Why you should ignore the AIAG MSA Guidelines for % Gage R&R, and what to do instead

Contents

• Review of the AIAG Measurement System Analysis Guidelines
• Modeling the Process and Measurement System
• Running Some Scenarios Through The Model

Review of the AIAG MSA Guidelines

From AIAG Measurement Systems Analysis Reference Manual – 3rd Edition
Chapter II Section D Analysis of the Results
“For measurement systems whose purpose is to analyze a process, a general rule of thumb for measurement system acceptability is as follows:
Under 10 percent error – generally considered to be an acceptable measurement system
10 percent to 30 percent error – may be acceptable based upon importance of application, cost of measurement device, cost of repair, etc.
Over 30 percent – considered to be not acceptable – every effort should be made to improve the measurement system
Further, the number of distinct categories (ndc) the process can be divided into by the measurement system ought to be greater than or equal to 5.”

So to summarize the rule of thumb:

1. Less than 10% – Acceptable
2. 10% to 30% – May be acceptable
3. Greater than 30% – Unacceptable

Modeling the Process and Measurement System

The 4 Parts of the Model

2. The process that produces product
3. The specifications I need my product to meet
4. The measuring system

I want to use the most cost-effective way of measuring output from my process. Before I even think about optimizing processes, my initial concern is that if I produce out-of-spec product, my measuring system needs to tell me.

Measurement Error

The process produces each product at a certain size, but I can never exactly know the true size of any particular product. That’s because, I have to use a measuring device to measure the product, and this device will always introduce some amount of measurement error. The measurement error may be so small as to be irrelevant, or it may be large enough to completely mislead me about the state of the product. The danger in a poor measurement system is that it may tell me that a product is within spec., when in fact the product is out of spec, or vice versa.

Process and Specifications

I also have to take into account that the process will not produce every single product at exactly the same size – it will vary from one product to the next. I will try to make sure that most products are produced so that their size equals the center point of the specifications, but there’s no getting away from the fact that I need to deal with a spread of sizes from the process. Let’s look at a couple of extreme cases for the process spread.
Stable, Low Variation Process – Assume that we have a stable process where the spread, or variation, of the products is very small compared to the specification limits. In this case, I have a process that is very cheap to run. I can inspect the product less often because the process can drift way from center, or spread more, before I start producing out-of spec product
High Variation Process – On the other hand, if the output from the process has an output spread wider than the specification limits then this is a very expensive process to run. I have to inspect every product, and if the process moves off center, or the spread becomes even slightly wider, I am producing even more out-of-spec product. This is an expensive process to run, because I need to give it constant attention, not to mention that I am spending more money on rework or scrapping product, or both.
So, process variation is an important part of my model and I’ll be using the normal distribution to model all the variation in this model

Measuring System

Things get even more complicated when we introduce the measuring system, because the measuring system itself has variation. If I use it to measure the same product 3 times and get 3 different measurements, or if myself and my colleague measure the same product and get measurements that disagree, then I need to take this variation into account
Just like process variation, we’ll use the normal distribution to model the measurement variation.

The Mathematical Model

It’s fairly obvious that:

$\scriptsize Observed\ Size = True\ Value\ Size + Measurement\ Error$

Because I’m using the normal distribution to model the variations, the following holds up:

$\scriptsize Observed\ Process \ Variance = True\ Value\ Process \ Variance + Measurement\ System \ Variance$

The observed process is what we see after we have measured the true value process output

Precision To Tolerance Ratio (PTR)
$\scriptsize Precision\ To\ Tolerance\ Ratio = \frac{6\ \times\ Measurement\ System\ Standard Deviation}{Upper\ Spec.\ Limit - Lower \ Spec. \ Limit}$

Observed Process Capability
$\scriptsize Observed\ Process\ Capability - PC_{obs} = \frac{Upper\ Spec.\ Limit - Lower \ Spec. \ Limit}{6\ \times\ Observed\ Process\ Standard \ Deviation}$

6 is used as the multiplier in both these formulas, because for the normal distribution it covers 99.73% of the process. To learn more about the properties of the normal distribution, see the Normal Distribution wikipedia page

True Value Process Capability
$\scriptsize True\ Value\ Process\ Capability - PC_{TV} = \frac{Upper\ Spec.\ Limit - Lower \ Spec. \ Limit}{6\ \times\ True\ Value\ Process\ Standard \ Deviation}$

We cannot measure the standard deviation of the true value process, but we can do a process capability study to determine the observed process capability, and we can conduct a gage r&r study to estimate the standard deviation of the measurement system variation.

If we manipulate the formula we can set up an expression to calculate the true value process capability in terms of known factors – i.e. the observed process capability and the Precision To Tolerance Ratio – as below.

$\scriptsize True\ Value\ Process\ Capability\ -\ PC_{TV} = \frac{PC_{obs}}{\sqrt{1 - {(PC_{obs} \times PTR)}^2}}$

This is the same model that’s derived in Appendix B of the AIAG MSA Manual 3rd Edition

Running Some Scenarios Through The Model

NOTE: You can try all these scenarios yourself by going to my True Process Capability Calculator Page
We can take a “good” process, an “average” process, and a “poor” process and model the impact of using various gages. Selected charts are shown, for process / gage combinations

Observed Process Capability Measurement System Precision To Tolerance Ratio (%)      Business Implications (in terms of the risk of producing out-of-spec. product)
“Good” Process
2.0 10% No action needed – good process, room for drift. The chart below shows how close the lines are
2.0 30% No action needed – still a good process
2.0 49% No action needed – The true value process capability is an incredible 10.31 – I can tolerate loads of process drift, before the true value process gets anywhere near the spec limit. Furthermore, if the process does drift, it’s highly unlikely that the true value of the part will be out of spec.
See the chart below. The blue line is the true value process capability, and the red line is the observed process capability

Process Capability of 2.0 measured by a Gage with GRR of 49% (?? to Tol)

“OK” Process
1.33 10% Not as good as the process above, but OK – Probably no action needed
1.33 30% No action needed
1.33 50% No action needed. The chart below shows the observed process as a red line, and the true value process as a blue line
1.33 70% If no action is needed with a 10% gage, then this is even more true for a 70% gage, because the true process is so good that I am even less likely to produce out-of-spec product.
“Poor” Process
1.0 10% This process is going to require a lot of attention – Any drift and I get out-of-spec product. Spend money on the process. The gage has hardly any impact on process capability. The curves overlap each other on the chart below, so only the blue line is visible
1.0 30% Same as above. Even though my gage is above the AIAG recommended % it doesn’t really matter. My priority for spending money has to be reducing the true value process spread. Even if I improve the gage to 10%, I still have a process problem
1.0 50% Maybe here it’s worth improving the gage, rather than the process, but you would have to answer – What’s the cheapest way to improve this system? – it may be the gage, it may be the process.Chart below.
1.0 70% Improve the gage – The true value of the process looks OK – The true value process capability index is 1.4 (blue line), and the measurement system variation is spreading the variation, so the observed process capability is reduced to 1.0 (red line). If you can improve the gage it will save you a lot of heartache with false measurements