A robust property of the ${ m OC}$ of binomial and Poisson sampling inspection plans

Abstract

The paper assumes prior distribution for quality of lots submitted for acceptance inspection. For any acceptance plan and a given prior distribution, calculate the average probability of acceptance of a lot. The definition of equitable quality level (EQL) as given in this paper ensures that the proportion of lots of quality better than the EQL (as obtained under the assumed prior distribution) shall be equal to the average probability of acceptance. This paper shows that under fairly general conditions on the prior distribution, for binomial or Poisson plans involving a large sample size $n$, the EQL is approximately given by $(c+1)/(n+1)$ and $(c+1)/n$, respectively, when $c$ is the acceptance number.