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Gage R&R


Gage R&R is the type of Measurement System Analysis (MSA) that is used to quantify how well a variable (continuous) measurement system is working.




Xbar-R (Mean and Range) is a pair of control charts primarily used in Statistical Process Control (SPC) for variable (or continuous) metric when samples are collected at regular intervals from a process. It is a preferred option when the sample size is between 2 and 8. The Range chart helps understand the process variation (and hence is the first chart that is reviewed) while the Xbar chart helps understand the process center. The process is said to be stable only if both the Range and Xbar charts are in control


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by     
Amlan Dutta on 12th June  2019.


Applause for all the respondents- Amlan Dutta, Natwar Lal. 


Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.


Q. 167  While analyzing the XBar R Chart in Gage R&R Output, a sound measurement system will have more than 50% of the data points falling outside of the control limits. It is intuitively the reverse of what we want to see (data points to be inside the control limits for a well controlled process). Explain this seeming aberration. 


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Well! I would try to keep it short

Why GR&R?

You are basically measuring Part-to-Part variation, Equipment Variation (Repeatability), Appraiser Variation (Reproducibility). We expect most of the variation to be caused by variation between the parts than caused by the appraisers and equipment.

If the one or more appraiser can’t get the same measurement on same part, then the measurement system is source of error.


How it is done? (An example of 5 parts, 3 appraisers, 2 trails each on all parts, See file attached)

1.       Pick a part (identified by unique part number, say a hexagonal bolt) with known specification tolerance level. Ex. 20 cm with ±1 cm

2.       Choose 5 specimens of same part from one batch or lot, that covers the specification tolerance. i.e. if the specification tolerance is 20 ±1 cm; select specimen that start at 19.1 and go to 20.9 (19.1, 19.6, 20, 20.5, 20.9)

3.       The part should represent the actual or expected range of process variation. if you're measuring to 0.1 cm, the range of specimens should be 10 times the resolution. Number each specimen for the study but don't put them in any kind of order


4.       Three appraisers (people who measure the specimens)

5.       One measurement tool or gage; Resolution of 0.1cm

6.       Two measurement trials, on each specimen, by each appraiser

7.       Randomly have each appraiser measure each specimen at least twice

(In text books, the word specimen doesn’t appear but I used it for clarity)


The second step above is noteworthy.

  • It’s not a random sampling from assembly line but cherry-picked specimens of part which covers expected range
  • Gage R&R study is evaluating measurement system and NOT part, it doesn’t care not care how good parts are but how well they are measured over the specified range
  • You also need bad parts to perform a Gage R&R study, a bad part can be outside tolerance limits


Now the answer lies in the way the X-bar and R Charts are constructed. The values on the R-Chart are calculated by taking the differences between the highest and lowest measurements obtained by each appraiser for each part through random trials. It represents only measurement variation in the system. The control limits for the X-bar Chart are based on the R-Bar of R-Chart. Thus, the area between the control limits on the X-bar Chart represents the amount of measurement system variation.

When plotted on the X-bar Chart, it contains both part-to-part variation and measurement variation. Hence, >50% of points on X-Bar chart should fall outside the control limits representing acceptable measurement system variation while highlighting prominent part-to-part variation.

(provided range of specimens is very high as compared to resolution of gage)


However, it’s not so with R-Chart but is used to compare operator bias.

If there are values above UCL of R-Chart then it should be investigated for invalid measurement or data entry error before proceeding.

Nevertheless, when values are within CL it shows acceptable discrimination by measurement system. If the R-Chart cannot discriminate between different sample parts then measurement system is not sensitive enough to be used any further. Below is an example of poor R-Chart in GR&R, it can discriminate only 3 distinct categories shown with blue arrows.



Below are output of doing GR&R right way (right) vs. wrong way (left) using fictitious data generated from normal distribution. The right way is discussed above in “How it is done?” while wrong way is elaborated below in last section.

(The so called right way is not so good as one of the point is outside UCL in R-Chart but it’s computer generated data!)


   image.png.ae97c14509021fb2affc1c21ee746b43.png image.png.c7aaf77f8209b12253485a667353377e.png


The X-bar chart (right image above) looks like a process out of control with many point outside the control limits but it is NOT a process chart but a measurement system analysis chart. The tighter the limits and the more point outside those limits, the better the measurement system. Thereby contributing very little to the total variation in GR&R.

It's apparent from R-Chart that the number of distinct categories = 6 (minimum 5 is desirable)


As explained control limits are calculated based on measurement error. Consequently, the control limits define a blackout zone inside which the gage cannot see anything. The gage can only see a measurement when the it exceeds this blackout zone. Ideally, you would want as many points as possible to exceed this zone.


