From: Greg
Date: 22 Feb 2004
Time: 00:12:19
Lot size is often ignored in these calculations because the fraction defective of a process (the x-axis in the OC Curve) is in many cases a constant percent defective, produced randomly. i.e. a machine in control may display a long run defective rate of 1.5%. This is the same for 1,000 units or 10,000. In those cases, the average expected defectives are 15 and 150 on a proportional basis. The Sampling Plan should provide similar protection for both cases.
But, say that there is a situation where there is not a constant defective rate and there are actually 90 critical defectives (you do not know this beforehand) bunched in a group produced in a non random manner (a one off bad batch of components from a supplier). Using a lot size of 10,000, the theoretical position on the x-axis of an OC Curve is 0.9% (90/10,000). This Lot stands a very high chance of being accepted depending on the number of samples taken. If you reduced the Lot size to 1000, the fraction defective is now 9% and the chance of a Type II error is low.
I often see the statement that equal protection is given by a Sampling Plan regardless of Lot size. Correct... maybe, except for the case I mention above. The misuse is often compounded by judicious use of accept numbers of greater than zero. If you can increase your Lot size and also convince someone that using an accept number of 2 is more economical than an accept on zero, you will probably have a low rejection rate and demonstrate good quality... but is it??