# Help Manual

### Contents

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

Sigma Magic Help Version 15

# Gage Linearity and Bias

## Overview

Gage Linearity and Bias can be used to determine if the measurement data contains any bias in its measurements 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 both a Type 1 Gage Study for a single gage and a single reference part to check if the gage is repeatable and does not have any 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 using the instrument of interest and a Master Gage to determine if the gage is linear in the range of measurements. Gage Linearity and Bias compares the two sets of data and reports on the presence of Gage linearity and bias. If Gage linearity and bias are present in the data, you need to correct the measurement system before you can use 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. Since we are measuring the part multiple times we can also get an estimate of the repeatability of the gage.
Linearity & BiasFor this study, we measure a range of parts to determine if the gage is linear with respect to 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 would be added to the bottom of the list. In this case, we only have 3 columns of data. The number of rows is equal to the number of parts times the number of repeats.
Unstacked DataData is arranged in multiple columns. The first column contains the items numbers, and each repeated measurement is placed in an adjacent column. Hence, the number of columns of measurement is equal to 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 pick sufficent number of parts that span the range of measurements of the gage.
4
Num Repeats: Enter the number of times we are repeating 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 requirements. Typically, the tolerance is the difference between the Upper Specification Limit (USL) minus 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 then 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 the first time you are using this template, click on this button to format the worksheet template. You can also update the worksheet format at any time but remember that you may lose any data you may have entered on this worksheet. Once you are happy with the worksheet template layout, you will need to 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 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

If you click on the Data button, you will see the following dialog box. 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 first 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 to speed up finding the right data to use 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 does not have any 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 important that you not only specify the column name but also the table name.
3
Add or View Data: Click on this button either to add more data into 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 up the Data Editor dialog box where you can import more data into your workbook, or you can 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, then you will need to select only numeric columns. If the code starts with a T, then you can select both 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, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data 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 select 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 select the data is to double click on the columns in the list of Available Data. Finally, you can also 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: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the 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 you have specified in the Setup tab. If you are performing the Type 1 Gage Study analysis, then you only need to specify the measurement values. You can either 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 respectively under the Items, References, and Measurements Variables. For example, if you have 10 items and 3 repeats then you would have 30 data points for each of these columns.
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 10 items and 3 repeats, then the items column will contain 10 data points, the reference column will contain 10 data points, and there will be 3 measurement columns of 10 data points each.
7
View Selection: Click on this button to view the data you have specified for this analysis. The data can be viewed either in a tablular format or in a graphical summary.

### Options

If you click on the Options button, you will see the following dialog box. Here you can specify the optional data for this analysis.
 1 Gage Name: Specify the name of the gage that you are performing your study for. 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, then 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, then 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, then 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 for Gage Linearity studies. For Type 1 Gage Study the data needs to be entered in the order of measurement. 6 Percent Tolerance: Specify the percent of tolerance to use for the limits on the time series chart of measurements. This specification only applies for 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

If you click on the Charts button, you will see the following dialog box.

### 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 objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software will check 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, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color 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.

### Worksheet

On the worksheet, for each item, get it inspected by the inspectors and enter the measured values in the worksheet. For a Type 1 Gage Study, there are two columns, the first column 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.

## Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet for Type 1 Gage 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 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 number of 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 shows a summary of the analysis performed such as the actual number of data points used, the bias that is present in your gage, the standard deviation of the measurements, the Cg and Cgk values of the measurement gage. If these values are greater than 1.33 then the measurement gage is acceptable. This comparison is made depending on the options you have specified under Options > Thresholds. The default values are the gage is unacceptable if the Cgk values are less than 1.33, acceptable if it is 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 repetability and due to repetability 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 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 with respect to the reference values. The model equation is shown in the subtitle. The regression fit along with the lower and upper confidence intervals are shown on the plot as well.

The notes section describes a summary of the input data: the number of input rows, number of 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, along with the regression equation and the P values for the constant (bias term) and slope (linearity term). If the P-value is greater than the significance level, then 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 is not acceptable.

## Examples

Following examples can be found in the Examples folder.
• Determine if the measurement system Gage linearity and bias is acceptable for the data given in the reference file. Data is given for the time to repair an equipment (Gage Linearity 1.xlsm).