17 Design of experiments with selection and ranking goals

Abstract

Publisher Summary Selection and ranking problems have generally been formulated adopting one of two main approaches now familiarly known as the “indifference-zone formulation” and “the subset selection formulation.” This chapter discusses the selection procedures for both the approaches—that is, the indifference-zone and the subset formulations. Related to the selection and ranking objectives is the multiple comparison approach in which one seeks simultaneous confidence sets for meaningful contrasts among a set of given treatments. There may not always be sufficient quantities of homogeneous experimental material available for an experiment using a completely randomized design. However, it may be possible to group experimental units into blocks of homogeneous material. Then one can employ a traditional blocking design, which minimizes possible bias and reduces the error variance. Factorial experimentation when employed in ranking and selection problems can produce considerable savings in total sample size relative to independent single-factor experimentation when the probability requirements are comparable in both cases. The chapter concludes with a discussion of several models such as single-factor Bernoulli models, multinomial models and reliability models, such as increasing failure rate (IFR) and increasing failure rate on the average (IFRA).