# Designing a Mil-Std-105 or ANSI/ASQ Z1.4 Sampling Plan

I

#### ivan99

AQL vs Six Sigma

Can someone do the math fast:
I am inspecting lots of 1200 parts, using an AQL of 1.00 at c=0, how does that relate to Six Sigma? To reverse this:
If I want my supplier to be at 3 or 4 Sigma level, what AQL should I use?

J

#### J-Excel

Six Sigma really can't be inspected in. Is your lot size 1200 or sample size 1200?

If your sample size is 1200 (not lot size), and you accept on 0 you will accept lots that are 0.004% defective 95% of the time (AQL) and you will reject lots that are 0.192% defective 90% of the time (LTPD). Your probability of accepting a 3 sigma quality lot is 0.000%. Your proobability of accepting a 4 sigma quality lot is 0.057%. Your probability of accepting a 5 sigma quality lot is 75.606%. And your probability of accepting a 6 sigma quality lot is 99.593%.

If your lot size is 1200 and you are shooting for 3 sigma to 4 sigma quality a sampling plan of n=57, c=1 would work. That would set your LTPD to 66800 dPPM (3 sigma) and AQL to 6210 dPPM (4 sigma). If you want to see what your OC Curve would look like you can plot these numbers in a scatter diagram:
Pd(x) Pa
0.1% 99.8%
0.5% 96.7%
1.0% 88.9%
1.5% 78.9%
2.0% 68.4%
2.5% 58.1%
3.0% 48.7%
3.5% 40.3%
4.0% 32.9%
4.5% 26.7%
5.0% 21.5%
5.5% 17.2%
6.0% 13.6%
6.5% 10.8%
7.0% 8.5%
7.5% 6.6%
8.0% 5.1%
8.5% 4.0%
9.0% 3.1%
9.5% 2.4%
10.0% 1.8%

Assuming I did my math correctly.

D

#### dfevans

I see that this post was started in 2001 but it brings up some inportant points:

1. How much/many defects can your customer stand? Really a basic question but has implications, namely that a certain customer base will stand a lot more defects where as others Military/automotive/aerospace/nuclear...etc can stand very little if at all. Based on what your customer base requires then you need to determine your risks and costs of rejected a good lot. There is more in this than I can go into here...but I think you get the idea.

2. And this most important to consider - At any AQL or AOQL or LTPD and with proper sampling, you are guaranteeing that you will send out bad product. This is built into the any plan. A sample plan is based on probability as one poster has shown mathmatically. Can you and your customer afford to have ANY reject? If not then you need to make your process robust or relatively impervious to outside influence, next, insure that the raw material coming in is defect free (not imposible - except for rogue units, etc). Of course, you also will have some rogue product but once discovered can be anticipated (usually they occure in cycles).

And last (for this post) is that we (quality professionals) are in the middle of a 6-sigma quality cycle where we talk about DPPM as less then one and Ppk's greater then 2 (accounting for long term shift of 1.5 sigma).

So how much risk can you and you customer stand?

Q

#### qualitytrec

Along with this does anyone have a DOC or XLS form they would be willing to share as an example/useful tool for those of us trying to better establish this system in our own facilities? By the way thanks for the many helpful link this was a very useful thread for me.

D

#### dfevans

Doesn't really answer the observation other than a simple "use the ANSI tables."

Refer to AS9101 - No defect will knowingly be sent to the customer. I have received a CAR from my AS registrar on doing the sample plans. I had to go to 100% inspection on incoming parts for the AS program.

NOTE: All sample plans have a built in defect level.

#### Al Rosen

Staff member
Super Moderator
Doesn't really answer the observation other than a simple "use the ANSI tables."

Refer to AS9101 - No defect will knowingly be sent to the customer. I have received a CAR from my AS registrar on doing the sample plans. I had to go to 100% inspection on incoming parts for the AS program.

NOTE: All sample plans have a built in defect level.
You may be able to approach it another way.

If you reject a lot using Z1.4, you may opt to screen it 100%, other lots are accepted without 100% inspection. This may not be acceptable for everything, but certainly for parts, if nonconforming, that would be caught later on in the process. It depends on the level of risk. You will not knowingly send defects to the customer.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Doesn't really answer the observation other than a simple "use the ANSI tables."

Refer to AS9101 - No defect will knowingly be sent to the customer. I have received a CAR from my AS registrar on doing the sample plans. I had to go to 100% inspection on incoming parts for the AS program.

NOTE: All sample plans have a built in defect level.
100% inspection gives you no more assurance than a sampling plan that NO defect will be sent to the customer. The key word is knowingly...which the registrar implies to mean 100% inspection, I doubt that is the intention of that word.

#### v9991

Trusted
Need help on how to determine:
1) AQL
2) Producer’s risk
3) LTPD
4) Consumer’s risk
Supposing this is a new product.
unless i have rushed thru the contents or missed to read the specific points; ....
i think i did not see definitive answer to this question, beyond the definition and options;

we are trying to figure out a risk based approach to determine it viz.,
LTPD & Producer's risk vs process capability
AQL / consumer's risk with criticality of the feature.
any help or reference is highly appreciated.

further, i have one another question, is it OK to inspect different sample-size for different quality-characteristics., viz.,
1. parameters achieved by design and higher process-capability :- to allow higher consumer risk; hence smaller sample size
2. apart from criticailtiy, parameters achieved through process-control and/or to be established process-capability :- to assign lower consumer risk, hence higher sample size.

#### v9991

Trusted
Johnny,

Complete answers to your questions go beyond the scope of answers from the Cove I think. Some of these questions can only be answered by your organization and the customer. What do you/they want/need? Please take the time to read MIL-STD-105 or ANSI Z1.4 and you should have many of your questions answered by doing so (definitions are in there). Then, if you have a specific question write back.

BTW -- Most electrical components/products companies I have worked with use "single normal" sampling plans, General Inspection Level II. This may or may not work for you.
it can be seen at three levels at the least. 1. definition(directional), 2. criteria (indicative) 3. mathematical / decision tree ( definitive)

so, request and look forward for certain inputs on criteria or decision tree to arrive at determining AQL levels.
viz.,how does the following approach sounds in determining an decision tree..
for a given scenario where components/materials are received for assembly,
alpha - the process capability levels ( again dependent on the consumer's risk)
LTPD - consumer's process capability or tolerance of the defects/rate
consumer's risk - business decision of sensitivity / criticality.