ANSI/ASQ tables (Z1.4) / OC Curves - Percent accepted, how'd I do?

[paperclip]

I used the ANSI/ASQ tables (Z1.4) to inspect lots that had quantities of 151 units to 500 units. AQL was .40 (point four zero) and used single normal, G 2.

The number of samples worked out to 32. Per the OC curves, how high a probability of accepting lots? The way I read the curves, it's about 99 percent. Am I right? If not, what is the percentage of lots expected to be accepted?

Thanks!

 

[howste]

Re: Percent accepted, how'd I do?

That depends on the actual percent defective in the lot. If there are zero defectives, then the chance of acceptance should be 100% If the lot has 100% defectives, then the probability would drop to 0% The rest would fall somewhere in between. Look at the Operating Characteristic (OC) curves and they will show the probability of acceptance with a given % defective.

 

[howste]

Re: Percent accepted, how'd I do?

It probably would be more helpful if I gave some examples:
There would be a 99% probability of accepting a lot with .0314% nonconforming.
There would be a 95% probability of accepting a lot with .160% nonconforming.
There would be a 50% probability of accepting a lot with 2.14% nonconforming.
There would be a 10% probability of accepting a lot with 6.94% nonconforming.
There would be a 1% probability of accepting a lot with 13.4% nonconforming.

 

[paperclip]

Re: Percent accepted, how'd I do?

I'm sort of getting it. Does that mean that accepting a lot with .40 will fall just under 95 percent (based on .16 being 95 percent)?

Perhaps my question should be: Customer doesn't want lots with AQL more than .40 and wants Z1.4 tables used. If I want to say we are 95 percent confident (or even 90) that the lot is equal to or no worse than .40 percent defective, what inspection level should I have used?

Thanks for help given so far!

 

[Tim Folkerts]

If you keep thumbing thru the Z1.4 standard, you will find that Table P has 5% chance of accepting 0.37% defective. That of course means a 95% chance of rejecting a lot with 0.37% defective.

That would require, however, 800 samples with no defects to accept the lot! That is quite a step up from 32 samples you are doing now! You could also us the binomial distribution to calculate the exact odds ... presumably you would get a similar sample size.

The point is that it is very difficult to be sure of very small defect rates like this. If possible, you should see about measuring a variable instead of a pass/fail text.


Tim F

 

[howste]

If you keep thumbing thru the Z1.4 standard, you will find that Table P has 5% chance of accepting 0.37% defective. That of course means a 95% chance of rejecting a lot with 0.37% defective.

That would require, however, 800 samples with no defects to accept the lot! That is quite a step up from 32 samples you are doing now! You could also us the binomial distribution to calculate the exact odds ... presumably you would get a similar sample size.

The point is that it is very difficult to be sure of very small defect rates like this. If possible, you should see about measuring a variable instead of a pass/fail text.


Tim F

The numbers you gave are for an AQL of 0.015 though, not 0.4. If the AQL is 0.4, the probability of acceptance for a lot with .36% defective is actually 99%. Of course the sample size in this case exceeds the lot size, so there would be 100% inspection and (theoretically) all defectives would be removed.