Variable Data Gage R&R Examples

Locked lesson.

Upgrade

About this lesson

This lesson walks through an example of a variable data Gage R&R analysis. The example is demonstrated using manual data collection and equations with a spreadsheet in Microsoft Excel. The same example is then demonstrated using the statistical software program Minitab, which is often used to conduct analyses for Lean Six Sigma projects.

Quick reference

Variable Data Gage R&R Examples

An example of a variable data Gage R&R analysis will illustrate the power of the technique. This example is demonstrated using Means and Ranges equations with a spreadsheet in Microsoft Excel. The same example is then demonstrated using ANOVA with 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.

Instructions

This examples will be based upon the data set shown below.  It is for a study with three Appraisers, then items, and three trials.

The ranges for each part and appraiser have been calculated. The Mean for each part and the mean for each appraiser have also been calculated. With these the Means and Ranges calculations can be completed.

  1.  
  2.  
  3.  
  4.  
  5.  

The other approach is to use the ANOVA statistical analysis methodology. This normally requires a statistical application. The most popular application for statistical analysis within the Lean Six Sigma community is Minitab. That application will be used to illustrate how to create and analyze a variable data Gage R&R Study.

Minitab provide a wizard for measurement systems analysis that is found under the Assistant pull down menu. When selecting Measurement Systems Analysis the wizard panel appears.

Variable data analysis is on the left side of the first diagonal and is labelled "measurement". The attribute data analysis is the right side 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 selecting the analysis side for variable 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.
  • In the process variation section, I normally will check the box for “Estimate from parts in the study.”

  • 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. I find the most helpful results to be the panel shown below. In this case you can see a breakdown of repeatability and reproducibility. As mentioned before, the values are not the same as though calculated with the Means and Ranges approach, but they are similar.

