Credit-based accept-zero sampling schemes for the control of outgoing quality

A general procedure is presented for switching between accept-zero attributes or variables sampling plans to provide acceptance sampling schemes with a specified limit on the (suitably defined) average outgoing quality (AOQ). The switching procedure is based on credit, defined as the total number of items accepted since the last rejection. The limit on the AOQ is maintained by mandatory 100 % inspection of lots that are rejected when the credit is zero, with acceptance of all inspected items found to be conforming in such lots. The general procedure is developed and the application of the procedure to three situations is considered. Denoting the smallest value in a sample by $X_{(1)}$, a single, lower specification limit by $L$ and a constant by $c$, the method is applied to:- sampling by attributes, with acceptance criterion $X_{(1)}\geq L;$- sampling by variables from a normal distribution with unknown process mean $\mu$ and known process standard deviation $\sigma$, with acceptance criterion $X_{(1)}\geq L+c\sigma;$- sampling by variables from a normal distribution with unknown process mean $\mu$ and unknown process standard deviation $\sigma$, with acceptance criterion $X_{(1)}\geq L+cs$, where $s$ is the sample standard deviation.Finally it is shown that the guarantee on the upper limit to the AOQ remains valid when all rejected lots are submitted to 100 % inspection.