Help Manual

Contents






Sigma Magic Help Version 15

Gage Repeatability and Reproducibility

Overview

Gage Repeatability and Reproducibility (Gage R&R) can be used to determine if the measurement data is good or not. Gage R&R can be used for both 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 deg 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).
2
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 repeatability of an equipment.
3
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 and hence there is less chance of biasing your study.
6
Num Repeats: Enter the number of trials/repeats. You can have up to 10 repeats.
7
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. If there are any reference values, one column for the reference values.
Unstacked DataData is arranged in multiple columns. Typically, all measurements for the same operator/appraiser are grouped together. Hence, if there are 2 appraisers and 3 repeats. The first three columns are for the first appraiser, the next three columns are for the second appraiser and so on.
8
External Standard: Specify the external standard values to compute the accuracy. This option is only valid for Discrete data and is not applicable for continuous data. If the Data Type is Continuous, then this textbox is disabled.
9
Help Button: Click on this button to open the help file for this topic.
10
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
11
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 and then Compute Outputs to generate analysis results.
12
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 data) then 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, make sure that 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. If external standard is available, then accuracy numbers are reported, otherwise only repeatability / reproducibility numbers are reported.

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. Data
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.
OptionDescription
1If your data type is Continuous and your 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 appraisers and a single column of measurement values. These columns would be specified respectively under the Items, Appraisers, and Measurements Variables. The Standards Variable is disabled for Continuous data type. For example, if you have 10 items, 2 appraisers, and 3 repeats then you would have 60 data points for each of these columns.
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 10 items, 2 appraisers, and 3 repeats then you would have 10 rows of data for the items column, 2 rows of data for the appraiser column, and 6 columns of measurement data with 10 rows each. Note that all appraiser columns are grouped together. 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 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 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 respectively under the Items, Appraisers, Standards, and Measurements Variables. For example, if you have 10 items, 2 appraisers, and 3 repeats then you would have 60 data points for each of these columns.
4If your data type is Discrete (Nominal or Ordinal) and your Input Type is Unstacked Data, then you would have separate columns of measurement data. For example, if you have 10 items, 2 appraisers, and 3 repeats then you would have 10 rows of data for the items column, 2 rows of data for the appraiser column, 10 rows of data for the external standards, and 6 columns of measurement data with 10 rows each. Note that all appraiser columns are grouped together. 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).
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. Options
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: 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.
5
LSL Value: Specify the lower specification limit for the study.
6
USL Value: Specify the upper specification limit for the study.
7
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.
8
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

If you click on the Charts button, you will see the following dialog box. Charts
0
Pick Charts: Select the charts you would like to display for this analysis.
1
Title: The system will automatically pick a title for your chart. However, if you would like to override that with your own 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 would like to override that with your own subtitle you can 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 own 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 own 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 then 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 will not be able to 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 then the minimum y-axis scale is set at 10 and the maximum y-axis scale 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: If you want to add a few extra horizontal reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15 then two horizontal lines are plotted at Y = 12 and Y = 15 respectively. Note that this input is optional.
8
Vertical Lines: If you want to add a few extra vertical reference lines on top of your chart you can specify the values here. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5 then two vertical lines are plotted at X = 2 and X = 5 respectively. Note that this input is optional.

Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. Verify The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may 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.

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 5 parts, the first appraiser measures these 5 parts and stores the values in a single column. When the appraiser measures these 5 parts a second time, they are stored in another column.
  • If there is any external standard (for discrete data), enter the external standard values.

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% then 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 either binary or nominal, then the software will compute the percentage match and the Kappa values. The sample output is shown below. outputs2 If the data entered is ordinal, the software will compute the Kendall coefficients. 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 and not on the % match.
  • For ordinal data, a percentage match is not recommended as 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

Following examples can be found in the Examples folder.
  • Determine if the measurement system is acceptable for the data given in the reference file (MSA 1.xlsm).