LTPD, Alpha and Beta for this plan.

D

dhouser

#1
Could somebody give me the LTPD, Alpha, and Beta for these plans.

AQL: 2.5

n=33...88...132
ac=5...8...11
re=6...9...12

AQL: 2.5

n=30...80...120
ac=5...8...11
re=6...9...12

AQL: 0.65

n=30...80...120
ac=3...4...5
re=4...5...6


apparently these n, ac and re are sufficient for these AQL's. I am arguing against that.

any comments would be great. thanks.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#3
there is not enough information to answer the OP's real question. His stated question is rather straightforward to answer, but one thing we've found here at the cove is that questions such as this are usually the result of one or more assumptions that the OP has made and to give the straightforward math answer that is requested may not be helpful relevant or even correct given the real reason for the OP's question.

I can't see how knowing the LTPD, alpha and beta for these plans helps him understand if the plans are sufficient...
 
D

dhouser

#4
there is not enough information to answer the OP's real question. His stated question is rather straightforward to answer, but one thing we've found here at the cove is that questions such as this are usually the result of one or more assumptions that the OP has made and to give the straightforward math answer that is requested may not be helpful relevant or even correct given the real reason for the OP's question.

I can't see how knowing the LTPD, alpha and beta for these plans helps him understand if the plans are sufficient...
I should clarify then.

I am not trying to find out whether or not these plans will be appriopriate sampling plans. When i look at the plan that I wrote down above, it seems to me that an AC of 3 out of 33 samples would never equate to an AQL of 0.65. If they ever did - the alpha and beta would be ridiculously high - this defeating the purpose of the test. What I am trying to do is determine the alpha, beta, and ltpd so I can say : "this plan is insufficient because it gives you an alpha of X and beta of Y, and your LTPD could be as high as Z.

In some crazy combination, there may be a combination of alpha beta and ltpd that would produce a plan that has an aql of 0.65, n=33 and ac=3, but I dont think it exists. Does it exist, if so, what are the alpha beta and ltpd.

thanks
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
I should clarify then.

I am not trying to find out whether or not these plans will be appriopriate sampling plans. When i look at the plan that I wrote down above, it seems to me that an AC of 3 out of 33 samples would never equate to an AQL of 0.65. If they ever did - the alpha and beta would be ridiculously high - this defeating the purpose of the test. What I am trying to do is determine the alpha, beta, and ltpd so I can say : "this plan is insufficient because it gives you an alpha of X and beta of Y, and your LTPD could be as high as Z.

In some crazy combination, there may be a combination of alpha beta and ltpd that would produce a plan that has an aql of 0.65, n=33 and ac=3, but I dont think it exists. Does it exist, if so, what are the alpha beta and ltpd.

thanks
Ah that's better!

Before we get to the math (and I'm sure that somone like Tim F is out there doing this already!) I would say that perhaps your natural skeptism can be cleared up a bit better if we poke at the AQL thing. The AQL is always the defect rate that you will accept usually (per mil-std / ANSI Z1.4) 95% of the time. thus the alpha is 5%. The LTPD is the defect rate that you will detect and reject usually 90% of the time and therefore Beta is 10%...

Now the reason I'm not going to do the math is that I've moved past the Mil-Std and the Ansi standards and the whole concept of AQLs. I now use the Binomial or Poisson directly to calculate the sample size needed to detect (and therefore) reject a given defect rate with a given % of the time. I reject on c=1. I've posted the formulas here in other threads...

There are those who can describe why going to larger reject values can provide better 'protection', but I've found that the actual difference in real life is too small to bother with. (While it's an interesting theoretical excercise and can help us to understand sampling in general). If my product requires more 'precise' protection I move away from categorical sampling to continuous data sampling, process controls and mistake proofing.
 
D

dhouser

#7
by the way - where did you get those numbers???
I can't say.

However - it has been my understanding that alpha and beta are not a fixed 5% - 10%. I recognize that they may be industry standards, but they can certainly be adjusted.

I use biniomial distribution and hypergeometric distribution when calculating my sample size, both of these methods require an alpha and beta for an Ac and Re. Compiling sampling plans this way allows me to better define what my results mean. This is why I asked the original question, because if somebody tells me that a plan will meet an AQL of 0.65 - it means absolutely nothing to me because there are 3 other variables involved.
 

Proud Liberal

Quite Involved in Discussions
#8
I've always looked at the AOQL level when evaluating sampling plans. The max AOQL are highlighted in the attached spreadsheet. The max represents the worst case exposure to the customer. There are large differences between the sampling plans you posted.

Note the strong correlation between sample size and protection rather that sample size and lot size (included information from Grant & Leavenworth).

The closer the curves are to vertical (when plotted normally, the plot in my spreadsheet is rotated 90°, so in my charts horizontal), the better the resolving power to distinguish
% defective.

I hope this is helpful.
 

Attachments

Tim Folkerts

Super Moderator
#9
There are typically many choices for LTPD, Alpha, and Beta that will fit a given sampling plan

Could somebody give me the LTPD, Alpha, and Beta for these plans.

AQL: 2.5

n=33...88...132
ac=5...8...11
re=6...9...12
The 33/5/6 plan would seem to fit for

AQL....Alpha
2.5.....0.01%
3........0.03%
4........0.1%
6........0.6%
8........3%
10......5%

The last line would suggest that this is plan is closer to AQL=10.

Similarly,

LTPD...Beta
10......92%
12......85%
15......70%
20......40%
25......18%
28......10%
30......7%


Basically, you just have to play around with the binomial distribution to see what values fit the numbers.


Tim
 
D

dhouser

#10
I've always looked at the AOQL level when evaluating sampling plans. The max AOQL are highlighted in the attached spreadsheet. The max represents the worst case exposure to the customer. There are large differences between the sampling plans you posted.

Note the strong correlation between sample size and protection rather that sample size and lot size (included information from Grant & Leavenworth).

The closer the curves are to vertical (when plotted normally, the plot in my spreadsheet is rotated 90°, so in my charts horizontal), the better the resolving power to distinguish
% defective.

I hope this is helpful.

Thanks for the spreadsheet, it is very well presented.

I have a question regarding the tables:

I understand that the first column is a list of probabilities. I do not understand how the second column is calculated. It is titled as percent defective, though where did these numbers come from? Lastly, the last coumn is AOQL, with AQL set at 95%, and RQL set at 10%, though why is the value highlighted at 75%? Is 75% the standard value for AOQL?

Thanks!
 
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