Case in RR studies:Can we MARK the measurement point to reduce within part variation?



A Case in R&R studies

Hi everybody,

I'm currently working with a screw manufacturing company, producing various kinds of screws from 2 to 10 mm in diameter.

We are faced with the a case in doing R&R study, which I try to describe below:

1- the measuring device is a 0.001 mm resolution (digital) micrometer,

2- The product is a screw with (stem)diameter
LSL=2.60 and USL=2.64 mm,

3- The product characteristic measured is the screw (stem) diameter,

4-Initially, the resulting %R&R were very bad (about 90%)!

5- We suspected the main reason was too much within-part variation due to diameter change along AND around the screw stem,

6- We finally managed to reduce %R&R to about 15% by MARKING the measurement point on the screws. (This is apparently allowed by the MSA manual where there is excess WIV, page 64 or so).

Question 1: Can we reliably use this device for process control and analysis, given the fact that R&R results were produced by marking the screws? if not:

Question 2: What can we do in this specific case to improve the measurement technique / system to get better %R&R WITHOUT marking the screws, and without using the cumbersome WIV-method of calculating R&R?

Anybody out there ?

Thanks in advance

Rick Goodson


With all due respect, you have not reduced the % R&R to 15%. You have changed the prcoess for measuring gage R&R by intentionally not measuring within part variation. You have determined that the system for measurement is 'acceptable', given the cavet that within part variation is not considered. Based on the information you have supplierd, the problem is not the measurement system but the parts. You need to improve the within part variation of the parts, not the measurement system.



KenK - 2009

Yes, but the good news is that the source of variation HAS been identified. That's possibly more than half the battle.

It also points out that the gage is sufficient for measurement and CAN be used to assess the result of screw dimension improvement studies.

Yes, a method needs to be devised consistently measuring the same location on the screw (distance from head).

Yes, you've identified possible screw diameter variation - that will always have to be taken into consideration when measuring screw diameter. Is that something you wish to reduce? Maybe or Maybe Not. It may be that this variation in screw diameter does not exceed customer expectations or affect the customer's perception of quality.


Dear Rick,

You are right, we have a problem with the production process. But the issue is "whether the measuring system is acceptable? "

Regarding the above question, I go with Ken's answer. His reasoning seems reasonable.

Whether this WIV is acceptable, till now there has not been any complaint from any customer. Maybe because the srews are not supplied for super high precision applications.

Thanks to both of you,
appreciate your help,



You need to select a MSA method conducive to analyzing product with excessive WIV (within part variation). WIV may be a perfectly natural and acceptable bi-product of your processes. But excessive WIV, such as taper or out-of-round, can cause the measurement system evaluations to provide misleading results.

There is a method listed in the MSA designed specifically to analyze product with WIV. See page 64 in the MSA “Quantifying the effect of excessive within-part-variation”. This method separates WIV from gage repeatability variation for a better gage assessment.

The odds are your gage is adequate, your product is fine and even the methods employed to measure are ok, but you need to review the method of analysis. Let us know how it turns out.


Dear AJLenarz,

Thank you for your comment. Some time back I had tried the WIV method. I can tell you it is quite time consuming! Because you have to do all the calculations by hand. MitiTab V13 doesn't support this method either.

Anyway, I'll give it another try, and inform you of the results. By all means.


KenK - 2009

OK, I don't know if this will all fit - if not, I'll continue it in another post. I had this in Word already so I'm copying it here:

Gage R&R Using MINITAB’s GLM Tool

Don't do this stuff by hand!! Especially if you have MINITAB.

Any crossed Gage R&R (as opposed to nested), no matter how many factors (typically parts, operators, repeated measurements) can be analyzed using MINITAB's General Linear Model tool. First I'll explain how to use it for a typical GR&R so you get the idea, then I'll mention the within part variation.

For a typical GR&R, think if it as a general factorial DOE with two factors - PARTS at 10 levels and OPERATORS at 3 levels.

Create columns as you normally would, with each measurement on a unique row, a column to identify the part, a column to identify the operator, a column that contains the measurement, and optionally a column that contains the repeat number (not really used in the analysis).

Open the MINITAB General Linear Model tool under the ANOVA menu. Enter the MEASURE variable into the Responses field. Enter the PART , OPERATOR, and PART*OPERATOR variables into the Model field. The later item is the part*operator interaction, which you really should look at. Enter the PART and OPERATOR variables AGAIN in the Random Factors field – don’t enter the interaction term there. This tells MINITAB that you want to analyze the variation between parts & the variation between operators (unlike the typical DOE).

