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Sigma Magic Help Version 17

Gage Repeatability and Reproducibility

Overview

Gage Repeatability and Reproducibility (Gage R& R) can be used to determine whether the measurement data is good. It can be used for continuous data or discrete / attribute data (nominal and ordinal).

This template can be added to your active workbook by clicking on Stats and then selecting MSA > Repeatability & Reproducibility.

Inputs

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

Setup

A sample screenshot of the setup menu is shown below.
inputs
1
Data Type: Specify the type of data you have. The following options are available:
OptionDescription
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example, 34.53 degrees centigrade).
NominalNominal data has more than two categories, but they cannot be ranked (like nationality, religion, etc.).
OrdinalOrdinal data has more than two categories, and they can be compared with each other and ranked (like the grades in an exam A > B > C).
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Analysis Type: Specify the type of analysis to be performed. The following options are available:
OptionDescription
CrossedIn a crossed design, every part can be inspected by every operator multiple times.
NestedIn a nested design, one part can only be inspected once (for example, destructive testing).
Type 3Use this analysis when you want to determine the repeatability of equipment.
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Num Items: Specify the number of items inspected. You can optionally enter the item numbers on the right. You can have up to 100 items.
4
Num Appraisers: Enter the total number of inspectors for this study. You can have up to 20 inspectors.
5
Randomize: Specify if you want to randomize your test runs. A random test run will ensure that the operators don't remember earlier measurement results; hence, there is less chance of biasing your study.
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Num Repeats: Enter the number of trials/repeats. You can have up to 10 repeats.
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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 - typically one column for item numbers, one column for appraisers, and one column for measurement values. Use one column for the reference values if there are any reference values.
Unstacked DataData is arranged in multiple columns. Typically, all measurements for the same operator/appraiser are grouped. Hence, if there are two appraisers and three repeats. The first three columns are for the first appraiser; the next three columns are for the second appraiser, and so on.
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External Standard: Specify the external standard values to compute the accuracy. This option is only valid for Discrete data and does not apply to continuous data. If the Data Type is Continuous, then this textbox is disabled.
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Help Button: Click on this button to open the help file for this topic.
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Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
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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 and then Compute Outputs to generate analysis results.
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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.
If your data type is discrete (nominal or ordinal), the following dialog box would have been opened. inputs2 The menu options for the discrete case are similar to the continuous case except for the following settings:
1
Data Type: Specify the type of data you have. In this case, the data type is either nominal or ordinal data.
2
Analysis Type: Specify the type of analysis to be performed. The following options are available:
OptionDescription
MatchUse the % match values to check measurement system. Typically used for nominal data.
KappaUse the Kappa statistic to check measurement system. Typically used for nominal data.
KendallUse the Kendall coefficient to check measurement system. Typically used for ordinal data.
3
Input Type: Specify whether your data is organized in a single column or across multiple columns. For Type 3 analysis, ensure you enter the data in the time order in which you collect the data without randomization.
4
External Standard: Specify whether external standards are available. Accuracy numbers are reported if external standards are available; otherwise, only repeatability/reproducibility numbers are reported.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis. Data
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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 finding 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.
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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.
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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.
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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.
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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.
OptionDescription
1If your data type is Continuous and your Input Type is Stacked Data, then you would stack all the data and have a single column that represents the items, a single column that represents the appraisers and a single column of measurement values. These columns would be specified under the Items, Appraisers, and Measurements Variables. The Standards Variable is disabled for Continuous data type. For example, if you have ten items, two appraisers, and three repeats, you would have 60 data points for each column.
2If your data type is Continuous and your Input Type is Unstacked Data, then you would have separate columns of measurement data. For example, if you have ten items, two appraisers, and three repeats, then you would have ten rows of data for the items column, two rows for the appraiser column, and six columns of measurement data with ten rows each. Note that all appraiser columns are grouped. For this example, your measurement data should be measurements for appraiser 1, measurements for appraiser 1 (repeat 1), measurements for appraiser 1 (repeat 2), and then measurements for appraiser 2, measurements for appraiser 2 (repeat 1), measurements for appraiser 2 (repeat 2). The Standards Variable is disabled for Continuous data type.
3If your data type is Discrete (Nominal or Ordinal) and your Input Type is Stacked Data, then you would stack all the data and have a single column that represents the items, a single column that represents the appraisers, a single column for reference values (if you have an external standard) and a single column of measurement values. These columns would be specified under the Items, Appraisers, Standards, and Measurements Variables. For example, if you have ten items, two appraisers, and three repeats, you would have 60 data points for each column.
4If your data type is Discrete (Nominal or Ordinal) and your Input Type is Unstacked Data, then you will have separate columns of measurement data. For example, if you have ten items, two appraisers, and three repeats, then you would have ten rows of data for the items column, two rows of data for the appraiser column, ten rows of data for the external standards, and six columns of measurement data with ten rows each. Note that all appraiser columns are grouped. For this example, your measurement data should be measurements for appraiser 1, measurements for appraiser 1 (repeat 1), measurements for appraiser 1 (repeat 2), and then measurements for appraiser 2, measurements for appraiser 2 (repeat 1), measurements for appraiser 2 (repeat 2).
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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. Options
1
Gage Name: Specify the name of the gage for which you are performing your study. This is an optional field; 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: 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.
5
LSL Value: Specify the lower specification limit for the study.
6
USL Value: Specify the upper specification limit for the study.
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Appraiser Names: If you are not entering data through the Data tab, you can use the Options tab to specify the Appraiser Names. Make sure that the names you provide are unique across all appraisers. Note that this is an optional field.
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Item Names: If you are not entering data through the Data tab, you can use the Options tab to specify the Item Names. Make sure that the names you provide are unique across all items. Typically, we would enter the part numbers here or assign a unique code to each item. Note that this is an optional field.

