On a class of multistage selection procedures with screening for the normal means problem

The problem of selecting the population associated with the largest mean from k normal populations which have a common known variance is considered. A class of L-stage selection procedures, which have the desirable property that they screen out the noncontending populations as the sampling proceeds from one stage to the next, is proposed. The proposed procedures are adaptive, capitalizing on favorable configurations of population means, and have the added advantage that they terminate in at most L stages (where L is typically small, two to five). Tables of "optimal" design constants required to implement the procedures are provided as are the performance assessments based on Monte Carlo simulations for the procedures using these design constants. The proposed procedures are compared with some existing procedures and it is found that the former offer considerable improvement over the latter in large number of situations.