How to Calculate Sample Size at 95% Confidence Interval on Surface Roughness

kwalityguy

Starting to get Involved
#1
I'm used to seeing sampling tables such as the old MIL-STD-105E that specifies a sample size based upon an AQL. We have a customer who requested the following:

number of lots = 2, number of pieces per lot is approximately 510

Surface roughness evaluations on enough pieces to allow for the following

1. 95% confidence interval that no more than 5% of the pieces in the lot will fail to meet the surface roughness criteria being evaluated for.

I've Googled what I can and came up with nothing useful. Any suggestions on how to calculate the sample size?
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
What you are looking for is an RQL plan (or some refer to it as an LTPD based plan). RQL is the defect rate that will be detected 95% of the time.

you can use the exact binomial equation (although the Poisson will work equally well at a 5% defect rate).

n = [-LN(1-P(detection)]/p

where
P(detection) is the confidence level
LN is the natural log
p is the defect rate you want to detect and reject

so n= [-LN(1-.95)]/.05 = 60 per lot
Accept on 0, reject on 1 defect in the sample.

Lot size has nothing to do with the sample size.

note that this is NOT really a 95% confidence interval. Confidence intervals are used to determine the precision of a point estimate of the defect rate for the lot. Statistically these are different things.
Confidence levels are used for acceptance sampling to determine if a lot has more or less than some stated defect rate. I know it is confusing, but I am reasonably sure that your customer is asking for acceptance sampling...


if you look here, I have provided a spreadsheet that does these calculations.
 
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