# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 17

# Gage Linearity and Bias

## Overview

Gage Linearity and Bias can determine if the measurement data contains any bias and if the gage is linear in the range of measurements. This analysis is usually performed for continuous data. You can use this template to perform a Type 1 Gage Study for a single gage and a single reference part to check if the gage is repeatable and has no bias. You can also use this template to perform gage linearity and bias studies where you would measure a range of parts of varying nominal dimensions utilizing the instrument of interest and a Master Gage to determine if the gage is linear in the range of measurements. Gage Linearity and Bias compare the two data sets and reports on Gage linearity and bias. If Gage linearity and bias are present in the data, you must correct the measurement system before using the instrument. Once you have an acceptable measurement gage, you can then use that gage to perform Gage Repeatability and Reproducibility (R&R) studies.

This tool can be added to your active workbook by clicking on Stats and then selecting MSA > Gage Linearity & Bias.

## Inputs

Click on Analysis Setup to open the menu options for this tool.

### Setup

A sample screenshot of the setup menu is shown below.
1
Analysis Type: Specify the type of analysis you want to perform. The available options are:
OptionDescription
Type 1 Gage StudyType 1 Gage Study is performed for a single gage that is used to measure a part multiple times. The part would also be measured using a known standard or master gage so we can check the bias of this gage. We can also estimate the gage's repeatability since we are measuring the part multiple times.
Linearity & BiasFor this study, we measure a range of parts to determine if the gage is linear concerning the measured values. Typically, you would have parts that span the entire range of measurement of the gage. If the gage is linear and has no appreciable bias, we can certify that the gage is acceptable for measurements.
2
Input Type: Specify how the input data for analysis has been formatted. The available options are:
OptionDescription
Stacked DataData is arranged in a single column - one column for item numbers, one column for measurement values, and one column for reference values. If the same part is inspected again, that reading will be added to the bottom of the list. In this case, we only have three columns of data. The number of rows equals the number of parts times the number of repeats.
Unstacked DataData is arranged in multiple columns. The first column contains the item numbers, and each repeated measurement is placed in an adjacent column. Hence, the number of measurement columns equals the number of repeats. The number of rows refers to the number of parts used in the study. This option is not available for the Type 1 Gage Study.
3
Num Items: Enter the number of items to measure for this study. For a Type 1 Gage study, there is only one item as the same item is measured multiple times. For gage linearity studies, a sufficient number of parts are picked that span the range of gage measurements.
4
Num Repeats: Please enter the number of times we have repeated the measurement for a given item using the same measuring instrument. For Type 1 Gage study, it is recommended that you perform at least 50 measurements.
5
Reference Value: For a Type 1 Gage Study, specify the reference value of the part that is being inspected. This value would come from measuring the part using a master gage. Note that for gage linearity studies, there are multiple parts, so the reference values are entered directly on the worksheet.
6
Tolerance Value: For a Type 1 Gage Study, specify the tolerance value of the part that is being inspected. This value would come from the customer's requirements. Typically, the tolerance is the difference between the Upper Specification Limit (USL) and the Lower Specification Limit (LSL). If only an Upper Specification Limit is present and there is no Lower Specification Limit, check if the lower limit is bounded by zero. You can use the Upper Specification Limit as the tolerance value.
7
Help Button: Click on this button to open the help file for this topic.
8
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
9
Create Design: If this is your first time using this template, click this button to format the worksheet template. You can also update the worksheet format any time, but remember that you may lose any data entered on this worksheet. Once you are happy with the worksheet template layout, you must enter any required data on the worksheet. When the data entered into the worksheet is complete, you can click on Analysis Setup on the main menu bar and then click on the Analyze button or directly on the Compute Outputs button on the main menu bar to generate analysis results.
10
Analyze Design: Click on this button to save all changes and compute the outputs for this analysis. Review the results of your analysis and make changes to your inputs if required to update analysis results.

### Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. For this analysis, you can enter the data in the dialog box or directly on the worksheet. Even if you specify data in the dialog box, they are copied to the worksheet before performing the analysis.
1
Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up the search for the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box.
2
Available Data: The available data box contains the list of data available for analysis. If your workbook has no data in tabular format, this box will display "No Data Found." The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name.
3
Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
4
Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, you must select only numeric columns. If the code begins with a T, you can select numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box.
5
Select Button: Click on this button to select the data for analysis. Any data you choose for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to choose the data is to double-click on the columns in the list of Available Data. Finally, you can drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
6
Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data has not been specified, then the list box header will be displayed in red color. Note that you can double-click on any of the columns in this box to remove them from the box.

The data you specify for this analysis depends on the options in the Setup tab. If performing the Type 1 Gage Study analysis, you only need to specify the measurement values. You can specify the values in the dialog box or enter them directly on the worksheet. The following options are available for Gage Linearity and Bias studies:
OptionDescription
1If you have specified the Input Type as Stacked Data, then you would stack all the data and have a single column that represents the items, a single column that represents the external reference values, and a single column that contains the user measurement values. These columns would be specified under the Items, References, and Measurements Variables. For example, if you have ten items and three repeats, you would have 30 data points for each column.
2If you have specified the Input Type as Unstacked Data, then you would have one column that contains the Item numbers, a single column that contains the external references, and N columns of measurements where N is the number of repeats. For example, if you have ten items and three repeats, then the items column will contain 10 data points, the reference column will contain 10 data points, and three measurement columns of 10 data points each.
7
View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

