Sample Size for 95% CI - Lot size is 25,000 - 2% Defect Rate Process

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Bev D

Heretical Statistician
Staff member
Super Moderator
#12
a google search or a search of this forum will yiled what you are looking for. research is good - you stumble across all kinds of goodies out there.

but since it's early and I havent' even finished my first cup of coffee:

for the Poisson: n = -ln(1-P(Detection)) / p

for the Binomial: n = ln(1-P(Detection)) / ln(1-p)

P(Detection) is the probability of detecting a lot or batch that is p defective or greater...expressed as a fraction 95% = .95

p is of course the fraction defective. 1% = .01
 

DWPOZE

Registered Visitor
#15
Thanks for all your help. I have another question. I have 13,000 pcs and I have a .65% defect rate. How many pieces would I have to check to find 1 defective part and be 95% confident? I don't want to sort all 13,000 pcs.Thanks for your help!!!!
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#16
Thanks for all your help. I have another question. I have 13,000 pcs and I have a .65% defect rate. How many pieces would I have to check to find 1 defective part and be 95% confident? I don't want to sort all 13,000 pcs.Thanks for your help!!!!

if you use the formulas provided you will get your answer.
however, I'm not sure of what you're really asking for given how you phrased the question. If your lot may contain defectives, and you want to have a 95% probability of detecting a defective rate of .65% or worse, then your sample size is (using the formulas I provided above) 460 (Binomial) or 461 (Poisson).

again lot size has nothign to do with determining sample size.

teh fact that you chose a defect rate of .65% leads me to beleive that you are struggling with trying to understand ANSI / Mil Std tables for AQL inspection.

I guess to really help you we need to know what you are trying to understand....
 

DWPOZE

Registered Visitor
#17
I'm trying not to sort all parts. If I know I have a defect rate of .65% how many pieces would I have to check to find 1 defective piece. Thanks for your help.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#18
I'm trying not to sort all parts. If I know I have a defect rate of .65% how many pieces would I have to check to find 1 defective piece. Thanks for your help.

I'm afraid you are wishing for the impossible.
At a .0065 defect rate and 13,000 pcs in the lot there are 85 defective pieces in the lot. do you want to find them all? How do you KNOW there is an exactly .65% defective rate in the lot? is this defect randomly distributed or do they cluster/group together when they are created?

the math I gave you works if you only want to find 1 defective part then you will find it in a random sample of 460 parts 95% of the time. of course it's possible that you will find none or 2. why do you only want to find 1? dont' you want to find all of them? if you dont' want to find all of them then just ship the lot.

we need to be reasonable here. are the defects bad? should they be removed from the lot? if so then you must sort the entire lot. if they aren't "that bad" then let it go without any sort. if you are only trying to convince yourself that the lot is truly at least .65% defective then a sample of 461 will detect at least 1 defective part 95% of the time and you will have proof that the lot is probably .65% defective. but remember that there is still a 5% probability that you miss a defective part and then ship a .65% defective lot.

statistics is not the portal to getting out of doing the hard work...answer the questions in bold above for yourself.
 
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