Variable Data Gage R&R Calculations

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:06 I'd now like to walk through a variable data, Gage R&R Analysis.
• 00:10 This is actually a two part lesson.
• 00:12 In this first part, I'll explain the calculations.
• 00:16 The second part we'll use those formulas on a data set to determine the amount of
• 00:21 error that we have from repeatability and reproducability.
• 00:24 Let me quickly review the variable data Gage R&R study parameters.
• 00:30 The variable Gage R&R Study can get by with fewer
• 00:33 data points than what is needed for attribute Gage R&R.
• 00:36 That's because variable data is much richer in information than attribute data.
• 00:41 This richness will allow us to do more with the data and therefore
• 00:45 the calculations are more extensive and complex than with the attribute data.
• 00:49 Recall that in the study there will be two or three appraisers,
• 00:52 five to ten units to measure, and they will be repeated for two or three trials.
• 00:57 There are two different calculation approaches that are used with the variable
• 00:59 Gage R&R Study.
• 01:01 The ANOVA approach is an advanced statistical technique.
• 01:05 It gives more accurate answers and
• 01:06 that's what statistical applications like Minitab use.
• 01:09 A simpler approach is the Mean and Range approach with equations and
• 01:13 some statistically derive constants.
• 01:15 That is the approach that I recommend you use,
• 01:18 if you're doing the analysis in Excel.
• 01:20 The answer will be similar between the two approaches but not exactly the same.
• 01:24 Either approach will calculate a number of different values for variation.
• 01:27 Equipment Variation, which is essentially repeatability; Appraiser Variation, which
• 01:32 is reproducibility; Part Variation, which is based upon the range of parts used in
• 01:37 the study; Total Variation which is a combination of all those, and GRR, which
• 01:43 is the combination of the repeatability and reproducibility measures.
• 01:46 On the next few slides I'll give you formulas for Means and
• 01:49 Range calculation for each of these.
• 01:52 I'll start with Part Variation or PV.
• 01:54 Part Variation will be used to scale the GRR value.
• 01:57 It is based upon the actual variation of the parts used in the study.
• 02:01 We use it to represent the variation that is expected from the operational process
• 02:06 as compared to the measurement process.
• 02:08 It's not a repeatability and reproducability measure, but
• 02:11 it is a component of total variation and we need for that reason.
• 02:15 The calculation will depend upon the number of items in the study
• 02:19 that are being measured.
• 02:20 The formula is very easy to calculate.
• 02:22 Part Variation is equal to the average value for the largest item measured minus
• 02:26 the average value for the smallest value measured times a constant called K3.
• 02:31 The average value for the largest item is based upon combining the measurements for
• 02:36 that part from all appraisers and all trials.
• 02:39 Likewise, the average value for the smallest is based upon combining
• 02:42 the measurements for that part from all appraisals and all trials.
• 02:46 The K3 value comes from this table and
• 02:48 it changes based upon the number of parts in the study.
• 02:51 Now let's look at the Equipment Variation or EV.
• 02:55 Equipment Variation is often referred to as the within appraiser variation
• 02:59 since the analysis will eliminate the effect of the individual and
• 03:02 only look a variation within that appraiser's data set.
• 03:05 It is focused on what happens when one appraiser measures the same items using
• 03:10 the same equipment.
• 03:12 That's why it is our repeatability measure.
• 03:15 It is also a very simple measure,
• 03:16 it is the average of the average range from each appraiser times the constant K1.
• 03:23 Now let's talk about average of the average range for a minute.
• 03:26 To determine that, you need to find the range for each item for each appraiser.
• 03:31 If you only did two trials,
• 03:33 it's easy to determine the range, larger one minus the smaller one.
• 03:37 If you did three trials, it is the largest minus the smallest for that item.
• 03:42 Find the value for each item for each appraiser, then average the values for
• 03:47 each appraiser.
• 03:48 So if you had five items, you would have five range values for each appraiser.
