Acceptance Probabilities for a Sampling Procedure Based on the Mean and an Order Statistic

A dual acceptance criterion based on the sample mean and an extreme order is used in many inspection procedures. Computation of the acceptance probability for such a dual criterion is investigated. An approximation and a lower bound to the acceptance probability are derived and are applicable to any continuous distribution. In addition. the connection between this dual criterion and hypothesis testing of scale and location parameters is studied. In the case of the exponential distribution the exact evaluation of the acceptance probability yields the power of the test.