### Contents

- Review of the AIAG Measurement System Analysis Guidelines
- Modeling the Process and Measurement System
- Running Some Scenarios Through The Model
- What to do instead

### Review of the AIAG MSA Guidelines

Let’s start with a review of the 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:

- Less than 10% – Acceptable
- 10% to 30% – May be acceptable
- Greater than 30% – Unacceptable

### Modeling the Process and Measurement System

The 4 Parts of the Model

- My Business Objectives
- The process that produces product
- The specifications I need my product to meet
- The measuring system

#### Business Objectives

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:

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

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

##### Precision To Tolerance Ratio (PTR)

##### Observed Process Capability

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

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.

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

### What To Do Instead

The first thing you need to do is to get a picture of your process by using my True Process Capability Calculator.

Next, decide if you need to do anything at all. We all want to improve our processes, but we don’t have unlimited money, so we have to prioritize where the money gets spent. Just because a gage has a 30% Precision To Tolerance Ratio, doesn’t mean it’s no good for the process. It depends on the process. In fact, spending your money should really depend on what return you’ll get, not a % Precision To Tolerance Ratio.

If you do need to do something, you’ll need to weigh up the most cost-effective option. This may be improving the process, it may be improving the gaging, or both. But, again I’ll emphasize that a lot of things will go into this decision, and it’s not as simple as throwing out the gaging system based on some arbitrary percentage value.

#### High Gage R&R Percentages and Handling Customers and Auditors

For most people, if you can provide a sensible rationale for doing what you did, they are satisfied. With that in mind, print off the True Process Capability Calculator, write your reasoning onto the page, and shove it into your Gage R&R file – Most people are pleasantly surprised at how big gage variation can be before it starts to have a major impact on classifying product. This is especially true if you are running reasonably stable processes.