# What Theory is MIL-STD-105E Sample Size Code Letters Based on?

#### Chloe

##### Registered
Hi all,

I am new to this forum.

I am studying literature about sampling acceptance and knowing that sample size can be calculated by cumulative binomial formula, AQL, alpha, LTPD, beta, and Larson’s binomial nomograph.
However, I can not find literature that explain the theory of the sample size code letters in MIL-STD-105E or talk about how to calculate the sample size based on the lot size.

Does any one know the related theory or how American military developed the sample size code letters in MIL-STD-105E?

#### Bev D

##### Heretical Statistician
Super Moderator
The Sample plans based on lot size and hte accompanying code letters are the result of negotiation. There is no real basis in statistics for them.
There are some formulas that can of course adjust for lot sizes but they make very little difference for ‘large’ lots. Any connection between them and MIL-STD 105 (and it’s descendants) is imaginary.

At very small lot sizes the Hypergeometric distribution is appropriate. Moderate lot sizes can use the Binomial and the Poisson distribution will be close enough for other sample size calculations. You will note when you look a the Binomial and the Poisson that lot size does’t enter into the calculations at all.

Please also note that the truly important things about any sampling plan are the Rejectable Quality limit (not the AQL) and the randomness of the sampling.

In general, single sample sampling plans are not very effective. The assumptions that are required to make the theory work do not happen in real life. Modern quality practices involve moving beyond them to prevention and control. I do suggest reading the works of Donald Wheeler - as a start - to your studies.

#### Chloe

##### Registered

We have some technical and cost concerning to follow the ideal quality control system.
Thus, we survey literature about quality control and try to develop a suitable quality control system which may be more effective than our present one.
Could you recommend one book by Donald Wheeler?
I'm now reading "Introduction to Statistical Quality Control" by Douglas C. Montgomery and "Acceptance Sampling in Quality Control" by Edward G. Schilling and Dean V. Neubauer.
I have not finished my reading yet.

The Sample plans based on lot size and hte accompanying code letters are the result of negotiation. There is no real basis in statistics for them.
There are some formulas that can of course adjust for lot sizes but they make very little difference for ‘large’ lots. Any connection between them and MIL-STD 105 (and it’s descendants) is imaginary.

At very small lot sizes the Hypergeometric distribution is appropriate. Moderate lot sizes can use the Binomial and the Poisson distribution will be close enough for other sample size calculations. You will note when you look a the Binomial and the Poisson that lot size does’t enter into the calculations at all.

Please also note that the truly important things about any sampling plan are the Rejectable Quality limit (not the AQL) and the randomness of the sampling.

In general, single sample sampling plans are not very effective. The assumptions that are required to make the theory work do not happen in real life. Modern quality practices involve moving beyond them to prevention and control. I do suggest reading the works of Donald Wheeler - as a start - to your studies.

#### Bev D

##### Heretical Statistician
Super Moderator
You can start by reading these articles by Donald Wheeler: The Truth About Acceptance Sampling Part 1 and Part 2

I also highly recommend "Also Known as Sam Poisson" by John Heldt. It's an older book but is still available for sale. It is written for the layman and I found it much more understandable than the books you reference (Which I have read, but they made more sense after I read the Poisson book )

You may also find the attached spreadsheet helpful in playing with different sampling plans (the math has already been vetted and validated). It contains references to all approaches...

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