Practical statistics: cut-offs set

[statNovice]

I'm moving this post from statistics thread as if may be a little too complicated for a simple stat advice.


I'm a data analyst in a manufacturing comany, a one trick pony with a limited statistical toolbox that used to be adequate for my ANOVA-based daily job. I now face a non-trivial problem that I do not feel particularly confident about. Would you be able to advice me how to approach it?


1. I have a population of normally distributed QC values (i.e. random variable) with known mean and sigma.

2. I have an empiric cut-off T1 (i.e. fail if QC > T1), delivered by product development team. T1 roughly corresponds to 10% failure rate.

3. Each QC measure in (1) is associated with lot ID ( I have about 10 lots with many obs per each lot right now) and what I see is that within-lot means do vary while sigma are about the same in all lots,i.e. we have an underlying lot population with different mu's and same sigma's.

Question:

From now on, I will be sampling only 4 items per lot, i.e. 4 QC values are available. Based on T1, I need to derive a new lot-level cut-off T2 for mean(QC) so that I fail 95% of unacceptable lots.

I believe my difficulty is that I'm missing a definition of "unacceptable lots". If pressed I would define it as a lot with mean within 3 sigmas of T1.

Would you please help clarify and, possibly, solve this problem? Thank you very much!