# Question about sample size code letter and selecting sampling plan

W

#### wjylzm

Hi guys,

1.code letter and sample size

What's the principle when setting down sample size series (2,3,5,8,13...

2000)？I looked up some references and found sample size and AQL come

from a E5 preferred number series(Pls see attachment).So sample size is

determined before code letter(i mean that when designing the master

table),isn't it?

2.sampling plan searching

code letter N,AQL=6.5 GIL=Ⅱ

we can get a sample plan: (200,21,22)

can this plan meet the requirents of the lot size N(35,001-150,000),such as α

risk,why?

Thanks!

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V

#### Viktorko77

Hi,

Can't help on yr first question, for E5 is all Greek to me, yet my inputs on the second one may be of use.

According to MIL-STD-105E (I've never seen it's ANSI counterpart, but believe that grafic and tabulated data are same for both of them) it goes like this:
For lots over 35k the code letter is indeed N (n = 500 pcs). However, there is no data in 105E for Letter N @AQL 6.50. Instead, the standard recommends to use letter L, which is n=200 (Ac 21, Re 22) - see Table IIA.

Now what that gives you in terms of actual risks?
If you refer to Tables X-L of the 105E, which give both grafic and tabulated values for alpha and beta, you'll see that:
(a) for lots to be accepted in 95% cases (alpha 5%) the average defects percentage limit is 7.45% (i.e. lots having 7.45% non-conformant items will be accepted in 95% cases)
(b) for lots to be rejected in 90% cases (beta 10%) the defects percentage is 14.1%
(c) for beta 5% defects percentage limit is 15.1%

So it depends on which side of the barricade you stand. If you are supplier just wanting to pass an inspection, you can be pretty safe with n=200 (21,22).
If you are a client, or a supplier willing to keep the customer happy you better reduce AQL to, say, 4% (it will increase sample size to 315, so to stay within the QC-related budget you may want to use double sampling plan rather than single one).

Cutting the story short, it all depends on yr actual situation and if you give more specifics, I'm sure guru Covers will be happy to help you).

Regards,
Victor

PS: you may try to play with on-line calculator, which is a useful instrument. It even plots OC curves for selected sampling plans/AQLs (though, discrimination of their curves leaves much to be desired) .

http://www.sqconline.com/mil-std-105.html

#### CarolX

Trusted Information Resource
Victor,

Thanks for a great response and welcome to the Cove.

I, too, do not know what E5 is, but wjylzm is a student, according to their profile. This may be something that was given in class and not something familiar to us.

MIL-STD-105 was replaced by ANSI AQSC Z1.4-1993. The two are virtually identical.

#### Tim Folkerts

Trusted Information Resource
Hi guys,

1.code letter and sample size
What's the principle when setting down sample size series (2,3,5,8,13...
2000)？

I looked up some references and found sample size and AQL come from a E5 preferred number series(Pls see attachment).
I hadn't specifically noticed this property before, but it makes sense. You want the choices of sample size or AQL "evenly spaced" to give you the widest possible choices. But there are two ways to have numbers "evenly spaced".
• the difference between two consecutive numbers can be constant. For example, the sample sizes could each be 100 larger that the previous size (100, 200, 300, ... 2000). But for practical purposes, the difference between 1900 and 2000 is not that significant, and having 100 as the smallest sample size is ineffective.
• the ratio between two consecutive numbers can be constant. When you want both big numbers (like 2000) and small numbers (like 2), this can be a very effective approach. In this case, each number is apporximately 1.6x larger than the last. Or if you use a semi-log plot (not a log-log plot) you will get a straight line.
This same sort of result is seen in many situations, where smaller step sizes are seen for small items. For example, I just noticed that wire gauges are each about 1.12x larger diameter than the last. This takes 20 steps to become 10x larger (as opposed to 5 steps for the Z1.4 sample size to become 10x larger).

For your second question, I think Viktor gave an excellent answer. One small additional note is that the lot size has little to do with the risks involved. A random sample of 200 peices from a lot of 1000 or 100,000 or 10,000,000 will all have about he same risks that Viktor pointed out from the tables in Z1.4. (If the lot is small - like 250 or 300 - and you still draw 200, then the risks do go down significantly.)

