On a UMP and curtailed double sampling test for proportions

The test on proportions as prescribed in the double sampling plan of Dodge and Roming (1929) for inspection by attributes is revisited. A noticeable deficiency of this plan is that it may require more observations than could have been required by an 'equivalent' fixed-sample testing procedure having the same Type I and Type II error probabilities. Here, we propose a curtailed version of this sampling plan which assures the experimenter that the actual number of observations required to arrive at a terminal decision will never exceed that of the comparable fixed-size testing procedure while keeping the error probabilities at desired levels. In fact, we show that the entire power function of the proposed testing procedure matches that of the 'best' (UMP in its size) fixed-size-sample testing procedure. Other properties of this curtailed double sampling testing procedure, such as its Average Sample Number and its operational characteristics, are also discussed and illustrated.