Optimal group sequential tests with groups of random size

We consider sequential hypothesis testing based on observations that are received in groups of random size. The assumed to be independent both within and between the groups. assume group sizes their distributions known formed observations.We concerned with a problem simple against alternative. For any (group) test, we take into account following three characteristics: its type I II error probabilities average cost observations. Under mild conditions, characterize structure tests minimizing among all whose do not exceed some prescribed levels.