So, when will >50% of the data points NOT fall outside of the control limits, just the opposite as expected from good GR&R study

  • Measurement system has errors (…is blind as stated above); measurement system shows more variation than manufacturing process
  • Using only one specimen measurement for all 5 specimens of same part. If you only use one specimen, there can’t be any part variation, so people and equipment will be the only source of variation. This is shown above as the wrong way!
  • Process width has reduced beyond the gage can detect at current resolution, gage can measure at resolution of 0.1cm while part to part variation is measured down to .001cm
  • Range of specimens is very low as compared to resolution of gage. Using parts between 19.6 cm and 20 cm in current example 


Can't edit it anymore! :) 

fictitious data.MPJ

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Xbar-R or the mean and the range chart is ideally used for checking if the process is stable or in control. However, that is not the only purpose of this chart. It is also used in the Gage R&R study. Gage R&R is one of the tools that is used for measurement system analysis. 

In MSA, the objective is not to check the stability of the process. Rather, it is to check the contribution of the measurement system variation to overall variation. MS variation can be caused by the operator and/or the gauge that we use for measurement. 

Now while doing Gage R&R, it is important that we consider parts that cover the complete specification range or the tolerance limits. E.g. if the thickness of a metal piece should be 2mm±0.1mm then the specification range is 1.9 mm to 2.1 mm. Ideally we would want parts to have average thickness of 2mm but for our Gage R&R study we will include parts that have thickness of 1.9 and 2.1 as well. 

Now these parts are checked for thickness by multiple operators multiple times and the results are analyzed.

The R chart displays the range (i.e. max - min value for the same part) as measured by the operator and hence indicates the Repeatability or consistency by operators. The control limits for the Range chart are dependent on the following

1. Number of samples

2. Average Range

If operators are consistent, then average range will be small.

Now, Xbar chart displays the part to part variation. Its control limits are dependent on the following

1. Number of samples

2. Average Range

3. Mean of all observations

If the operators are consistent, then average range will be small. However since the parts are cover the entire range of the specification limit, we will observe that the means are different (due to part -to-part variation).

Therefore, ideally the control limits in the Xbar chart will be close to each other while the mean of different parts will be scattered. Hence, we tend to see that 50% of the points will be outside the control limits. E.g. In our example, let us say that UCL = 2.05 and LCL is 1.95. However there will be parts that will have average values between 2.05 and 2.1 and also between 1.95 and 1.9.


Now on the contrary, if we get all points within the control limits, it will mean two things

1. the parts selected do not cover the entire specification range

2. Operators are inconsistent

Both of the above points would indicate that the measurement system cannot be relied upon and needs to be fixed.


Hope this helps. Running short on time and hence not showing the same with data. Maybe next time.

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Benchmark Six Sigma Expert View by Venugopal R


To fully understand the explanation to this question, one has to be clear on the principles of XBar–R chart and also about the variations related to Gage R&R. While many of the ambassadors would have given good explanations, I will express my points briefly. Please be cautioned that this write-up will not give a full education on these topics and hence I request the readers who seek further clarity to read and develop more understanding of the two topics as mentioned above.


How does an XBar–R chart work?

XBar–R chart is constructed based on several groups of small samples processed under nearly similar conditions. Each such group is termed as “Rational sub-group”. The Range chart shows variation within these samples and the control limits for Range chart are statistically derived from the sample data. A reasonable time gap is allowed to pick the successive groups of samples, intending to bring out any process variations. The X-Bar represents the mean value of each of the sub-groups. It is to be noted that the control limits of the X-Bar chart are also derived using the average range values.


How is the X-bar R chart interpreted?

If all the X-Bar values are falling within the control limits, the variation between the subgroups cannot be distinguished from the variations within the sub-groups. This could mean that the Process variations are very low and do not show up over and above the ‘within’ group variations. It could also mean that the ‘within’ group variations are so high that the process variations are not being distinguished. If more values of X-Bar fall outside the control limits, then the process is considered to be influenced by assignable causes, whose influence is over and above the ‘within-group variations’. On the whole, more points falling within control limits is a desirable situation here.


Now let’s examine the X-Bar R chart used for interpreting Gage R&R

Here, each sub-group is represented by the readings taken by the same appraiser on the same part, assuming the range chart is made for each appraiser. The control limits for the X-Bar chart, being based on these R values, depict the variation of the measurement system. Each point on the X-Bar chart represents the average of the readings by each operator. The variations between X-Bar values are considered as due to Part to Part variation.


Now, if most of the X-Bar values fall within the control limits of the X-Bar chart, it means that the Part to Part variation is not distinguishable from the Measurement system variation. It either means that the Measurement System Variation is too high or the choice of the parts is not representative enough to bring out the Part to Part variation, or a combination of both.


If most of the X-Bar values fall outside the control limits, it means that the variation due to Measurement System is low enough to show up the variation due to Part to Part. In other words, here, we would like to have the relative variation of the measurement system to be low compared to the Part to Part variation that the system is expected to assess. Hence more points falling outside the control limits is a desirable situation here.

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The chosen best answer is that of Amlan Dutt for the detailed explanation with data. Must read is Natwar's answer which is very detailed and accurate, too. To read the Benchmark expert view, refer to Venugopal's answer.

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