Basis for the Derivation of Inspection Levels (I, II, III & Special)

M

medical_eng

#1
Hi Covers,

There's lots of information on the web and textbooks about AQLs and sample sizes, and lots of tutorials on how to read the Z1.4 charts and what not. Lots of very helpful information in thsi forum as well!

I am assuming that Z1.4 and MIL 105 are fundamentally based on the normal (gaussian) distribution and can be shown visually with an OC curve.

Does anyone have (or can point me to) a ***derivation*** of the basis of the General Inspection Levels I, II, & III, and the Special Inspection Levels. Hopefully it has an historical element to it as well, to show why the charts are the way they are (I am aware that this all started in WWII for military ordinance).

Thanks!
 
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J

Jason Dodds

#2
Hello medical eng,

Go to google and type in "why 7 different inspection levels" and click on the first link that shows up. Hopefully that helps a little.

Kind regards,
Jason D.
 
M

medical_eng

#3
Hi Jason,

Thanks for the reply.

I checked out the web like you suggested, but it just came back with the usual stuff: "Use level one if the supplier has done well, use level three for extra scrutiny, use the 'special' levels when there are only few samples, etc...". It's all the same explanations everywhere, as if everyone cross-copied each other. :frust:

What I am after is the mathematical calculations, and why the sample sizes ended up at the numbers that they are. Someone, somewhere had figured this all out and made up the charts. How did they do it?

Anyone else?

Thanks again in advance! :)
 

Jim Wynne

Staff member
Admin
#4
Hi Covers,

There's lots of information on the web and textbooks about AQLs and sample sizes, and lots of tutorials on how to read the Z1.4 charts and what not. Lots of very helpful information in thsi forum as well!

I am assuming that Z1.4 and MIL 105 are fundamentally based on the normal (gaussian) distribution and can be shown visually with an OC curve.

Does anyone have (or can point me to) a ***derivation*** of the basis of the General Inspection Levels I, II, & III, and the Special Inspection Levels. Hopefully it has an historical element to it as well, to show why the charts are the way they are (I am aware that this all started in WWII for military ordinance).

Thanks!
It's not clear whether you're looking for the mathematical basis of sampling plans themselves or the derivation of the differences between the various levels (e.g., when to use I and when to use II.) If it's the former you want, there's some good information here: Modern Acceptance Sampling. If it's the latter, I can't help, but my guess is that there is arbitrariness involved.
 
M

medical_eng

#5
Hi Jim,

Thanks for the reply, I'm more interested in the latter. I know about OQ curves. I'm interested in how they came up with the whole MIL105/Z1.4 given the ordinance history. Then, I'd like to see exactly the distinction between the different levels and how they compare/contrast for actual numerical probabilities and confidence levels (something more precise than terms like "extra scrutiny" or "few samples"). If there were arbitrary lines drawn in the sand for certain aspects, it'd be interesting to know that too.

I was hoping not to have to reinvent the wheel by attempting the derivations myself, if it already exists somewhere.

Thanks again!
 

Jim Wynne

Staff member
Admin
#6
Hi Jim,

Thanks for the reply, I'm more interested in the latter. I know about OQ curves. I'm interested in how they came up with the whole MIL105/Z1.4 given the ordinance history. Then, I'd like to see exactly the distinction between the different levels and how they compare/contrast for actual numerical probabilities and confidence levels (something more precise than terms like "extra scrutiny" or "few samples"). If there were arbitrary lines drawn in the sand for certain aspects, it'd be interesting to know that too.

I was hoping not to have to reinvent the wheel by attempting the derivations myself, if it already exists somewhere.

Thanks again!
It could be tough to find a copy, but there's this book that seems to have come from the horse's mouth.
 
B

Barbara B

#9
In another book

Wetherill, G. [1969]: Sampling Inspection and Quality Control
Methuen & Co, London, ISBN 978-0416128604

the theory of AQL, LTPD and continous sampling plans are described in a quite good manner and references of the origins of the methods used are given. Unfortunately it does not provide itself any information about the maths behind the inspection levels.

But there is a paper mentioned written by Hill in 1962. It is stated that in this paper pros and cons as well as theoretical aspects of inspection levels and other concepts concerning AQL:

Hill, I.D. [1962]: Sampling inspection and defence specification DEF-131.
Journal of the Royal Statistical Society, B, 28, p381-416

I'm planning to do a little bit of research on this topic in the college library in the next weeks and will try to find more informations about inspection levels. I'll keep you posted.

Best regards,

Barbara
 
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