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

#### kwalityguy

##### Involved In Discussions
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?

#### Bev D

##### Heretical Statistician
Super Moderator
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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