Sampling Plans - Inspection Levels I, II, III - I'm looking at ANSI/ASQ Z1.4-2003

S

Shasta Ell

#1
I'm looking at ANSI/ASQ Z1.4-2003 (sampling procedures for attributes), and in 9.2 Inspection Level, it says "Three inspection levels: I-III are given for general use. Unless otherwise specified, Level II will be used. Level I may be specified when less discrimination is needed, or III may be specified for greater discrimination."

When is this used? It makes sense to me that you would use one level of general, and then switch between tightened and reduced inspection, but the logic of having levels within General inspection levels is not clear to me. This would change the probability of finding defects but how much?
 
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J

Jeff Frost

#2
One way to look at the levels is as follows

Level I (Reduced Inspection) is implemented when it is evident that quality is running unusually well.

Level II (Normal Inspection) is used at the start of inspection when there is no evidence related to the quality of product being inspected.

Level III (Tighten Inspection) is used when it is evident that quality of the product is deteriorating.

I do not have a full copy of Z1.4 on hand but check the rules for switching inspection levels as this will indicate when you would make the switch from Level II.
 

Tim Folkerts

Super Moderator
#3
I've never been able to determine why Z1.4 is in use. There is (to my mind) little correlation between the sampling plans and any sort of rational thought.

First of all, the nomenclature seems to confuse people. Level II is considered standard, but it is not the same as "normal inspection". Level I reduces the sample size, but it is not the same as "reduced inspection." Level II Reduced Inspection is roughly (but certainly not exactly) the same as Level I Normal Inspection. And so on....

Your question "This would change the probability of finding defects but how much?" highlights another major problem. There is no specific connection between between sampling plans any statistical rationale. It would be logical to have some criterion like "Level II inspection has at least a 95% chance of accepting a lot that meets the nominal quality level", but there is no such consistancy. Likewise it would be logical to be able to relate normal, tighten and reduced to odds of rejecting bad lots, but that is also not the case.

The only real way to get a grip on just what the different plans means is to look in the back of the booklet at the OC curves.


:soap: With computers on every desk, it seems so archaic to have a set of tables as the standard. It would be so easy to generate a plan based on your own criteria! Just pick your parameters (like 95% chance of accepting 1% defects and 95% chance of rejecting 5% defects out of a batch of 12,000 pieces) and let the computer tell you the proper plan.

Tim F
 
B

Barbara B

#4
Hi,

does anybody know where the different levels come from and when they were developed (and additionally who was responsible for that stuff)?

I do not use them (my PC does this work better), I'm just curious :)

Barbara
 
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Tim Folkerts

Super Moderator
#6
As for the origin, the Z1.4 plan is an almost exact copy of the US Military standard MIL-STD-105 which dates back to 1950.

Level II is considered "standard" or "typical". Level I takes a smaller sample. I believe the general effect is to maintain a relatively constant producer's risk (i.e. odds of rejecting a good lot) while increasing the consumer's risk (i.e. the odds of accepting a bad lot). Level III is the reverse - a bigger sample which decreases the consumer's risk (i.e. there is an improved chance of catching a poor lot).

Let's try an example: AQL = 1, lot size = 2000. You get shipments - a "good" lot with 1% defective and a "bad" lot with 5% defective



For the good lot (using Excel):

....Tightened.....Normal......Reduced
I...81.1%..........91.3%......81.7%,..98.4%
II..87.5%..........96.8%......91.3%,.100.0%
III..86.6%.........98.9%......95.7%,.100.0%

For the bad lot:

....Tightened.....Normal......Reduced
I....8.2%..........27.6%......35.7%,..73.6%
II...4.3%..........11.6%......27.6%,..96.4%
III..0.7%...........5.3%......22.5%,..79.3%


There are two numbers for reduced inspection. The second is the odds of acceptance overall (with some chance of going to normal inspection). The first is the odds of outright acceptance. So the difference is the odds of going to normal inspection.


So, the good lot will accepted
* about 85% of the time on tightened inspection (for any Level)
* about 95% of the time on normal inspection
* about 99% of the time on reduced

On the other hand, the odds of rejecting the bad lot show more variation. The odds of rejecting the bad lot (i.e. 1- the odds of accepting the bad lot) improve considerably as you switch from Level I to Level II to Level III. They also improve considerably as you go from reduced to normal to tightened.

The specific percentages won't hold for other AQL's or orther lot sizes, but I expect the general trends will hold.


Tim F
 
B

Barbara B

#7
Thanks a lot for your detailed answer, Tim!

Do you have additional informations about the initial calculationg scheme used to make those tables? I hope they used a scheme and do not simply thrown dices... ;)

Barbara
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
The original scheme used the binomial distribution (? maybe the hypergeometric as lot size is involved) and involved calculating various percentages as Tim did. Hence huge tables and lots of curves.

There was a method but we must remember it was the late forties an dearly fifties before widespread us of the computer...

The key is that the standard was innovative for it's time but it is very confusing in it's terminology and there are better ways to develop sampling plans now that we have computers...
 
D

Dave Strouse

#9
Discrimination - easy way to think of it.

Tim Wrote -
Level II is considered "standard" or "typical". Level I takes a smaller sample. I believe the general effect is to maintain a relatively constant producer's risk (i.e. odds of rejecting a good lot) while increasing the consumer's risk (i.e. the odds of accepting a bad lot). Level III is the reverse - a bigger sample which decreases the consumer's risk (i.e. there is an improved chance of catching a poor lot).

Kind of, but the concept of discrimination is more to the effect of being able to tell a good lot from a bad, which is close to what you wrote. I like to think of it in the limit, if you will, however.

A "perfect" acceptance sampling plan would be a step function. So in your example, all lots with 0.99999... per cent defective or less at AQL 1% would be accepted and all with 1.000000....1 or more would be rejected.

Level one has more discrimination, level three less. The switching rules are an entirely separate issue.

In the past I've played around with this and found a plan with something like 1500 as sample size and accept on 200 gives a pretty close approximation around 1%. (I'll try to find my old file or recreate it.) However, it is of course a ridiculous plan for any practical purpose. Try to tell your operations manager you want to do that plan to be absolutely sure you accept all good lots and reject all bad!

It would be advisable to have the resume up to date, however.
 

Tim Folkerts

Super Moderator
#10
Personally, I'd like to see the current system scrapped and a new system implement, based on simple, specific statistics. With computers on every desk that can perform the calculations faster than you can look it up in a table, it would be a simple matter to generate a plan to meet any specifications.

To my mind, the simplest solution is to specify the alpha value (producer's risk) at a specific defect level (aka AQL) and the beta value (consumer's risk) at some higher level (aka RQL = reject quality level). You would also have to specify a lot size and whether you want single, double, or mulitple sampling. Tell the computer the parameters you want and out pops a sampling plan!

That is probably more flexibility than some people want, but some standardization could be employed. For example:
* sample sizes could be restricted to the values currently on the tables (2,3,5,8,13...). (For the mathematicians in the crowd, I just noticed that these numbers almost follow the Fibonnaci sequence. They also approximately follow the rule that the next number is about 1.6 x the previous number.)
* "Normal" could mean alpha & beta < 5%
* "Level II" could mean RQL = 5 x AQL

I have a feeling that most people would be surprised how big of a sample they would need to acheive the level of accuracy they desire.

It would probably be good to use new terminology to avoid confusion with the old plan, but you get the idea. Of course, the details would have to be worked out by some overpaid committee (Pick me! Pick me! Pick me! ;) )


Tim F
 
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