Gage R&R Explained

Understanding Repeatability, Reproducibility, Accuracy, Precision, Linearity, and Stability

What is Gage R&R?

Gage Repeatability and Reproducibility (GRR) is a statistical method used to evaluate the measurement system's ability to produce consistent and reliable results.

Key Insight

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.

The Six Key Components of MSA

Repeatability

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)

Think of it as: "How consistent is the measurement tool itself?"

Factors affecting repeatability:

  • Gage condition and calibration
  • Environmental conditions
  • Measurement procedure
  • Part positioning and fixturing
Reproducibility

Definition: The variation in measurements when different operators measure the same part using the same gage.

Also known as: Appraiser Variation (AV)

Think of it as: "How consistent are different operators when using the same tool?"

Factors affecting reproducibility:

  • Operator training and skill level
  • Measurement technique differences
  • Reading and interpretation variations
  • Setup and positioning differences
Accuracy (Bias)

Definition: The difference between the average of measurements and the true or reference value of the part.

Also known as: Bias or Systematic Error

Think of it as: "How close are our measurements to the true value?"

Common causes of bias:

  • Gage calibration errors
  • Worn or damaged measurement surfaces
  • Systematic operator errors
  • Environmental effects
Precision

Definition: The closeness of repeated measurements to each other (combination of repeatability and reproducibility).

Formula: Precision = √(Repeatability² + Reproducibility²)

Think of it as: "How consistent are our measurements with each other?"

Key points:

  • High precision = low variation between measurements
  • Can be precise but not accurate (systematic bias)
  • Essential for detecting small changes
  • Directly impacts measurement discrimination
Linearity

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?"

Think of it as: "Is our measurement tool equally accurate for small and large values?"

Linearity study involves:

  • Selecting parts across the measurement range
  • Obtaining reference values for each part
  • Multiple measurements by operators
  • Analyzing bias vs. reference value
Stability

Definition: The consistency of bias over time when measuring the same reference standard.

Question answered: "Does our measurement system maintain its accuracy over time?"

Think of it as: "How well does our measurement tool maintain its performance over time?"

Stability study involves:

  • Regular measurements of a reference standard
  • Tracking bias over extended periods
  • Monitoring for drift or sudden changes
  • Establishing control limits for bias

GRR Calculation and Interpretation

Key Formulas

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

Acceptance Criteria
%GRR Acceptability Action
< 10% Excellent Acceptable for all applications
10% - 30% Marginal May be acceptable depending on application
> 30% Unacceptable Measurement system needs improvement
Additional Metrics

NDC (Number of Distinct Categories): Should be ≥ 5

P/T Ratio: Should be ≤ 0.3 (equivalent to %GRR ≤ 30%)

What's Next?

Learn the Process

Follow our step-by-step guide to conduct a GRR study

Step-by-Step Guide
Interpret Results

Learn how to analyze and act on GRR study results

Interpreting Results
Try the Tool

Use our tool to optimize unit selection for your GRR study

Use Tool