# Sample Simplification

**Abstract:**An inspection plan for incoming parts in a manufacturing process is a necessary strategy for reducing chances of disruption by nonconforming parts. Decisions about the parts and features to be inspected are primary. Identifying an acceptable cost-risk trade-off is crucial to determine sample size. The sample size might be based on tradition or on standards, but a more effective approach uses mathematics and a spreadsheet to track incoming lot size, reject number, percent nonconformance and percentage of certainty of finding issues in a lot. Capturing these numbers in a spreadsheet allows them to be shared and reviewed. By using this spreadsheet method, one manufacturer was able to set an appropriate rate of certainty for detecting and rejecting nonconforming …

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I think the values used in the HYPGEOM.DIST formula are not correct. The result of present expression is correct when c=0 (choose r=1 in the workbook). But if you change that to any value higher than r=1, it starts to "blow up". Checking the Excel Help information for HYPGEOM.DIST, the present selections for the 5 arguments do not seem consistent with Excel Help is expecting. I am using the following expression instead and it seems to work so far - please advise if you see any issues after reviewing the Excel Help description:

=IFERROR(HYPGEOM.DIST((B$7-$E$3),B$7,($E$2*(1-$A9)),$E$2,TRUE),"").

This expression is specifically for the first cell in the table, B9.

--John Phillips, 06-06-2018

the download button is not working.

--Serik Kulchukov, 09-03-2017

I can not download the excel file.

--Serik Kulchukov, 09-03-2017

where can I find the spreadsheet??? i'm sure it's hiding in plain sight

--SKIP w, 01-06-2017

As usual, when I took the time to sit down and read my paper copy of the ASQ Quality progress magazine, I ran into yet another simple and practical article for the quality practitioner. In the past I've had to try and understand ANSI Z1.4 and it's black magic tables. This article does a decent job explaining a hypergeometric sampling plan, and even posts a spreadsheet template.

One nice thing is that he is focusing on the "Reject" quality level (probability of not rejecting a bad lot) instead of the usual discussion on its counterpart, AQL (probability of not accepting a good lot).

I did notice the 1- difference in the figure and the spreadsheet, but that was minor. However when I charted the table, it became clear that he was using the pdf instead of the cdf (so it was incorrect for c>0). Just add a 1 or "True" to the formula and it's good to go.

If only I had read that article a decade ago...

--Marc Bush, 09-28-2016

The downloadable template formulas are missing the 1- in front of the Hypergeometric function, (as shown in the article and in the comment above). This caused the table to be reversed (100% should be 0%,...)

--Andrew Stout, 09-01-2016

Simple and clear explanation. Useful approach. Thanks.

But does it assume the producer's risk and the consumer's risk are the same? The ISO2859-1 standard assumes an alpha risk of 5% and a beta risk of 10%, so it is more favorable to the producer/supplier.

--Renaud Anjoran, 08-26-2016

The spreadsheet formula in Figure 2 is incorrect. The argument for the hypergeometric distribution is missing a last argument of 1 for the cumulative distribution. The correct formula is shown below:

=IFERROR(((1-HYPGEOM.DIST($E$3,B$7,$A9*$E$2,$E$2,1))),"")

--David Trindade, 08-11-2016

A good, clear summation - plus a tool that can be easily used in Excel.

--Gerald Bowen, 08-04-2016

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I would have used Z1.4 / Z1.9 tables / procedures according to attributes or variables depending on product, type of data etc.

Aylin N. M.

ASQ CQPA, CQE, CQA

--Aylin N. Minikus, 11-23-2018