### Options

You will see the following dialog box if you click the Options button. Here, you can specify the optional data for this analysis.
 1 Gage Name: Specify the name of the gage for which you are performing your study. This is an optional field, and any data you enter here will be used to update the charts on analysis results. 2 Reported By: Specify the person conducting this study. This value is optional. If no value is entered, a value is estimated from the data you enter in the worksheet. 3 Date: Specify the date of the study. This value is optional. If no value is entered, a value is estimated from the data you enter in the worksheet. 4 Standard Deviation: If you are performing a Gage Linearity and Bias Study, you can specify the historical standard deviation. This value is optional. If no value is entered, a value is estimated from the data you enter in the worksheet. 4 Resolution: If you are performing a Type 1 Gage Study, you can specify a resolution for your gage. This value is optional. If a value is entered, then this value is compared to the gage tolerance to determine if the gage resolution is sufficient for your study. This check is skipped if you leave the resolution value blank. 5 Randomize: Specify if you want to randomize the measurements. If you select "Yes," the part numbers are randomized when the design is created in the worksheet. This selection is only applicable to Gage Linearity studies. For Type 1 Gage Study, the data must be entered in the measurement order. 6 Percent Tolerance: Specify the percent of tolerance to use for the limits on the time series chart of measurements. This specification only applies to the Type 1 Gage Study. The default value is 20, which means that the upper tolerance value is Reference + 0.10 * Tolerance, and the lower tolerance value is Reference - 0.10 * Tolerance. If the measurement values fall outside these limits, you may want to check the gage to see if it is acceptable.

### Charts

You will see the following dialog box if you click the Charts button.

### Worksheet

On the worksheet, inspect each item by the inspectors and enter the measured values in the worksheet. There are two columns for a Type 1 Gage Study; the first contains the measurement reference number (#) and the measurement value. Make sure to enter the measurement values in the order in which data is measured onto this worksheet. For Gage Linearity studies with stacked data, the first column contains the item or part numbers, the second column contains the measured values, and the third column contains the reference values (typically from a Master Gage). For unstacked data, the measurement values are spread across multiple columns.

### Verify

If you click on the Verify button, the software will perform some checks on the data you have entered to see if you have correctly specified the data for analysis. A sample screenshot of the dialog box is shown in the figure below. The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark, and finally, any checks that are required to be performed by the user are shown as blue info icons. Here are a few examples of where the checks could fail:
• You have not specified the reference value for Type 1 Gage Study, or the reference value is not numeric.
• You have not specified a tolerance value for Type 1 Gage Study, or the tolerance value is not numeric.
• You have not entered any data on the worksheet for analyzing the results.
 1 Item: The left-hand side shows the major tabs and the items checked within each section 2 Status: The right-hand side shows the status of the checks. 3 Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

## Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the Type 1 Gage Study worksheet is shown below. The table of values used for this analysis is shown on the left. The graph shows the hypothesized P value plot for the hypothesis test (bias = 0 vs. bias not equal to zero). The time series plot or the run chart shows how the measurements vary over time. Note that the two tolerance limits are shown in red, and if all the data points fall within these two tolerance limits, we can conclude that the measurement system is acceptable. The subtitle on the chart shows the number of data points, the reference value, and the tolerance limits.

The notes section describes a summary of the input data: the type of analysis performed, the reference value of the part, the tolerance value of the part, the portion of tolerance used for this analysis, the resolution of the gage (if entered), and the number of trials or repeated measurements of the part. Next, the software checks a few assumptions - whether you have sufficient data points and if your data is normally distributed. The third section shows a hypothesis test for bias = 0 vs. the bias is not equal to 0. A 1-sample t-test is performed and the P value is used to determine if the bias exists in your measurement gage. The analysis results section summarizes the analysis performed, such as the actual number of data points used, the bias present in your gage, the standard deviation of the measurements, and the Cg and Cgk values of the measurement gage. If these values exceed 1.33, then the measurement gage is acceptable. This comparison depends on the options you have specified under Options > Thresholds. The default values are the gage, which is unacceptable if the Cgk values are less than 1.33, acceptable between 1.33 and 1.67, and excellent if greater than 1.67. Of course, you can change these thresholds under options. Finally, the % variance due to repeatability and due to repeatability and bias are listed. These values should typically be less than 15% for the gage to be acceptable. The conclusions from this analysis are listed in the last section.

A sample screenshot of the worksheet for the Gage Linearity and Bias Study is shown below. The table of values used for this analysis is shown on the left. The graph shows the hypothesized P value plot for the regression model and a regression plot of the bias values concerning the reference values. The model equation is shown in the subtitle. The regression fit and lower and upper confidence intervals are also shown on the plot.

The notes section summarizes the input data: the number of input rows, repeats, and the confidence level. The assumption checks if there is sufficient data to perform the regression analysis. Finally, the analysis results section lists the ANOVA model fit, the regression equation, and the P values for the constant (bias term) and slope (linearity term). If the P-value exceeds the significance level, the bias and linearity terms are termed statistically insignificant, and the MSA is acceptable. If the P-value is statistically significant, then a bias or linearity may be present in the measured data, and the MSA may not be acceptable.

## Examples

The following examples are in the Examples folder.
• Determine if the measurement system Gage linearity and bias are acceptable for the data given in the reference file. Data is given for the time to repair equipment (Gage Linearity 1.xlsx).