The question asks about sampling plans and AQL

N

Nick Martinez

#1
Hi there-

I am working on a IVD disposable for which there is a categorical (pass / fail) test. I have looked at the standard sampling plans for relatively tight acceptable quality limits, and I find the output results to be slightly odd: the sample size doesn't go over a large range of lot sizes. For example, for a 0.1% AQL, for a 100 piece lot, I need to 100% test. For 1000, I test 125, for 10000, I test 125. I am not a stats expert, but this doesn't seem right to me. Surely the percentage sampled should decline as lot sizes grow, but I would imagine a 10,000 part lot should require more parts tested than 1000.

Is there a different methodology y'all could recommend that is defensible from a regulatory perspective but also contains more logically sound sampling frequency?

Thanks for your help,
Nick
 
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John Predmore

Trusted Information Resource
#2
The question [was originally] titled Statistical Process Control. But the question asks about sampling plans and AQL. They do not have the same objective. SPC uses data from a time ordered samples to detect trends or special causes affecting the process average in a stream of parts from a manufacturing process. Conventional SPC does not use part acceptance limits and does not judge part acceptance directly. One advantage of SPC is when it reacts to signals in the data before out-of-limits parts are produced.

Acceptance sampling uses random samples of a (presumably) homogeneous lot of parts already made. Acceptance sampling does not give direct process feedback, except in hindsight, in macroscopic terms (this lot of 10,000 widgets is rejected). Even if all lots have the same % non-conforming, sampling will accept some lots and reject others, and the rejected lots will be no different from the accepted. Acceptance sampling is justified only in comparison with 100% inspection, which is always more expensive.

The size of the samples in a sampling plan was questioned by the OP. The statistics involved in acceptance sampling is complex, even for people who are stats experts. It is beyond my capability to boil down a couple chapters of my stats book into a few paragraphs here. But acceptance sampling has been in wide use for 100 years, was popularized in Military Standard plans, and is indeed defensible from a regulatory perspective, as long as the objective is clear and plans are performed correctly.
 
Last edited:

Bev D

Heretical Statistician
Leader
Super Moderator
#5
I am working on a IVD disposable for which there is a categorical (pass / fail) test. I have looked at the standard sampling plans for relatively tight acceptable quality limits, and I find the output results to be slightly odd: the sample size doesn't go over a large range of lot sizes. For example, for a 0.1% AQL, for a 100 piece lot, I need to 100% test. For 1000, I test 125, for 10000, I test 125. I am not a stats expert, but this doesn't seem right to me. Surely the percentage sampled should decline as lot sizes grow, but I would imagine a 10,000 part lot should require more parts tested than 1000.

Is there a different methodology y'all could recommend that is defensible from a regulatory perspective but also contains more logically sound sampling frequency?


Nick
It sounds like you are asking about an inspection plan to accept or reject a lot? can you confirm this?
if so, what you are seeing in the inspection tables is 'correct' and is generally accepted in industry as beign statistically sound. (note: soem reviewers/stats groups in the medical/pharmacy industry do not accept it so your situation may be differnt.)

The tables are result of both sound statistics and 'negotiation.

The sound statistics is that a set sample size is far more effective than a percentage sample plan. The math is a bit complicated and is covered in any decent quality control text book.

The negotiation is having various sample sizes based on lot size. This was a compromise for the convenience of manufacturers. lot size (and population size in general) is irrelevant to the effectiveness of the sample size. the critical factor for sample size effectivenness is the standard deviation of the lot (and population). For categorical data the standard deviation is directly related to the defect rate.

There are other approaches to sample size calculations that are statistically purer than the AQL tables...you might find the attached spreadsheet helpful...
 

Attachments

Mike S.

Happy to be Alive
Trusted Information Resource
#6
Hi Nick,

Mathematically sound statistical and sampling theory often appears counter-intuitive and illogical -- at least to me. If you are working off of published and accepted sampling plans like MIL-STD-105 / ANSI Z1.4 etc. you can be sure the calculations are correct.

What the results of the sampling actually means is a whole 'nother issue.....
 
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