sometimes called appraiser variation: the variation seen when different appraisers measure the same part with the same gage. High reproducibility variation points to a problem with how the measurement procedure is being applied, such as unclear instructions or inconsistent technique between operators, rather than the equipment.

A typical Gage R&R study has several appraisers each measure the same set of parts multiple times, in random order, without knowing which part they measured before, and the results are analyzed to see what percentage of the total observed variation is coming from the measurement system rather than from real part-to-part differences. If the measurement system itself is consuming a large share of the total variation, any conclusion drawn later from that data is suspect, because the team cannot tell how much of what it is seeing is the process and how much is just measurement noise.

Variable and attribute MSA

The Gage R&R study described above is the standard approach for variable data, continuous measurements such as length, weight, or time, where the output is a number on a scale. For attribute data, discrete pass or fail, go or no-go, or categorical judgments, a different method is used, generally called attribute agreement analysis. Multiple appraisers classify the same set of items more than once, and the analysis checks how often each appraiser agrees with themselves across repeated trials, how often different appraisers agree with each other, and how often the appraisers, individually and collectively, agree with a known correct answer. A visual inspection process that different inspectors classify inconsistently has an attribute measurement system problem in exactly the same sense that an inconsistent gage does for variable data, and needs the same kind of fix: clearer standards, better training, or a better inspection method.

Reading and judging a %GRR result

A Gage R&R study's output is usually reported as %GRR, the measurement system's variation expressed as a percentage of the total observed variation (commonly calculated as %Study Variation, the Gage R&R standard deviation divided by the total standard deviation, times 100). Under widely used AIAG guidelines, a %GRR under 10 percent is generally considered an acceptable measurement system. A %GRR between 10 and 30 percent may be acceptable depending on the application, the importance of the measurement, the cost of the gage, and the cost of repair, and usually calls for a judgment call rather than an automatic pass or fail. A %GRR over 30 percent is generally considered unacceptable, and the measurement system needs improvement before the data it produces is trusted for decisions.

A second output, the number of distinct categories (ndc), estimates how many truly distinguishable groups of parts the measurement system can reliably tell apart across the range of parts studied. A commonly used minimum is five or more distinct categories; a measurement system below that threshold cannot reliably tell many parts apart from each other, even if its %GRR number looks acceptable on its own, which is why both figures are checked together rather than either one alone.