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Repeatability
Reproducibility

Introduction.

A Gauge Repeatability and Reproducibility (Gauge R & R) Study evaluates how a measuring system varies due to repeatability and reproducibility errors.

The assessment method used is based on statistical techniques and the study includes the effects of operators, the environment, the method of measurement as well as gauge variations when measuring items from the process in question.

There are different methods for undertaking a study depending on the depth of understanding of the measurement performance required. For example a range study provides a quick approximation of measurement variability, whereas the average and range method will determine both repeatability and reproducibility for a measurement system.

The ANOVA Method

The ANOVA method requires the data to be analysed using a computer but the resulting information not only shows the source of errors but allows their interaction to be evaluated.

Range Method

The range method uses two operators and five samples for the study. Each operator measures the coating thickness on the sample once and records the readings.

The range for each part is the absolute difference between the reading obtained by operator A and the reading obtained by operator B.

The sum of the ranges is determined and the average range is calculated. The total measurement variability is found by multiplying the average range by 4.33.

The percentage of the process variation (tolerance) that is due to measurement variation can be calculated by dividing the total measurement variability by the tolerance range and multiplying by 100.

The guideline for interpreting the gauge R &R result is that if the process variation is greater than or equal to 30% then there is need for improvement in the measurement system. This improvement may be operator training, gauge re-calibration or gauge design improvement and this method does not provide an indication of what is causing the variations.

Average and Range Method

This method allows the overall repeatability and reproducibility to be analysed as two separate components, repeatability and reproducibility but not their interaction. This in turn will help with the determination of the cause and can lead to process improvement.

For example, if repeatability is large compared to reproducibility, the reasons may be:

  • The gauge needs servicing or repair.
  • The gauge set-up should be redesigned to be more rigid.
  • The clamp or location for the probe needs to be improved.
  • There is excessive within-part variation.

If reproducibility is large compared to repeatability, then possible causes could be:

  • The operators need to be better trained.
  • The resolution of the gauge is not sufficient.

Help is required to allow the operator to use the gauge more consistently.

The method uses three operators and 10 parts. The parts are measured in random order by one of the operators then the other two measure the parts in the same order but without seeing the original results. It is good practise to have a fourth person record the results. The order of the parts is then changed and the measurements repeated. The data is then plotted to show the errors.

The errors are calculated as either:

  • Error = Master Measurement - Observed Measurement, or
  • Error = Average Measurement - Observed Measurement

The following terms are used in Gauge R & R studies:

  • EV is the repeatability or equipment variation.
  • AV is the reproducibility or operator variation.
  • R & R is the measurement system variation.
  • PV is the part variation.

The above are often quoted as a percentage of the total variation (TV) but it must be noted that due to the interaction between these values they will not total 100% when added together.

ANOVA Method

Analysis of Variance (ANOVA) is a standard statistical technique and is used to assess the error in a measurement system.

The overall variation can be separated into four areas, parts, operators, interaction between parts and operators and replication error due to the gauge.

The advantages of this method over other Gauge R & R techniques are that it can handle any experimental set-up, it can estimate variance more accurately and extract more information from the data.

The disadvantages are that, as stated earlier a computer is required to perform the calculations and a degree of knowledge and experience is required to interpret the results.

Data is collected randomly to prevent bias.

Interpretation Guidelines

The guidelines for acceptance of Gauge Repeatability and Reproducibility (% R & R) are:

  • Under 10% error - The measurement system is acceptable.
  • 10% - 30% error - May be acceptable depending on factors like the importance of the application, the cost of the gauge, the cost of repair to the measurement system etc.
  • Over 30% error - The measurement system needs improvements.

For further information and additional background reading on the subject of Gauge R & R Studies, the reference manual Measurement Systems Analysis (MSA), jointly compiled and copyright Ford/General Motors/Chrysler, is recommended.