Tim I find your post and your template extremely well put together and easily understood. Consider this: a 3 Sigma process produces 15,000 units (approx 1,000) defects per month (monthly cycle). If I want to reduce the alpha (producers risk) costs associated with over inspection, how large should my sample size be?

Tim I find your post and your template extremely well put together and easily understood. Consider this: a 3 Sigma process produces 15,000 units (approx 1,000) defects per month (monthly cycle). If I want to reduce the alpha (producers risk) costs associated with over inspection, how large should my sample size be?

Of course, the most effective way to reduce costs associated with sampling is not to do sampling - then there are no inspection costs! :rolleyes::lol:

Seriously, I think a little more information is need to make such a decision. There are several costs involved, and the "best" decision depends to some extent on whether you are the producer or the consumer. Some question include...
what is the cost to make one piece?
what is the cost to inspect one piece?
what is the cost if a bad piece continues on to the next stages?
what is the cost to return a lot?
what is the cost to rework or scrap a lot?
what is the cost of "bad will" when a lot is rejected?
how big are typical lots?The "normal, level II" Z1.4 (aka MIL-STD-105) plans tend to be designed for a roughly constant alpha (around 5% of good lots will be rejected). In this case, obviously the smaller the sample size, the less it will cost to do inspection. However, this means that "bad" lots will more likely be accepted - i.e. the consumer's risk goes up. Even if you aren't the consumer, eventually those bad lots getting accepted could cause your customer to drop you as a supplier.

Being mostly a mathematician, I used to think that tayloring a sampling plan to an exact alpha & beta was a great goal, so that you knew the exact risks and you could catch small drifts in quality. However, I am coming to realize that sampling is most effectly just for catching gross problems.

In your case, about 1/15 pieces are bad. Trying to come up with a sampling plan that will allow 1/15 pieces to be bad, but will catch when 1/10 are bad is a tough job that will require a large sample size. You are probably better off with sampling plan that can catch when 1/3 are bad (for instance some of the wrong items were shipped or a tool broke in the middle of production).


Rather that worry about details of sampling and the associated risks, you may well be better off looking to the root causes of the 1/15 defect rate and trying to improve that number. If the lots improve, then you have little worrys about rejection no matter what sampling plan is used! As an alternative to sampling, try control charts with continuous variables, which will be much better at watching for problems and keeping production running smoothly.


Tim F