Measurement System Analysis (MSA) and Gage R&R

Measurement system analysis (MSA) checks whether your gauges, people, and methods measure well enough for the decision you need to make. Every reading is the true value plus measurement error. MSA estimates that error, mainly through a Gage R&R study that splits it into repeatability (the instrument) and reproducibility (the people).

In DMAIC it belongs early in Measure, before you trust a baseline, a capability index, or a hypothesis test.

Measurement system analysis: how observed variation splits into part variation and measurement variation A tree diagram. Observed variation splits into part-to-part variation and measurement system variation. Measurement system variation splits into repeatability, the equipment variation, and reproducibility, the appraiser variation. A bar beneath shows the worked example: gage R and R is 26.8 percent of study variation and part-to-part is 96.4 percent, with 5 distinct categories. Observed variation Part-to-part variation what you want to see Measurement system Gage R&R: noise to remove Repeatability (EV) same appraiser, same part, gauge Reproducibility (AV) different appraisers, same part Beyond Gage R&R, the measurement system also needs: bias, linearity, stability, and resolution checks Worked example (% of study variation, standard deviation basis) %GRR 26.8% Part-to-part 96.4% · ndc = 5
An original diagram. Observed variation is part-to-part variation plus measurement-system variation. A Gage R&R study estimates the measurement share and compares it with the parts and the tolerance.

What properties does a measurement system need?

PropertyQuestion it answersTypical check
Bias (accuracy)Is the average reading off from a reference value?Measure a master or reference part repeatedly
LinearityIs the bias the same across the operating range?Bias study at several reference sizes
StabilityDoes the system drift over time?Control chart of a reference part measured periodically
RepeatabilityDoes one appraiser get the same reading again on the same part?Gage R&R (equipment variation)
ReproducibilityDo different appraisers get the same average?Gage R&R (appraiser variation)

Resolution matters too. A rule of thumb is that the gauge should read in increments no larger than one-tenth of the tolerance or of the process spread, whichever you are trying to see.

Running a crossed Gage R&R study

  1. Pick about 10 parts that span the real process range, not 10 nearly identical parts.
  2. Choose 2 or 3 appraisers who normally do the measurement.
  3. Have each appraiser measure each part 2 or 3 times in random order, blind to part number and to earlier readings.
  4. Analyze with the ANOVA method (preferred) or the average-and-range method to estimate repeatability, reproducibility, and part-to-part variation.
  5. Judge the result against the guidelines below, then fix the gauge, the method, or training before you collect project data.

When parts are destroyed by testing, use a nested design. For pass/fail or category judgments, use an attribute agreement analysis with kappa statistics instead.

What Gage R&R results are acceptable?

%GRR (of study variation or tolerance)Common interpretation
Under 10%Acceptable
10% to 30%May be acceptable depending on the importance of the characteristic, cost of the gauge, and cost of repairs
Over 30%Not acceptable; improve the measurement system

The number of distinct categories (ndc) = 1.41 × (σparts ÷ σGRR) should be 5 or more, meaning the system can sort parts into at least five groups. These are widely used automotive (AIAG) guidelines; your customer may set different ones.

Worked example

A crossed study of 10 parts, 3 appraisers, and 3 trials gives σrepeatability = 0.020 mm, σreproducibility = 0.015 mm, and σparts = 0.090 mm.

  • σGRR = √(0.020² + 0.015²) = 0.025 mm
  • σtotal = √(0.025² + 0.090²) = 0.0934 mm
  • %GRR of study variation = 0.025 ÷ 0.0934 = 26.8% (as a share of variance, the %contribution is 7.2%)
  • ndc = 1.41 × 0.090 ÷ 0.025 = 5.08, so 5
  • Against a 0.60 mm tolerance, %GRR = 6 × 0.025 ÷ 0.60 = 25%

The system is in the “may be acceptable” band. Repeatability is the larger piece, so the first place to look is the gauge and the fixture, not appraiser training.

Frequently asked questions

What is the difference between repeatability and reproducibility?

Repeatability is the variation when the same person measures the same part with the same gauge several times; it mostly reflects the instrument. Reproducibility is the variation between the averages of different people measuring the same parts; it mostly reflects method and training.

Why do MSA before a capability study?

Measurement error adds to observed variation, so a poor gauge makes a process look less capable than it is, and it can hide or invent differences in hypothesis tests. Fix the measurement first; see process capability and hypothesis testing.

Is calibration the same as MSA?

No. Calibration checks and adjusts bias against a traceable standard. MSA also measures precision, repeatability and reproducibility, under real conditions with real appraisers. A freshly calibrated gauge can still fail a Gage R&R.

Can MSA be done on attribute data?

Yes. An attribute agreement analysis has several appraisers judge the same set of known good and bad items more than once, then reports agreement within appraisers, between appraisers, and against the standard, often with Cohen’s or Fleiss’ kappa. See attribute MSA and kappa for a worked example.

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