Tim F

W

#### wjylzm

Hi,

Can't help on yr first question, for E5 is all Greek to me, yet my inputs on the second one may be of use.

According to MIL-STD-105E (I've never seen it's ANSI counterpart, but believe that grafic and tabulated data are same for both of them) it goes like this:
For lots over 35k the code letter is indeed N (n = 500 pcs). However, there is no data in 105E for Letter N @AQL 6.50. Instead, the standard recommends to use letter L, which is n=200 (Ac 21, Re 22) - see Table IIA.

Now what that gives you in terms of actual risks?
If you refer to Tables X-L of the 105E, which give both grafic and tabulated values for alpha and beta, you'll see that:
(a) for lots to be accepted in 95% cases (alpha 5%) the average defects percentage limit is 7.45% (i.e. lots having 7.45% non-conformant items will be accepted in 95% cases)
(b) for lots to be rejected in 90% cases (beta 10%) the defects percentage is 14.1%
(c) for beta 5% defects percentage limit is 15.1%

So it depends on which side of the barricade you stand. If you are supplier just wanting to pass an inspection, you can be pretty safe with n=200 (21,22).
If you are a client, or a supplier willing to keep the customer happy you better reduce AQL to, say, 4% (it will increase sample size to 315, so to stay within the QC-related budget you may want to use double sampling plan rather than single one).

Cutting the story short, it all depends on yr actual situation and if you give more specifics, I'm sure guru Covers will be happy to help you).

Regards,
Victor

PS: you may try to play with on-line calculator, which is a useful instrument. It even plots OC curves for selected sampling plans/AQLs (though, discrimination of their curves leaves much to be desired) .

http://www.sqconline.com/mil-std-105.html
Thank you all for the excellent reply.
Victor.Sorry for not giving more details.I'm from China and I get "E5" from chinese books.It's a common ratio of a preffered number series,10^(1/5),and there are some other common ratioes such as 10^(1/10),10^(1/20) etc.Thanks Tim gives the detailed explaination.

The question is that I'm not very clear about why there is no data in 105E for Letter N @AQL 6.50. not economic?not need to inspect 500 pcs @AQL 6.5?What's the priciple when designing the table?

Best regards,

Li Yongjie

Last edited by a moderator:
V

#### Viktorko77

Li Yongjie, ni hao. (sorry, don't have the software to type Chinese characters)

As for lack of data for Letter N for AQL 6.50, I once came to the same question. And as my interest in the subject is merely practical one, so I never bothered to look for an answer. Hence, I can have only uneducated guesses:

You are probably right: it's not feasible to test large amount of samples for such pretty lax AQL (Iwould point my supplier to the door the moment he suggests to use AQL 6.5 even for minor defects). If you look at the master table of 105E (Table IIA) you'll see the trend - the bigger AQL number, the less amount of drawn samples.

And there seems to be 2 reasons behind that (actually they are 2 sides of the same coin):
(a) as Tim said, it'll hardly give you any additional safety;
(b) it'd be just impractical economically.
Being based on hard statistics, MIL STD is actually pursuing down-to-earth approach, and targeted to ensure sufficient results at lowest possible cost (it was first launched somewhen between two Big Wars - God damn those politicians! - to test quality of bullets batches). One of the downsides of this "practicality" is that it can be used as reference source only by those who have basic (at least) knowledge of prinicples it was designed around. In other words, you have to know pretty much to use its data (for any purpose). And to use it in the field, one at least should be a "trained monkey". I personally used Defence Personnel Support Centre Manual (DPSCM 4155.18) for my monkey-training. It's a useful source, but if you want to be a "nei hang" (is it correct Chinese for "expert" ?) in statistical QC, you better do with some good book(s) on the subject (surf the Cove, I'm sure you'll find a lot of recommendations).

Rgds,
Victor

W

#### wjylzm

Victor,

It seems you have often been in contact with Chinese.Your mandarin is very well.

Best regards,

Li Yongjie

W

#### wjylzm

Hi,guys
There is another question about lot size.what are the range of lot size determined by?I don't know how does the sample size correspond to the lot size?
Thanks!

best regards,

LYJ

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