Linking Acceptable Quality Levels (AQL) and Average Output Quality

[Cartier]

Hi,

I am currently working on the relation between AQLs and average quality output for the following reason:

AQLs for critical product defects (which render the product non-functional) are often defined at 0.15%, which corresponds to 15 parts per ten thousand. If you are talking about beer cans, if 15 leak every thousand that is a lot of cans leaking.

Suppliers usually say that if you define an AQL of 0.15%, the actual quality of the production is likely to be better than that percentage.

Would you agree with that statement?

If so, how do people link up actual quality output and average quality levels. My contact with suppliers has led me to believe that quite often they themselves do not fully understand the military standard 105.

My understanding is that if you define an AQL of 0.15% and you apply a normal sampling plan using military standard tables, as a buyer you only have a 10% chance that what you purchase is going to be outside of that acceptable quality level. That means there is a 90% chance that your purchase will be within that quality level, but then what is the chance that your quality will exceed that quality level.

On a standard OC curve (from http://iew3.technion.ac.il/sqconline/milstd.php3, aql 0.15%, II 35000-150000). I am interested if anyone knows how I can get a better picture of the probability between p=[0.0 0.0015].

Does anyone know about military standard history or where I can find out about how it was created. I am interested to know whether it was established through extensive testing by the military, or whether it stems from binomial distribution type mathematics.

Owen Cartier

[Charmed]

Dear Cartier:

Here's my $0.01 worth.

You have, I am sure, heard about the normal, or Gaussian, distribution curve. If you test the lifetime of a light bulb, for example, the data, follows the normal distribution. If you test the lifetime of tires, again we will see a normal distribution! That's the marvel of mathematical logic.

We can take the area under the normal distribution curve as a measure of the probability of the occurrence of an event. For the standard normal curve (see textbooks), the total area under the curve is taken as 1. This area can now be divided into two parts. One part of the area is probability of success. Let's say it is 0.85. The probability of failiure, or producing defect, is the other part of the area. This is 1 - 0.85 = 0.15. I picked this because you were talking about 15% defects. Probability of success plus probability of failure equals 1.

Now, how do we find these areas? We make measurements. Let's call each such measurement X. We make a lot of measurements. We get an 'average' or the mean value. Let's call it M. (In statistics books, they call it mu, the Greek letter). Then, we can find the standard deviation. Let's call it S. (They call it sigma, another Greek letter.)

Now, we can go from X, which is called raw score, to what they call Z score. The Z-score is defined as Z = (X - M)/S.

There are tables which give the area under the normal curve, up to the desired Z value. The Z-values go from minus infinity to plus infinity. If Z = 0, X = M, the average value and so on both sides of the mean. Statistical packages (MINITAB) also make these calculations very easy. You can write your own program, using Microsoft Excel, which is what I would do for this purpose. (This also helps me avoid some approximations made in the calculations, commonly carried into statistical packages. This can be avoided now, since we have such awesome computing power in our hands now.)

Once, you get all your measurements, you refer to the tables and find the probability of being outside certain limits (converted to Z values). Hence, we calculate the area between Z = 0 to Z = USL, the Upper Specification Limit, converted to Z using the M and S values. You can also do the area calculations using the library of functions in Microsoft Excel.

You should be able to get actual worked examples in many standard statistics books. The example of lifetime of light bulbs, or tire life (e.g. to offer a warranty of exceeding a certain miles to the customer) is discussed in many books.

Hope this is helpful.

Charmed

P. S. If you have some numbers, please feel free to post them and let's do the calculations here.

[Cartier]

Thanks for your feedback. I understand the normal distribution curve theory, but rather than using numbers to work out probabilities between 0 and 0.0015, I am more interested in the maths behind the actual acceptable quality level tables. Where does all this information come from.

For probabilities between 0 and 0.0015, I am trying to figure out if I set an AQL of 0.15%, what is the probability that my production will have an average output quality of 0.05%?? Is there a way to measure this? Why do suppliers often suggest that this is the case.

[Govind]

Cartier,
See attached.Here is my attempt to explain this by an example. I have made several assumptions due to lack of supporting specification.
Regards,
Govind.

[Tim Folkerts]

Cartier,

Two comments.

1) The relationship between AQL and risk is tenuous at best. I worked out the numbers once for a variety of AQL levels and lot sizes, an discovered that I couldn't find any specific criteron for how the accept/reject numbers were set. Typically, about 95% of the lots are excepted when a) the actual quality of the lot = AQL and b) the lot size is large. When the lot size is smaller, then the lot has to be considerably better than the AQL to be accepted 95% of the time (about 1/3 AQL).

In other words, there is no simple rule and you have to look at the OC curve if you really want to know the odds of accepting lots at any specific quality and for any specified MIL-STD-105E (ASQ Z1.4) sampling plan.


2) The average quality that you accept can only be determined if you know something about the quality coming in. Consider your plan with AQL = 0.15 (=0.15% defective). As an extreme example, suppose that every one of the incoming lots is exactly 0.5% defective. You will reject many of the lots, but you will also accept many of the lots. The quality of the accepted lots will, of course be 0.5% defective in this example, which is much worse that the 0.15% "acceptable" quality level!

Tim F

[brutas]

Originally Posted by Cartier

AQLs for critical product defects (which render the product non-functional) are often defined at 0.15%, which corresponds to 15 parts per ten thousand.

Can anybody explain this to me?
I thought that AQL=0.15% means that your process produces 15 failed devices per 100 units.
Why per 10 000? There is something I am missing...

[Jim Wynne]

Originally Posted by brutas

Can anybody explain this to me?
I thought that AQL=0.15% means that your process produces 15 failed devices per 100 units.
Why per 10 000? There is something I am missing...

You're missing decimal places. 0.15 = 15%, but what's being referred to here is 0.15%. or 15-hundredths of 1%, or .0015.

[thomastang]

from reveiw point of application of Sample Table, it abusolutely exist risk, so we call it "sample" checking.
if apply same AQL in your company and your supplier, whatever, they need agree it.