In the Variability Chart platform, the Linearity Study option performs a regression analysis using the standard variable as the X variable and the bias as the Y variable. This analysis examines the relationship between bias and the size of the part. If the slope is significantly different from zero, you can conclude that there is a significant relationship between the size of the part or variable measured as a standard and the ability to measure.
The Linearity Study option is available only when a Standard variable is provided in the launch window. To obtain a complete results report, you also need to specify values for the sigma multiplier and the historical process sigma. These values are multiplied to calculate the Process Variation. The sigma multiplier is specified in the launch window. There are several ways to specify the historical process sigma.
• Prior to analysis, you can assign the MSA column property to the response and specify the historical process sigma in the column property.
• In the launch window, you can specify the historical process sigma by selecting the Show MSA Metadata Entry Dialog.
• In the report window, you can click the Variability Gauge Analysis red triangle and select Gauge Studies > Edit MSA Metadata.
• You can directly specify the historical process sigma in a script.
The Linearity Study report shows the following information:
• Bias summary statistics for each standard.
• An ANOVA table that tests if the slope of the line is equal to zero.
• The line parameters, including tests for the slope (linearity) and intercept (bias). The test for the intercept is useful only if the test on the slope fails to reject the hypothesis of slope = 0.
• A table that contains the values for Process Variation, Linearity, % Linearity, Overall Avg Bias, % Bias, and Alpha.
• The equation of the line appears directly beneath the graph, along with the R Squared value.
The Linearity Study red triangle menu contains the following options:
Set Alpha Level
Changes the alpha level that is used in the bias confidence intervals.
Linearity by Groups
Produces separate linearity plots for each level of the X, Grouping variables that you specified in the launch window.
Show Bias Points
Shows or hides the bias points on the graph.
Show Line of Fit
Shows or hides the line of fit on the graph.
Show Fit Confidence Curves
Shows or hides the line of fit confidence curves on the graph.
Show Overall Avg Bias Line
Shows or hides the overall average bias line on the graph.
Show Avg Bias Points
Shows or hides the average bias points on the graph.