Solving the Ranking and Selection Indifference-Zone Formulation for NormalDistributions Using Computer Software

摘要

Ranking and selection procedures are statistical methods used to compare andchoose the best among a group of similar statistically distributed populations. The two predominant approaches to solving ranking and selection problems are Gupta's subset selection formulation and Bechhofer's indifference-zone formulation. For the indifference-zone formulation where the populations have equal sample sizes, Barr and Rizvi developed an integral expression of the probability of correct selection (PCS). Given appropriate parameters, the integral expression can be solved to determine the common sample size required to attain a desired PCS. Tables with selected solutions to the integral expression are available for a variety of population distributions. These tables, however, are not included in any single reference, sometimes require interpolation, and only provide approximate results for the case of unequal sample sizes. Using a computer software program to solve the integral expression for the unknown parameters can eliminate these burdens. This paper describes the computer software developed to solve the integral expression of the indifference-zone formulation for normally distributed populations having either equal or unequal sample sizes, The software was written in QuickBASIC and Mathematica. The QuickBASIC code is a menu-driven interface that develops input files for Mathematica. Mathematica is the mathematical software package which performs the computationally intensive calculations required to solve the integral expressions. Ranking and selection, Ranking and selection procedures, Indifference-Zone, Indifference-Zone formulation.