Understanding Repeatability, Reproducibility, Accuracy, Precision, Linearity, and Stability
Gage Repeatability and Reproducibility (GRR) is a statistical method used to evaluate the measurement system's ability to produce consistent and reliable results.
GRR studies help distinguish between variation caused by the measurement system versus variation in the actual parts being measured. This is crucial for making informed decisions based on measurement data.
Definition: The variation in measurements when the same operator measures the same part multiple times using the same gage under the same conditions.
Also known as: Equipment Variation (EV)
Factors affecting repeatability:
Definition: The variation in measurements when different operators measure the same part using the same gage.
Also known as: Appraiser Variation (AV)
Factors affecting reproducibility:
Definition: The difference between the average of measurements and the true or reference value of the part.
Also known as: Bias or Systematic Error
Common causes of bias:
Definition: The closeness of repeated measurements to each other (combination of repeatability and reproducibility).
Formula: Precision = √(Repeatability² + Reproducibility²)
Key points:
Definition: The consistency of bias across the expected operating range of the gage.
Question answered: "Does the gage maintain the same accuracy across its full measurement range?"
Linearity study involves:
Definition: The consistency of bias over time when measuring the same reference standard.
Question answered: "Does our measurement system maintain its accuracy over time?"
Stability study involves:
Repeatability (EV):
EV = R̄ × K₁
Reproducibility (AV):
AV = √[(X̄diff × K₂)² - (EV²/nr)]
GRR:
GRR = √(EV² + AV²)
%GRR:
%GRR = (GRR / TV) × 100
Where: R̄ = average range, K₁, K₂ = constants based on sample size, X̄diff = difference between operator averages, TV = total variation
| %GRR | Acceptability | Action |
|---|---|---|
| < 10% | Excellent | Acceptable for all applications |
| 10% - 30% | Marginal | May be acceptable depending on application |
| > 30% | Unacceptable | Measurement system needs improvement |
NDC (Number of Distinct Categories): Should be ≥ 5
P/T Ratio: Should be ≤ 0.3 (equivalent to %GRR ≤ 30%)