Measurement System Precision

It is the ability to repeat the same measurement by the same operator at or near the same time with nearness of measurement in any random measurement.

Two major things contribute to total variation – the process and the measurement system. The formula for calculating measurement variance is –

σ² Measurement = σ² Repeatability + σ² Reproducibility

Measurement variance is the product of repeatability and reproducibility. Variation, variability, and variance are terms which often are interchanged with one another in this kind of discussion and used alternatively in different sources.

The components of precision are

Reproducibility – The reproducibility of a single gage is customarily checked by comparing the results of different operators taken at different times. It is the variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic on the same part.

The measurement system variation f or reproducibility, appraiser variation (AV) is used – AV concerns the human factor. Are you using different operators or are you remaining consistent? Are you using the same parts and the same devices to reduce the variability of interest? Are you repeating it multiple times? The reason for doing this is to reduce and control appraiser validation issues. This is to prevent issues resulting from having to train many different operators, who may have different interpretations or not follow exactly the same procedures to get consistent results.

Deviation for reproducibility, or σ reproducibility, is equal to the range of total averages, or Xbar-R, divided by a constant based on the sample or subgroup size, or d₂. So you first calculate the Xbar-R, which is the difference between the largest and smallest operator averages, using the following formula – Xbar-R = Xbar max – Xbar min

For example, the largest operator average, or Xbar max, is 6.07 and the smallest operator average, or Xbar min, is .594. Therefore the range of total averages is .013. Then you use the Xbar-R value and the d₂ value to calculate the reproducibility. The Xbar-R value of .013 is divided by the d₂ value of 1.693. That returns a σ reproducibility value of .077.

Repeatability – It is the variation in measurements obtained with one measurement instrument when used several times by one appraiser, while measuring the identical characteristic on the same part. Variation obtained when the measurement system is applied repeatedly under the same conditions is usually caused by conditions inherent in the measurement system. The measurement system variation for repeatability, equipment variation (EV) is used – EV uses the same operators and the same parts to reduce the variable of interest, in terms of what is being used as a base line. It uses the same device and is repeated multiple times to validate repeatability. When you see issues with repeatability, often you’ll get into root cause analysis and find these kinds of problems. Problems could result from a different viewing angle on the part of the operator, leading to variation in repeatability or tools wearing out and compromising precision and repeatability.

Repeatability serves as the foundation that must be present in order to achieve reproducibility. Reproducibility must be present before achieving accuracy. Precision requires that the same measurement results are achieved for the condition of interest with the selected measurement method.