• 03:53 Add those and divide by 5 and then go to the next appraiser and do the same.
• 03:57 Once that is done, average those values you just calculated and
• 04:01 that is what you use in this equation.
• 04:03 It's the average of the appraiser's average range values.
• 04:07 Finally the K1 value is selected based upon the number of trials.
• 04:11 Next we look at the Appraiser Variation or AV.
• 04:15 That will look at the variation that's occurring between appraisers
• 04:18 when they measure the same part.
• 04:20 These are a reproducibility measure.
• 04:22 Now there are three things to watch out for in this measure.
• 04:25 First, we'll be using the mean values not the ranges.
• 04:29 Second, we will use our value for equipment variation in the calculation, so
• 04:34 you always have to do the calculation for EV before you can calculate AV.
• 04:38 And third, this equation takes the square root of a mathematical calculation
• 04:43 that could be a negative number.
• 04:45 When that occurs, use the values zero for your AV.
• 04:48 That just means that the repeatability variants will overwhelm a tiny amount of
• 04:53 reproducibility variants.
• 04:55 Unlike the previous equation,
• 04:57 this one is rather complex, it is a square root of a bunch of stuff.
• 05:01 Inside that square root, we take the mean value of the measurement
• 05:05 from the appraiser who had the largest mean and
• 05:07 subtract the mean value from the appraiser with the smallest mean.
• 05:11 Multiply that times the constant K2, then we square that result.
• 05:17 Next we need to subtract out the equipment variation effect, so we take the EV value
• 05:21 and square that, but divide that by the number of items and number of trails.
• 05:26 If the number is negative,
• 05:27 replace it with zero, otherwise we take the square root of that value to get AV.
• 05:31 And you can see all of these items are defined here, the average for
• 05:36 the appraiser is the average value of all parts in all trails for that appraiser.
• 05:41 Of course, n and r are based upon your study design and
• 05:45 K2 is based upon the number of appraisers in the study.
• 05:48 Well the rest is pretty simple.
• 05:50 Let's look at total variation.
• 05:52 Total Variation is just a combination of Part Variation,
• 05:54 Equipment Variation and Appraiser Variation.
• 05:57 So it will combine repeatability and reproducibility.
• 06:00 It is called the the total variation because it considers all aspects of
• 06:04 the variation.
• 06:05 As such, it is a good overall measure for
• 06:07 process variation, which is what we need to know to evaluate precision.
• 06:12 Notice, one thing in this analysis,
• 06:14 it does not tell us whether the items are good or bad.
• 06:17 That is not the purpose of this analysis.
• 06:19 It is to measure the magnitude of the expected variation
• 06:22 within the measurement process.
• 06:25 And the formula is very straightforward, it's the square root of the sum of
• 06:28 the squares of part variation, equipment variation, and appraiser variation.
• 06:32 And with that we're finally ready to calculate Gage Repeatability and
• 06:36 Reproducability.
• 06:37 GRR is just a combination of the equipment variation and appraiser variation.
• 06:42 As such, it is the measurement system variation.
• 06:45 Total variation looked at all the variation in all the measurement values.
• 06:49 When we eliminate the part variation,
• 06:51 what's left is the measurement system variation, and that's what's in the GRR.
• 06:55 The calculation is simple, it's the square root of the sum of the equivalent
• 06:59 variation squared and the appraiser variation squared.
• 07:03 However, we express GRR not as as an absolute value, but
• 07:06 rather as a percentage.
• 07:08 So to convert it to a percent, we divide the GRR by the total variation, and
• 07:12 then multiply time 100%.
• 07:15 Now with the GRR as a percent of total variation, we can go to our target values.
• 07:20 If GRR is less than 10%, the measurement system is acceptable.
• 07:24 10% to 30% is marginal, and over 30% either get a new system, or
• 07:28 improve your existing one.
• 07:32 Well, that's how the calculations work.
• 07:34 Now in part two we'll use those with an example problem set.

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