Statistics Question?

Question

If a person produces 175 widgets each day, how many widgets do I need to quality check each month to ensure they are creating a quality widget?

Ok, well to add some details. These people will be written up unless at least 97% of the widgets sampled are of perfect quality. (This is actually a real world question). So with say a 95% confidence level.

Answer 1

The answer you are looking for is based on how much uncertainty you are willing to have in the estimation.

I would look at sampling n widgets and counting x defects.

let p be approximated by ( x + 2 ) / ( n + 4 )
the addition of 2 success and four total trials helps to make the size of the CI correct.

the width of the interval, for a 95% CI is
1.96 * Sqrt( p*(1 - p)/(n + 4)

using p = 0.03 for a starting point, the width of the interval as a function of n is 0.898185 * Sqrt(1 / (n + 4 ))

I would think that an interval with a total width of 3% would be good so
2 * 0.015 = 0.898185 * Sqrt(1 / (n + 4 ))
n = 893.

Now I figure that you're looking at about 3500 widgets produced in a month so sampling 893 of them for QA.

I sure there is something better to do, but based on the info here, this is the only think I can think of.

Answer 2

5 percent is a good number for quality assurance/

Answer 3

That depends on your QC protocol, there is no statistically defined answer for this.

Answer 4

Not enough information.