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Re: Selecting the Sample size

From: Stan Hilliard
Date: 30 Jun 2000
Time: 22:50:47

Comments

Hi Davis,

From your question, for a population of N=639, you want to control the precision of the sample estimate of fraction defective. That is, you want a sample size (n) that produces 95% confidence limits that are plus and minus 5.0% from whatever sample percentage (100*x/n) the data gives. (x=number of defectives in the sample.) There is no accept/reject rule to be calculated.

One complicating factor is that the standard error that is used to calculate the confidence limits depends on the actual percent defective (p') of the population -- which is unknown. The required n is always maximum at p'=50%. Thus to be conservative, you could base n on p'=50%.

I used Audit Sample Planner (see: www.samplingplans.com/software_me.htm) to calculate these results:

for N=639, p'=50%: n=240

for N=639, p'=10%: n=114

You could use your best guess for p' to calculate n, and then calculate the actual confidence limits from the sample after you have the data. For example, if N=639, n=100, and x=10 defectives Audit Sample Planner calculates these 95% confidence limits:

L=4.59%, p'=10.00%, U=15.40%,

In terms of the number of defective in the lot originally:

L=29, Estimate=64%, U=98%

By the way, if you need to generate the random selected item numbers, and an analysis report that interprets the result; ASP will do that too.

I hope that this helps,

Stan Hilliard


Last changed: November 20, 2007