ARTICLES

# Simple BIAS Analysis

Bias in the measurement system is the difference between the average of measured values and the actual value of a part. The actual value of the part is called the reference value. Ideally the bias should be zero.

The above image shows the variation in the different measurements on the same part and the deviation of the average from the reference value. In this instance the bias is negative.

The simple analysis assumes that bias is constant over all measurement ranges. This may not necessarily be the case. Bias may be dependent on the magnitude of the reference value and even testers. Different testers may obtain a different bias. A Linearity and Analysis of Variance analysis can highlight problems in these areas.

A Simple Bias analysis is performed by the same tester taking at least 10 samples. However, this may not be enough if the repeatability error is high. It is important to look at the confidence interval to determine if the estimated bias is reliable. If not, the BISNET Sample Size App should be used to determine the required sample size to obtain a specified margin of error.

It is important to review a histogram of the data to validate the analysis results. This will identify suspect results which should be excluded from the analysis. For example, the histogram below places doubt on the analysis. One would expect a symmetrical bell-shaped distribution for measurement error. Instead there appear to be 3 distributions. Possible explanations are that the appraiser was not the only one taking measurements, or that the appraiser conducted the exercise at different times, during which ambient conditions differed. The appraiser may need to be retrained.

The following two tables show the expected output of a Simple Independent Sample Bias Analysis

Arguably, the most important part of the output is the confidence interval section. Although statistical significance testing is important, because it enables the appraiser to determine if an observed bias is due to sampling error or not, statistical significance testing does not discriminate between practically significant and practically insignificant bias. Referring to the worst-case situation in the example output, the appraiser will know that there is a high chance that the true bias is above -.61. Although there is a non-zero bias, that is statistically significant, this amount may not be practically significant, especially if the process variation is high.

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