Multiple Decision Procedures

An encyclopaedic coverage of the literature in the area of ranking and selection procedures. It also deals with the estimation of unknown ordered parameters. This book can serve as a text for a graduate topics course in ranking and selection. It is also a valuable reference for researchers and practitioners.

The problem of selecting the multinomial event which has the highest probability is formulated as a multiple-decision selection problem. Before experimentation starts the experimenter must specify two constants ([theta]*, P*) which are incorporated into the requirement: "The probability of a correct selection is to be equal to or greater than P* whenever the true (but unknown) ratio of the largest to the second largest of the poplation probabilities is equal to or greater than [theta]*." A single-sample procedure which meets the requirement is proposed. The heart of the procedure is the proper choice of N, the number of trials. Two methods of determining N are described: the first is exact and is to be used when N is small; the second is approximate and is to be used when N is large. Tables and sample calculations are provided.

Contents: Statement of the statistical problem S atistical assumptions The experimenter's goal, specification, and requirement Procedure D and the new computing formulae Description of Procedure D Definition of symbols The sampling, stopping, and terminal de cision rules Computation of the stopping statistic Use of Procedure D (method B) with various experimental designs Simplified computing formulae Numerical example Monte Carlo sampling results with Procedure D Description of the sampling procedure Sampling results Discussion of sampling results.