Destructive Testing Failure Mode Sampling Plan

A

Aileen84

#1
I've been trying to find answers on my own but to no avail.
We just proposed a sample size reduction to our customer on one of the destructive tests that we are doing.
Now, our customer wants to incorporate the failure mode in the sampling plan.

Acceptable: After pull test, it should break in the middle
Failed: Lifted after pull test
Actual data/process performance: 100% break in the middle

Our customer wants to see analysis that our proposed sample size reduction makes sure that it will be able to detect if there are failures (i.e. lifted) after destructive test.

So i tried the AQL, LTPD, Zero acceptance sampling plan.. but I ended up not knowing how to proceed.

Other infos:
Customer's AQL = 0.1%, Level II, Acc=0 for visual inspection.

The answer could just be in front of me but I'm missing it. :(
I hope someone could give input how to close this. Thanks in advance!
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
Well you could use the reduced sample size code letters but I think the real issue facing you is that most commonly published tables dont' have a .001 AQL level (.1% = .001). that's pretty tight

I have an AQL/RQL spreadsheet that I have updated and attached to this post. It adds a tab for determining the AQL and RQL levels for varying sample sizes (n) fro a c=0 plan (Thanks to Statistical Steven for posting the derivation and formulas last year!!)

If you use the tab "AQL RQL levels fro varying n" and enter the confidence levels you want for the AQL and RQL levels it will provide you a series of sample sizes and their associated AQL and RQL levels.

for example, for a confidence level of 95% for the AQL and RQL levels, a .1% AQL is achieved with a sample size of 50. the corresponding RQL is 6%, meaning that you will reject a lot that is 6% defective 95% of the time it's present.
 

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A

Aileen84

#3
Thanks Bev D. This is a really helpful template. I am wondering if I can also use the 'c=0 Sample Plan Generator'? If yes, at what distribution should I based my analysis - Poisson or Binomial?
Also, given that I don't have reject from the start, what is the appropriate p value I should use?
Thanks once again!
 
S

supreecha

#4
Acceptance Sampling by Attributes

Measurement type: Number of defects
Lot quality in defects per unit
Lot size: 50
Use Poisson distribution to calculate probability of acceptance


Acceptable Quality Level (AQL) 0.1
Producer's Risk (Alpha) 0.05

Rejectable Quality Level (RQL or LTPD) 50
Consumer's Risk (Beta) 0.1


Generated Plan(s)

Sample Size 1
Acceptance Number 40

Accept lot if number of defects in 1 items <= 40; Otherwise reject.


Defects Probability Probability
Per Unit Accepting Rejecting AOQ ATI
0.1 1.000 0.000 0.09800 1.0
50.0 0.086 0.914 4.21743 45.8

Average outgoing quality limit (AOQL) = 0.98000 at 1.00000 defects per unit.
 

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Bev D

Heretical Statistician
Staff member
Super Moderator
#5
I am wondering if I can also use the 'c=0 Sample Plan Generator'?
yes you can. but it is an RQL plan generator. so if you put in your .1% AQL then it will give a really large sample size. remember an RQL is the defect rate at which you will detect and REJECT XX% (typically 95%) of the time. The sample size will be 2996. The AQL for this plan (which is generated by default) is 0.000015 or 0.0015% Since your customer's AQL is much larger than that you may not want this plan.

If yes, at what distribution should I based my analysis - Poisson or Binomial?
BOTH will be generated. in reality the sampel sizes are usually within 1, so it won't matter much.

Also, given that I don't have reject from the start, what is the appropriate p value I should use?
OK you can use whatever defect rate YOU want to detect/reject and not ship to the customer. Just be sure to check the corresponding AQL as you wouldn't want to have a higher AQL than your Customer has stated. When you are restricted to a c=0 plan you can typically only specify either the AQL or the RQL and the other level will be whatever it is. When you are not restricted t c=0 then you can specify AQL and RQL and get a sample size that will provide both quality levels. The accept number may be 3 or 4 and while these plans are actually better at providing both you and your customer the protection you need, many people who don't understand get really nervous when you accept a lot that had any defects in the inspection sample. sad but true.
 
A

Aileen84

#6
Wow so much to take in! But they are all really good and I appreciate so much the input.
Thank you so much supreecha and Bev D.

I'll work around what you have provided and hopefully see the light at the end of the tunnel. :)
 
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