IMPORTANT! - Make sure you select the Results button and check the Display expected mean squares and variance components checkbox. This makes MINITAB output the variance estimates for Parts, Operators, and Repeatability – which is just what you want.

Now, look in the session window for the variance estimates. They’ll be in the table called Variance Components. We’re almost there.

Now, just to clarify, the row labeled Error represents the Repeatability, the rows that contain the label Operator combine to represent the Reproducibility, and all the rows that except the one that says Part combine to represent the combined Gage R&R. This next part is easiest to do in Excel. To build the VarComp column that is found in the MINITAB GR&R:

Variance Source = Variance Component
(upper case terms refer to the values in the Variance Component table)

Repeatability = ERROR
Reproducibility = OPERATOR + OPERATOR*PART
Operator = OPERATOR
Operator*Part = OPERATOR*PART
Part-to-Part = PART

Now just divide each of these row Variances values by the Total Variation value to calculate the %Contribution column.

Now create the StdDev column by taking the square root of the respective variances.

Now multiply each of the StdDev values by 5.15 to create the StudyVar column.

Now divide each of the StdDev values by the Total Variation StdDev value to create the respective %Study Var.

You’re done. You can create the main effect and interaction plots typically provided in the GR&R output by using the Stat > ANOVA > Main Effects Plot and Interactions Plot tools. For the Interactions Plot I’d suggest you enter OPERATOR before PART in the Factors field, just to be the look you expect.

Now, about the Within Part Variation. This is done the exact same way. Make sure you measure each part several times (repeatability) in several standard locations (the within part variation – I’ll call this data’s column LOCATION). Enter the data into the General Linear Model dialog box as follows:




The Model field tells MINITAB to include not only the main effects, but also all of the possible interactions, which should be looked at. If these are insignificant (the respective ANOVA table’s p-values are less than 0.05) then they can be left out of the model. Don’t forget to check the Variance Components option in the Results dialog box.

Now you’re ready to start combining variance components. Any variance component that contains the OPERATOR term is considered part of Reproducibility, and thus also part of the Total Gage R&R. The LOCATION and PART*LOCATION terms aren’t part of the Total Gage R&R – they are characteristics of the stuff being measured – more akin to part-to-part variation So the table might look like this:

Total Gage R&R
-Repeatability (the Error variance component)
-Reproducibility (the sum of all terms containing Operator – or any other measurement error sources)
Total (the sum of all the variance components

Get the relative percentages (% Contribution), take the square roots to get the StdDev, calculate the 5.15*StdDev’s, and divide the StdDev’s by the Total StdDev to get the %Study Variations. You’re done.

You can create the respective main effect and interaction plots using the same technique.

Now that was easy wasn’t it? You can use the same general method to analyze any measurement system with just about any source of variation (multiple test bays, multiple test heads, etc)

Al Dyer

What is the purpose of a gage R&R study?

To measure the accuracy of the gage and the variation between the "inspectors"

I see no problem in marking the inspection point on the part being measured, this will tell you how well the gage functions.

In the case of a screw head diameter, the caliper or micrometer may be a perfectly acceptable gage but possible the wrong gage to use in measuring concentricity or roundness.

Just a thought!



Originally posted by Al Dyer:
What is the purpose of a gage R&R study?

To measure the accuracy of the gage and the variation between the "inspectors"

Al –

The purpose of a gage R&R is to assess the quality of the measurement system. The measurement system is defined as: the collection of operations, procedures, gages and other equipment, software, and personnel used to assign a number to the characteristic being measured; the complete process used to obtain measurements.

It would be acceptable for a gage R&R to mark the part and measure a specific area on the part if this is a normal part of the day-to-day process of determining product quality. However, if this is not part of your normal measurement process, it would be unacceptable to conduct a gage R&R in this fashion.

Again, part of the R&R is to evaluate the process. If you change the process specifically for the R&R then you are not getting a true evaluation on the process that is normally used on a day-to-day basis.

Any other views?

Al Dyer


I may be over-simplifying the subject but:

I am a small shop that has one caliper that we use to measure the five washers we produce. We do a gage R&R on one of the washers and find that the total R&R is 3.5.

Can we assume that the gage is within reasonable functionality to measure the other 4 washers, or must we perform a gage R&R an all 5 washers.

If we do so and find that the R&R ranges from 3.2 to 3.7 must we buy for additional calipers, on for each product?

Just a question, I'm not a calibration guru!

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