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About this lesson
This lesson walks through an example of an attribute data Gage R&R analysis. The example is demonstrated using manual data collection and equations with the Microsoft Excel spreadsheet application. The same example is then demonstrated using the statistical software program Minitab, which is often used for analyses with Lean Six Sigma projects.
Download this lesson’s related exercise files.Attribute Data Gage R&R Examples.xlsx
13.9 KB Attribute Data Gage R&R Examples - Solution.xlsx
Attribute Data Gage R&R Examples
An example of an attribute data Gage R&R analysis will illustrate the power of the technique. This example is demonstrated using comparison equations with a spreadsheet in Microsoft Excel. The same example is then demonstrated the statistical software program Minitab, which is often used to conduct analyses for Lean Six Sigma projects.
When to use
The example illustrates the technique. When doing your first few Gage R&R Studies, you will want to refer to the example to guide you through the process.
This example will be based upon the data set shown below. It is for a study with three Appraisers, 25 items, and two trials.
Repeatability calculations are first conducted at the individual level first. This is done by determining the number of times an appraiser is consistent in their evaluation (which is the match column) divided by the number of items, and then converted to a percentage.
- Appraiser #1 is 23/25 = 92%
- Appraiser #2 is 22/25 = 88%
- Appraiser #3 is 25/25 = 100%
The System Repeatability is the average of those three: (92% + 88% + 100%)/3 = 93.3%
Reproducibility is the calculation of the number of times all Appraiser #1 = all Appraiser #2, all Appraiser #1 = all Appraiser #3, and all Appraiser #2 = all Appraiser #3 divided by three times the number of items and then converted to a percentage.
Reproducibility = (21 + 23 + 22) / 75 = 88%
The accuracy measures will include the use of the Reference Standard column in the comparisons. First is the measure of accuracy, which is the number of times that each appraiser correctly assessed the item value divided by the total number of inspections and then converted to a percentage.
- Appraiser #1 – first pass = 24 times, – second pass 22 times
- Appraiser #2 – first pass = 22 times, – second pass 23 times
- Appraiser #3 – first pass = 24 times, – second pass 24 times
Total Accuracy = 139 / 150 = 92.7%
The Miss Rate is based upon the Appraiser assessing a “Pass” for what should be a “Fail.” The Miss Rate is the number of times that occurred divided by the number of assessments of units whose true status was “Fail” and then converted to a percentage.
- Appraiser #1 = 2 occurrences, Appraiser #2 = 4 occurrences, Appraiser #3 = 2 occurrences
- Miss Rate = 8 / 66 = 12.12%
False Alarm Rate is based upon the Appraiser assessing a “Fail” for what should be a “Pass.” The False Alarm Rate is the number of times that occurred divided by the number of assessments of units whose true status was “Pass” and that converted to a percentage.
- Appraiser #1 = 2 occurrences, Appraiser #2 = 1 occurrence, Appraiser #3 = 0 occurrences
- False Alarm Rate = 3 / 84 = 3.57%
The system effectiveness is the number of times that all appraisers agreed on all trials with each other and the reference standard for an item divided by the number of items and that converted to a percentage.
System Effectiveness = 20/25 = 80%
Minitab provides a wizard for measurement systems analysis that is found under the "Assistant" pull down menu. When selecting Measurement Systems Analysis the wizard panel shown below appears.
- Attribute data analysis is on the right side of the first diamond and is labelled "appraisal".
- Whichever path you choose, you then have two options, either to set up the study which will create the data collection form for you, or the analysis side which will perform the calculations.
- When setting up the study, you will need to provide the true status for each item in order for Minitab to create the Reference Standard column.
- When selecting the analysis side for attribute data, a second panel is displayed. This panel will ask where information is found in your Minitab workbook.
- The Minitab workbook operates similar to an Excel spreadsheet – in fact you can directly copy and paste data form one application to the other.
- One limitation within Minitab, is that it almost always requires the information to be in columns not rows.
- If you used Minitab to set up the study, the form it created will be organized for easy analysis.
- You will need to tell Minitab which columns are your appraiser names, your item numbers and of course your data. Be sure to select which of the entries is considered good in the “Value of good or acceptable items” window.
- If you are not familiar with Minitab, the way to select a column for one of their entry fields is to first place your cursor in the field. This will cause all available columns that are not already assigned to be shown in the window on the left.
- Highlight the column you want to use for the selected field, then drop just below the window listing all columns and click on the Select button. That column name will now be in your field.
- Do this to select a column name for every open field on the panel.
- Then when ready, click the OK button at the bottom of the panel. Minitab will soon give you results.
The Minitab results are both graphical and numerical. It provides a summary of the analysis, but Minitab will break down the data into further detail in additional graphs. These show detail by operator, by trial and even by item.
Hints & tips
- If planning on doing the analysis in Minitab, do the setup with it also and use the Minitab form. The analysis then takes about 15 seconds to select the columns and see the result.