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.
Login to download
  • 00:04 Hi, I'm Ray Sheen.
  • 00:06 It's now time for
  • 00:06 part two on the lesson for analyzing the Variable Data Gage R&R study.
  • 00:12 This time we will work through an example.
  • 00:14 So since we're working an example on how to do the analysis,
  • 00:18 let's start with the data.
  • 00:20 As the study progresses, you record the data in the study form or
  • 00:23 format you created.
  • 00:25 For our example, we're using this data set.
  • 00:27 Notice, some of the calculations that are already done on the data set,
  • 00:31 there is a part mean at the bottom of the table which is the average of
  • 00:35 the part values across all three appraisers and all three trials.
  • 00:39 We have a mean for each appraiser off to the right of the table, which
  • 00:43 is their average for all measurements on all 10 items, in all three trials.
  • 00:47 And you can see all for each appraiser that there is a range calculated for
  • 00:51 each of the items.
  • 00:53 You adjust the difference between the highest and lowest measure value that they
  • 00:56 had for that item, with those ranges, a range mean is calculated for
  • 01:01 each appraiser and that is also on the right side of the data.
  • 01:05 With all of that data and all of the approrpriate means and
  • 01:08 ranges calculated, the formulas we covered in part one can be brought to bear and
  • 01:13 we can calculate PB, EB, AB, TB and GRR.
  • 01:18 The PV or part variation is the max part value average-
  • 01:21 the minimum part value average * K3.
  • 01:24 So that means it's the average for part 8- the average for part 2 * K3 value for
  • 01:30 10 items and our PV is 0.2394.
  • 01:35 The EV is K1 times the average of the appraiser's average range value.
  • 01:40 The appraiser's range values are .0485, .0382 and .0413 respectively.
  • 01:48 We average those and use the K1 value for three trials.
  • 01:52 This gives us an EV of .0252.
  • 01:55 All though the AV equation is kind of ugly, we just plug in our numbers.
  • 02:00 Appraiser three had the maximum mean and appraiser two have the minimum mean.
  • 02:04 The EV value we already calculated and of course,
  • 02:07 there are 10 items in three trials.
  • 02:09 Plug those in, do the math.
  • 02:11 The number was positive, so we take the square root and we get our AV of 0.00821.
  • 02:17 The total variance is the square root of the sum of the PV squared,
  • 02:21 EV squared and AB squared.
  • 02:23 So that is 0.24091.
  • 02:24 The GRR is the square root of the EV squared and the AV squared.
  • 02:30 That gives us a GRR of 0.02651,
  • 02:34 divide that by TV and we get a value of 11.01%.
  • 02:39 That tells us that the system is not quite as good as we would like.
  • 02:43 Were in the marginal zone but just barely.
  • 02:45 And depending upon the system,
  • 02:46 there may be some ways to tighten things up just a little bit.
  • 02:49 Now, I would focus on the EV,
  • 02:51 since it is three times larger than the AV, if I'm going to make an improvement.
  • 02:56 Well, that wasn't so hard.
  • 02:57 Now let's look at doing a Variable Gage R&R study in Minitab.
  • 03:01 You'll find it's even easier.
  • 03:03 There are several different ways that you can initiate a Gage R&R in Minitab.
  • 03:07 I'll show you my favorite.
  • 03:09 I start from the assistant pull down menu at the top of the screen and
  • 03:13 select Measurement Systems Analysis.
  • 03:15 That should bring up a screen that looks like this.
  • 03:18 The left side is labelled Measurement for a Variable Gage R&R study.
  • 03:22 The right side is called Appraisal for attribute studies.
  • 03:25 If you're setting up your study, click on the icon for Set up.
  • 03:30 Now it'll bring up a panel where you can enter the number of appraisers,
  • 03:33 the number of items and the number of trials or replicates.
  • 03:37 Minitab will then create the data collection form,
  • 03:40 which will already have randomized the measurement sequence.
  • 03:44 But we're no longer doing set up, we're doing analysis.
  • 03:47 So let's take a look at that.
  • 03:49 If you've collected all your data, then go back to that assistant,
  • 03:53 select the measurement systems analysis path.
  • 03:56 And this time, select the icon at the end of the analysis path and
  • 03:59 you should get a panel in Minitab that looks like this.
  • 04:02 Select the column for your appraisals, which Minitab calls Operators, your items,
  • 04:06 which Minitab calls Parts and your Measurements.
  • 04:10 If you aren't familiar with using Minitab, here are a few ground rules.
  • 04:13 Minitab likes everything in columns, so when I created the form for
  • 04:17 recording data.
  • 04:19 All the data was in one column.
  • 04:21 Another column, had the appraiser for that data entry and
  • 04:24 a third column have the item number for that data entry.
  • 04:28 Now to select these columns on this panel, on Minitab,
  • 04:31 place your cursor in the field where you want to enter the column name, when you do
  • 04:36 that, all the column names will show up in the window on the left side of the panel.
  • 04:40 Highlight the column you want,
  • 04:42 then click on the select button just below the window.
  • 04:45 When you do that, the column name should now appear in the window where
  • 04:48 you had first placed your cursor.
  • 04:50 Once you've selected everything, click the okay button at the bottom of the panel and
  • 04:54 Minitab will do the analysis.
  • 04:56 So let's look at the results.
  • 04:58 Minitab will present the results in several formats.
  • 05:01 I think the best is the graphical format.
  • 05:03 However, if you want a more detailed statistical analysis,
  • 05:07 that's available also in the session window view.
  • 05:10 In this case, the reproducibility graphs are on the left.
  • 05:14 And you can see that they're broken out by part at the top and
  • 05:18 by appraiser at the bottom.
  • 05:20 The repeatability graphs are on the right.
  • 05:22 Again, a part view and an operator view.
  • 05:25 The panel also has the statistics in the bottom right corner.
  • 05:29 Minitab use the analysis of variance or
  • 05:31 ANOVA technique, which will be more accurate analysis
  • 05:35 because it will take into account combination effects or interactions.
  • 05:39 So the Minitab answer will be slightly different from the one that we
  • 05:42 calculated in the spreadsheet.
  • 05:44 Overall, minitab found 13.4% GRR.
  • 05:47 Not quite as good as we had manually calculated but
  • 05:49 close, still in the marginal range and indicating a need for some improvement.
  • 05:54 And this analysis also show that reproducibility
  • 05:58 was better than repeatability but not by as wide a margin.
  • 06:03 Once your data is collected, the math for a Variable Data Gage R&R study is really
  • 06:07 not very difficult and Minitab will make it even easier.

Lesson notes are only available for subscribers.

PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.

Gift this course