# Use of sampling plans like MIL-STD-105 E or ANSI Z1.4?

#### AndyN

##### Moved On
O.K - here's some background, then my question(s)

I inherited, many years ago, the Receiving Function. A predecessor had set an AQL on all incoming parts at 0.4%, so on a (usual) lot size of 151 - 280 (letter 'G') we sampled 32, accepted 0 defectives and rejected on 1 defective found. I'm cool with the use of the tables!

I could never get a satisfactory answer on why a 0.4% AQL was chosen and it has bugged me ever since (well, maybe once a year when I indulge in some deja vu of my enjoyable worklife experiences!!)

If I read table X-H-1, on page 46 of the ANSI Z1.4 (1993) doc, I need to reconcile my expected percentage of lots to be accepted 'Pa', with the 'p' value (% non-conforming) of submitted product, to derive my AQL, I think.

So, if I expect that 99% of received product is conforming, then I choose an AQL of 4.0%, and follow the acceptance/rejection rules from table II A (page 12) - I'm actually (statistically) likely to 'see' 3.69% defectives (from estimating on the curve or reading off the table)

Did I get the rationale correct? If so, was it simply a guestimate if the originator of the 0.4% AQL if they couldn't explain what the 'Pa' value was or the impact (risk of the 'p' value), either?

Or am I hosed in my understanding?

#### AndyN

##### Moved On
Anyone? This is a commonly used standard employed in Receiving Inspection etc. So, there must be a lot of experience out there......

#### Tim Folkerts

Super Moderator
Later today I will have a little more time, but I think you are looking at the numbers backwards.

In Table H for AQL 4, the row for PA = probability of accepting corresponds to p = defect rate = 3.69.

If the defect rate is indeed 3.69, then there is a 99% chance of accepting the lot. In other words, when the defect rate is close to the AQL, then you will almost always accept the lot. This is pretty much the definition of AQL, although the exact odds of accepting a lot where the (defect rate) = (AQL) varies - depending on the inspection level & sample size.

Tim F

#### AndyN

##### Moved On
Aha! Indeed, then we need to talk. This has been bugging me over nearly 20 years! I know/knew that something wasn't correct with the 'selection' of an AQL, but I may not yet have all the info as to why!

Where were you, back in 1985!

#### AndyN

##### Moved On
So, does anyone have anything further to add? Any practical examples of application of this table to the Receiving Inspection function? A 'Dummies Guide to ANSI 1.4'?

There must be someone who's applied this tool to a similar situation!