# LTPD (Lot Tolerance Percent Defective) Sampling Plan with %Defect

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#### RungS

Dear sir

I have some question about property of LTPD sampling plan.
Example LTPD 2% with sampling size 116 pcs.
If I have 1100 lots with various defect rate in each lot. (Zero to 5%)
With this samping plan , If I get 1000 lots for Accepted lots. In 1000 Lots will have 900 Lots that have defect <2% and 100 Lots that have defect 2-5%.

Is it correct?

Best Regards.

#### somashekar

Staff member
Super Moderator
Re: LTPD with %Defect

Dear sir

I have some question about property of LTPD sampling plan.
Example LTPD 2% with sampling size 116 pcs.
If I have 1100 lots with various defect rate in each lot. (Zero to 5%)
With this samping plan , If I get 1000 lots for Accepted lots. In 1000 Lots will have 900 Lots that have defect <2% and 100 Lots that have defect 2-5%.

Is it correct?

Best Regards.
Hi RungS.
Welcome here.
Perhaps you may find some lead.

R

#### RungS

Somashekar BV

However , I still can not understanding about "The quality level at 10% probability of acceptance." I know its is very basic of Stat. But I am confusing now.
Please help tech me by refer my Example that I think that its will make clear for me.

Thank you & Best Regards.
Rung S.

Last edited by a moderator:

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
I think your example is probably incorrect.

when dealing with LTPD, the 10% means that you have a 90% probability of detecting and therefore rejecting a lot that has the stated %defective. You only have a 10% chance of accepting a lot that bad. But remember that the LTPD point is a single point on the curve of probabilities of detecting (Rejecting) or missing (Accepting).

SO: for your example of a 2% LTPD and a sample size of 116:

at a 5% defect rate there is only a 0.3% chance of having no defects in the sample and thus acceptign the lot; there is a whopping 99.7% chance that you will find at least one defct and therefore reject the lot.

at a 1% defect rate there is a 31.35% chance of having no defects in the sampel and thus accepting the lot, so there is a 68.65% chance of having one or more defects in the sample and thus rejecting the lot.

An OC curve can be construted to show this

Does this help a little?

R

#### RungS

BEV D

With you explain ,
I understood that Each defect rate must be separated to calculate how many can be had in sampling result.

1 ) If I need to focus on 2% defect , the chance is 10%. So with result accept 1000 lots from 1100 lots , It will has chance to have overlook lot = 10% of 1100 = 110 Lots.

2 ) Or Other my understanding , if Expect there are 100 lots in 1100 lots have defect >2%. When sampling with LTPD2% , It will has overlook lot = 10% of 100 lots = 10 Lots.

Which is Correct 1) or 2) or no one?

Best Regards.
Rung S.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
2 is not correct, but close. Each defect rate will have a different probability of being detected as explained above. So if the defect rate is 2% or greater, then there is less of a chance of missing the lots that are substantially greater than 2% defective.

1 might be correct: IF each of the 1100 lots have exactly 2% defects, then you fail to detect that 10% of the time. But remember that probability gives the expected results over many sample sets. There is a chance that you may miss 9% of the 1100 lots or you may miss 11% of the 1100 lots...

Perhaps it woudl be helpful if you gave us more context about your question. is it purely hypothetical or is there a real world situation that is driving the question.