Linearity

Linearity is the difference in the tendency values during the desired operation range in the measurement device.

Linearity can be defined when you select parts during the desired operation range in the measurement device. The tendency of each chosen part is determined by the difference between reference value and noted average measurement. The inclination of regression line, that better adjusts average tendency versus reference values, multiplied by parts process variation (or by tolerance) is an index that can represent the measurement device linearity.

To convert the measurement device linearity in a percentage of process variation (or tolerance), multiply by 100 and divide by process variation (or tolerance). As with stability, the recommended analysis technique is graphic; that is, a dispersion diagram with a line with a better adjustment.

As in tendency study, part value references can be determined with tooling or metrology equipment. The chosen parts during the operation range are measured by one or more operators, and the average to each part is determined. The difference between reference value and the average is the tendency; this is determined to each chosen part. The linearity graphic is plotted, linking decentralization and reference values during operation range.

If a graphic shows that a line could represent the plotted points, then a linear regression, of a proper adjustment, between decentralization and reference values represent the linearity between that two parameters. The linear adjustment degree (R2) of linear regression line will determine if decentralization and reference values have a good linear relation. Linearity and system linearity percentage are calculated based on the inclination of regression line and of variation (or tolerance) of parts.

If the regression line has a good linear adjustment, then the magnitude of linearity and of linearity percentage can be evaluated to determine whether linearity is acceptable. If the regression line does not have a good linear adjustment, then, it is possible that average tendency and reference values can have a non-linear relation. To judge whether linearity measurement system is acceptable, a further analysis is required.

If a measurement system shows no-linearity, check possible causes:

1) Measurement device that is non-properly calibrated in both extremes, inferior or superior, of operation range.

2) Error in maximum or minimum standard.

3) Wasted measurement device.

4) Internal characteristics of project measurement device.

y = b + ax,

where:

x = reference value

y = tendency

a = inclination

M.S.A. Graphic by Stability

To generate a M.S.A. per Stability graphic, perform a M.S.A Graphic Query. and select in the parameter Type, option Stability.