Study Design & Measurement Data
Enter measurements as rows of comma- or tab-separated values. Each row contains all parts for one operator-trial combination.
Row format: Op1-Trial1 (parts 1–10), Op1-Trial2, Op2-Trial1, Op2-Trial2, Op3-Trial1, Op3-Trial2
Gage R&R Results
| Source | Std Dev (σ) | Variance (σ²) | % Contribution | % Study Var |
|---|---|---|---|---|
| Repeatability (EV) | -- | -- | -- | -- |
| Reproducibility (AV) | -- | -- | -- | -- |
| Gage R&R (GRR) | -- | -- | -- | -- |
| Part-to-Part (PV) | -- | -- | -- | -- |
| Total Variation (TV) | -- | -- | -- | -- |
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What is Gage R&R?
Gage R&R (Gage Repeatability and Reproducibility) is a statistical method used in Measurement System Analysis (MSA) to evaluate how much of the observed process variation is attributable to the measurement system itself. It is a core requirement of quality standards such as IATF 16949 and is described in the AIAG MSA Reference Manual.
A Gage R&R study decomposes measurement variation into two components:
- Repeatability (Equipment Variation, EV): The variation observed when the same operator measures the same part multiple times with the same gage. This reflects the inherent precision of the measurement instrument.
- Reproducibility (Appraiser Variation, AV): The variation observed when different operators measure the same parts with the same gage. This reflects differences in technique, training, or interpretation between operators.
Together, EV and AV form the total Gage R&R value. A capable measurement system should contribute only a small fraction of the total observed variation, with most variation coming from actual differences between the parts being measured.
How to Conduct a Gage R&R Study
A well-designed Gage R&R study follows the crossed design, where every operator measures every part multiple times. The typical steps are:
- Select Operators: Choose 2–3 operators who normally use the measurement system. They should represent the range of skill levels in your facility.
- Select Parts: Choose 10 parts that span the expected range of process variation. Parts should be representative of actual production, not hand-picked.
- Define Trials: Each operator measures every part at least 2–3 times. Trials should be randomized and blind — operators should not know which part they are measuring or what their previous readings were.
- Collect Data: Record all measurements systematically. Ensure consistent environmental conditions (temperature, lighting, etc.) throughout the study.
- Analyze: Use the Average & Range method (this calculator) or the ANOVA method to decompose the variation and compute %GRR and NDC.
Interpreting Gage R&R Results
The AIAG MSA Reference Manual provides widely accepted criteria for evaluating measurement system acceptability:
| %GRR (Study Variation) | Verdict | Action |
|---|---|---|
| < 10% | Measurement system is acceptable for the intended application. | |
| 10% – 30% | May be acceptable depending on application criticality, cost of the gage, and cost of repair. Improvement efforts should be considered. | |
| > 30% | Measurement system needs improvement. Identify and correct the root cause of excessive variation before using the gage for process decisions. |
In addition to %GRR, the Number of Distinct Categories (NDC) indicates how many non-overlapping confidence intervals span the product variation. The AIAG guideline requires NDC ≥ 5 for an adequate measurement system. An NDC of 1 means the measurement system cannot distinguish between parts at all.
Average & Range vs ANOVA Method
This calculator uses the Average & Range (X-bar & R) method, which is the traditional approach described in the AIAG MSA manual. It calculates EV from the average range of repeated measurements and AV from the range of operator averages, using d2 constants to convert ranges into standard deviation estimates.
The ANOVA (Analysis of Variance) method is a more advanced alternative that offers several advantages:
- It can separate the operator-by-part interaction effect, which the Average & Range method cannot isolate.
- It provides more precise variance estimates by using all data simultaneously rather than converting ranges.
- It can handle unbalanced designs (unequal numbers of trials per operator or part).
However, the Average & Range method remains popular because it is simpler to understand, can be performed by hand, and produces results that closely match the ANOVA method for standard balanced study designs (e.g., 3 operators, 10 parts, 2–3 trials). For most practical applications, either method is acceptable.