Hi Rivera, welcome to this forum. I have moved your topic to this area -- Techniques and Applications -- which you are now viewing.

Problem number 3 can be solved with the binomial distribution.

rivers16 wrote:3. A sample equeals to 10% of the lot is take. If 2% or less of the items are defective, the lot is accepted. If submited lots vary in size from 5,000 to 10,000 units, what can you say about the protection of this plan? If LTPD=0.05 is desired, does this scheme offers a reasonable protection to the consumers?

I would conclude that this scheme does offer reasonable protection to the consumers. I used the binomial nomograph to evaluate it. Here are two links to the binomial nomograph:

https://acc.dau.mil/docs/dtepi/pns/doc/nomogr/bdi.pdfhttp://webpages.sdsmt.edu/~djensen/IENG ... ograph.docHere is the analysis:

For this range of lot size, n=100 to 200.

The acceptance numbers at those two n's respectively are c=2 and c=4.

I have drawn a line on a binomial nomograph for each lot, through beta=5% (.05 on the right hand scale) and through the point (n=100,c=2) or through the point (n=200,c=4). I read LTPD on the left hand scale. The RQL=LTPD= 0.063 (6.3%) and 0.046 (4.6%).

Repeating for beta = 10%, the LTPDs are 0.056 (5.6%) and 0.04 (4%).

The whole OC curves are obtained by pivoting a line through the (n,c) points of each plan and reading the 'p of the OC curve's horizontal axis on the left hand scale and the Pa of the OC curve's vertical axis on the right hand scale.

The original article containing the nomograph and its many applications can be obtained from the ASQ site for only $5. It's a deal.

http://asq.org/qic/display-item/index.html?item=5004If you need to design and analyze attribute plans quickly and automatically and to generate reports that document all of their properties, my computer program does this and can be bought.

http://www.samplingplans.com/software_oc.htm