Estimating Total Measurement Variation

Repeatability is the variation in measurement obtained:

  • With one measuring instrument.
  • When used several times by the same operator.
  • When measuring an identical characteristic on the same part.

The standard deviation for repeatability (σe) is estimated by:

figure 1

where R is the average range of the repeated measurements.

Reproducibility is the variation in the average of measurements:

  • made by different operators who are …
  • using the same measuring instrument,
  • when measuring the identical characteristic on the same part.

Operator variation, or reproducibility, is estimated by determining the overall average for each appraiser and then finding the range (R0) by subtracting the smallest operator average from the largest.

The standard deviation for reproducibility (σ0) is estimated by:

figure 2

The measurement system variation (R&R) or gage R&R is represented by σR&R.

Part-to-Part Variation

Part-to-part variation also makes a contribution to the total variation in a measurement and can be determined from the measurement system data or an independent process capability study. If the measurement system study is used, the part standard deviation σp (PV) is estimated by Rp /d2*. Rp can be estimated as the average range of part measurements.

Total Variation

Total variation (TV or σTV) for the study is calculated by summing the square of both the repeatability and reproducibility (R&R) variation and the part-to-part variation PV, and taking the square root, as follows:

figure 3

The contribution of the equipment variation contribution EV is calculated as 100(EV/TV). The contribution of other factors to the total variation TV can be similarly calculated, as follows:

figure 4

Excerpted from Donald W. Benbow, Ahmad K. Elshennawy, and H. Fred Walker’s The Certified Quality Technician Handbook, ASQ Quality Press, 2003, pages 116-117.

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Using Data