Charts

You will see the following dialog box if you click the Charts button. Charts
0
Pick Charts: Select the charts you would like to display for this analysis.
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Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2
Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3
X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4
Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5
X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is currently disabled, and you cannot change this setting.
6
Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to specify the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10, and the maximum y-axis is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7
Horizontal Lines: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
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Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Worksheet

Enter the following information in the worksheet:
  • For each item, get it inspected by the inspectors and enter the measured values in the input worksheet. Note that if there are five parts, the first appraiser measures these five parts and stores the values in a single column. When the appraiser measures these five parts a second time, they are stored in another column.
  • If there is any external standard (for discrete data), enter the external standard values.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. Verify 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. Finally, any checks that are required to be performed by the user are shown as blue info icons.
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Item: The left-hand side shows the major tabs and the items checked within each section
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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 worksheet for continuous data is shown below. outputs1 The notes section describes a summary of the input data. The data type, the number of parts, appraisers, and the number of trials. The value of any entered specification limits and historical standard deviation. The analysis results contain the study variation and the contribution due to repeatability and reproducibility. For continuous data, if the percentage variation is less than 10%, it is usually a good measurement system (acceptable if the value is less than 30% for some situations). For discrete data (nominal), the measurement system is acceptable if the error is less than 10% or the Kappa value is greater than 0.9. For discrete (ordinal data), the measurement system is acceptable if Kendall's coefficient is greater than 0.9. The conclusions show if the MSA is acceptable, marginally acceptable, or Unacceptable.

If the data entered is binary or nominal, the software will compute the percentage match and the Kappa values. The sample output is shown below. outputs2 The software will compute the Kendall coefficients if the data entered is ordinal. The sample output is shown below. outputs3

Notes

Here are a few pointers regarding this analysis:
  • The MSA conclusion is based on statistical numbers like Kappa values or Kendall's Coefficients, not the % match.
  • A percentage match is not recommended for ordinal data as the order is not considered.
  • For continuous data, if you don't enter the specification limits or the historical standard deviation, then only the study GR&R is reported.
  • For continuous data, if specification limits are specified, then the GR&R for customer tolerance is reported.

Examples

The following examples are in the Examples folder.
  • Determine if the measurement system is acceptable for the data given in the reference file (MSA 1.xlsx).



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