# Gauge Repeatability & Reproducibility. Gauge (Gage) R and R....

## Information & Training. | SPC and Statistical Methods for Process Improvement.

**What is Gauge Repeatability & Reproducibility Analysis?**

A technique to establish confidence in the data to be used in an analysis.

Answers the question: “How much of the total engineering tolerance is consumed by measurement error (repeatability and reproducibility) alone?”

**An example Gauge Repeatability & Reproducibility Analysis would be as follows:**

2 Operators, 10 Parts, 2 Trials, Tolerance = 0.01

**Planning for a Gauge R & R:**

Step 1: Select the proper gauge

Step 2: Follow the 10% Rule of Discrimination.

Step 3: Ensure Operators are trained and have required skill level.

Step 4: Ensure Operators all use the same gauge

Step 5: Calibrate the gauge

**Performing a Gauge R & R Capability Analysis.**

Have each operator measure all samples once in random order and record the data on your data sheet.

Repeat the measurements one or more times of the same samples by each operator, making sure that previous results are not known to the operators.

It is important to maintain the identity of the sample that is being measured.

Setting up the Data for Analysis (example using a Calliper, recording Length Dimension)

Calculate the Average and Range

Calculate the Grand Average and Range for each Operator:

Calculating Repeatability and Reproducibility

• Repeatability (Variation due to the gauge itself)

– Based on the Average of the Ranges across all operators

• Reproducibility (Variation due to the variation in Operators)

– Based on the Range of the Grand Averages.

Calculating Repeatability

• Uses a factor, K1, which is derived from:

– Shewhart factor d2 and

– The number of standard deviations representing a 99% spread.

Calculate Repeatability

Calculate Reproducibility

Calculate Reproducibility

Calculate Total Gauge Variation

• Rule: You cannot combine standard deviations…you can only combine variances!

Results of Gauge Capability

• % Gauge R and R criteria:

– 10% or less is EXCELLENT

– 11-20% normally would be ADEQUATE

– 21-30% normally would be MARGINALLY ACCEPTABLE

– Greater than 30% would be UNACCEPTABLE.

**In Our Example:**• % Gauge R and R is 12.8%

• Possible actions

– If 12.8% is acceptable for the application, do nothing.

– For appraiser variation, retrain operators or address standardization of procedures.

– For equipment variation, investigate alternate inspection device or take multiple measurements and average.

**Is Calibration not enough, why do you need gauge R and R ?**

i) Calibration alone will not produce QUALITY measurements.

ii) A gauge can be perfectly ACCURATE and still be entirely unacceptable for measuring a product or controlling a process!

**Some Useful Concepts/Definitions which are applicable to Gauge R and R analysis:**

• Accuracy/ Bias – Does the gage produce the same result as the known standard?

• Linearity – Is the gage more accurate at low values than at high values?

• Stability – Does the gauge change over time?

• Discrimination/Resolution – Is the gauge capable of dividing measurements into “data categories” over the range of the part tolerance?

**Calibration’s Role**

Calibration is performed and gauges are ADJUSTED to correct for any bias.

Frequency of calibration is based on the stability of the gauge.

**Selection of a Gauge for a Measurement**

Ten Percent Rule

– The discrimination of the gauge should not exceed 10% of the total part tolerance.

Example: A part has a total tolerance of .010”. The selected gage should be capable of measuring to .001”.

**Gauges should be:**

i) Accurate (No bias)

ii) Precise (Low Variation)

**Total gage variation includes:**

Repeatability: Variation in measurements due to the gauge. (Called Equipment Variation – EV)

Reproducibility: Variation in measurements due to different operators. (Called Appraiser Variation – AV)

**Why Perform Gauge R and R analysis?**

i) Avoid measurement error on product acceptance, control charts, or process capability analysis.

ii) Provide criteria for selecting new measurement equipment.

iii) Can aid in a comparison between measurement devices.

iv) Can improve equipment maintenance, selection, and use.

v) Can identify need for operator training and skill improvements.

**When to Perform Gauge R and R?**

Preventive:

– When purchasing a new gauge.

– Before using a gauge to gather data or inspect parts.

Reactive:

– When control or capability problems arise that are unexplained by the process.

**Benefits of Gauge R and R study.**

Proven analytical method for measuring the capability of the measurement system.

Excellent tool to:

– Identify measurement processes that require improvement.

– Identify the source of the measurement error (gage or operator).

– Correct the error.

**Gauge R and R Studies.**

Most Common Techniques:

Automotive Industry Action Group (AIAG)

– Identifies Equipment, Appraiser, and Part-to-Part Variation as a % of the tolerance or total variation.

Analysis of Variance (ANOVA)

– Identifies Equipment and Appraiser Variation as a % of the tolerance.

– Identifies INTERACTION.

## Information & Training.

## SPC & Statistical Methods for Process Improvement.

- Process Capability. Variability Reduction. Statistical Process Control.
- Pre-Control. R&R Studies.
- Process capability indices Cp, Cpk, Cpm, Capability ratio.
- Performance indices Pp and Ppk.
- Variable Control Charts.
- Attribute Charts.
- Pareto Charts.
- Individual – X Charts.
- Histograms / Process Capability Analysis.
- Scatter Diagrams.
- Etc. … Etc. …
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