Operations Management: Processes and Supply Chains, 12th Edition

Average Outgoing Quality

We have shown how to choose the sample size and acceptance number for a single-sampling plan, given AQL, $\alpha ,$ LTPD, and $\beta$ parameters. To check whether the performance of the plan is what we want, we can calculate the plan’s average outgoing quality (AOQ), which is the expected proportion of defects that the plan will allow to pass. We assume that all defective items in the lot will be replaced with good items if the lot is rejected and that any defective items in the sample will be replaced if the lot is accepted. This approach is called rectified inspection. The equation for AOQ is

$$\text{AOQ}=\frac{p\left(P_a\right)\left(N-n\right)}{N}$$

where

• $p=\text{true proportion defective of the lot}$

• $P_a=\text{probability of accepting the lot}$