A modification of a truncated partial sequential procedure

Recently Billard (1977) introduced a truncated partial sequential procedure for testing a null hypothesis about a normal mean with known variance against a two-sided alternative hypothesis. That procedure had a disadvantage that a large number of observations was necessary if the null hypothesis was to be accepted. A new procedure is introduced which reduces the expected sample size for all mean values with considerable reductions for values near the null mean value. Theoretical operating characteristic and average sample number functions are derived.