# Evaluating Gage Bias and Linearity

In an earlier article in this series, I introduced some basic issues in measurement systems analysis such as granularity, accuracy, reproducibility, repeatability, stability and linearity.  In this article we will explore in more detail how to evaluate the performance of a measurement system with respect to bias and linearity.

Gage bias examines the difference between the observed average measurement and a reference or master value.  It answers the question “How biased is my gage when compared to a master reference value that is known to be a true value?”   As an example, consider a scale at the grocery store that is used to measure the weight of cold cuts at the delicatessen counter.  If the scale reads 1.05 pounds when a master reference weight that is known to be of 1.00 pounds is placed on the scale, then it has a bias of .05 pounds.

There are several possible causes of bias problems with a gage.  The gage may not be properly calibrated at the upper and lower extremes of the operating range.  The gage may be worn, dirty or in disrepair.  There may be internal design issues with the gage, such as in the area of electronics.  Extremes in temperature or humidity may influence bias.

Linearity has to do with how accurate the measurements are across the entire range of the measurements.  It answers the question “Does my gage have the same level of bias or accuracy for all sizes of objects being measured?”  For example, a gage that measures the diameter of a wheel rim may have a bias that increases as the rim becomes wider.

To determine whether your measurement system has the same bias for all sizes, you calculate linearity–the linear change in bias over the range of measurement values.

Gage linearity and bias studies are conducted in the following manner:

1. Select several parts that represent the expected range of measurements.
2. Measure each part to determine its master or reference value.
3. Have one operator measure each part multiple times (10 or more times) in random order using the same gage.
4. Evaluate the resulting data using the ANOVA method (Analysis of Variance). In Mintab, a commonly used statistical software package, the data is evaluated using the “Gage Linearity and Bias Study”.
5. The output of the ANOVA analysis is a percentage linearity and a percentage bias. Both are expressed as a percentage of the overall observed process variation.  The goal is to minimize the percentage of the overall process variation that is introduced by linearity and bias issues in the gage, and maximize the percentage that is actually due to part to part variation.