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Advanced MSA of Continuous Data - Part 1: Within Part Variation


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This is the eleventh in a series of articles on MSA, and the first in advanced MSA topics. The focus of this article will be on how to handle within product variation (WIV).

WIV is significant variation in the form of a product. Significant means that it detectable by your measurement device. Examples of variation in form include shaft diameter variation due to lobes, or a taper/barrel/hourglass shape; thickness variation due to parallelism and more.

WIV can have a significant impact on the acceptability of a measurement system. While technically part of the product not the measurement system, it definitely impacts the measurement system. It cannot be isolated using the standard AIAG Gage R&R study, but requires a special approach. The AIAG MSA manual touches on this and presents a Range method for calculating the WIV effect. I show an ANOVA approach that allows an evaluation of all of the interactions with WIV.

When I first decided to start this blog, I planned to demonstrate it using Minitab's General Linear Model (GLM). Fortunately, the new Minitab 16 made this easier with the Expanded Gage R&R Study feature. Note: Everything I show here can be duplicated with earlier versions of Minitab using GLM. The graphs must be created using the Graph commands and some creativity, and the metrics will have to be calculated by storing results and manually performing the calculations.

You can follow along by opening the attached PDF file.
  • First, determine whether WIV is a potential issue. You may know this already from process knowledge, or suspect it from high Repeatability variation or an Operator*Part interaction.
  • Create a Gage Study worksheet. Either copy the format used in the attachment, or use Minitab to create a full factorial design for 3 factors.
  • Identify specific locations on the product to be measured by all operators. These can be selected at random or by design. If selected by design, this must be entered as a Fixed factor into Minitab.
  • Perform study
  • Analyze following the attached file. I recommend starting with all factors and 2-way interactions in the model. Review the p-values and remove all 2-way interactions with p-values greater than 0.05. If all interactions involving the Operator are removed, then look at the p-value for the Operator. If the Operator p-value is greater than 0.05, remove it also.
  • Interpret the Session Window the same as a standard MSA for %SV, %Tol, etc.
  • Interpret Graph1 the same as a standard MSA.
  • Create Graph2 and interpret similar to Graph1. You will see two new graphs, the Measurement by WIV graph and the Part * WIV graph. The Measurement by WIV graph shows differences in the location measured on the part, and the interaction shows whether this location to location difference varies by part.
Now that you understand the impact of WIV on your measurement system, what do you do with that knowledge? It depends.

If the WIV varies randomly on the product (i.e., it is unpredictable), you cannot prevent it from affecting your measurement system. You can recognize it as part of your total variance equation (acknowledgements to bobdoering), but it will always affect your measurements.

If the WIV is predictable by location, you can take this into account and improve your R&R results by specifying measurement locations in your work instructions.

Last advice: Although it is possible to remove the effects of WIV from your R&R results, SPC and capability results, it will still have an impact on function. For example, a shaft with lobes may not fit a bearing correctly, so beware.


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For those of you that have been waiting over a year since I promised this post, I sincerely apologize. I hope it is worth your wait. :)


Stop X-bar/R Madness!!
It is absolutely critical to understand the impact of the within-part variation on the measurement system. But, one has to recognize what question they are trying to answer with the MSA study they are performing.

There are two independent factors in the total variance equation that are the result of measurement - gage error and measurement error. Gage error is the error the gage is responsible for when used in a measurement system. Measurement error is essentially the error of using the gage incorrectly.

If the question is what statistically significant resolution can the gage provide me when measuring a feature - or "gage error", then you need to eliminate the within part effect from variation about the part, because that variation is not the "fault" of the measuring device. It is a function of the technique employed when the device is put to use. The within-part variation that will remain is the effect of the part on the gage and visa versa - such as gage flex or gage pressure. Those are appropriate to consider for gage error.

If you want to capture both gage error and measurement error in an attempt to describe gage system error, then you can have the test operators measure the part randomly as a part of the gage R&R. It will inflate the error as the operators use the gage lacking proper measurement techniques, and it will be difficult to determine what action to take to minimize the error unless you perform the test described above separately. Not only will you pick up effects of roundness error, if the measurement technique is left wide open, you will also pick up taper. Gage R&R is capable of collecting a vast amount of error and reporting it. will usually leave a mess behind to clean up - especially if it "fails".

Even when trying to determine variation from measurement error, there are errors that can not be detected, such as using the wrong gage on two or three lobed diameter features. The measurement will be repeatably wrong, and the analysis will be, also. That is why even with the most sophisticated software, thinking is still required.

Miner has provided a very thorough analysis here, and I hope this additional clarification is also helpful.
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