6. Sequential Selection Procedures

Abstract

6.1 INTRODUCTIONEarly contributions to sequential ranking procedures under the indifference zone formulation date back to mid-fifties and these are attributed to Bechhofer and Sobel (1953, 1954b, 1956a, 1956b, 1956c, 1958a). Many of the results of these authors along with the contributions of Kiefer have taken the final form of a monograph by the three authors (1968). Their book lays special emphasis on selection from Koopman—Darmois family which includes many known particular cases. We do not attempt here to survey all their results; however, some of these results are referred to at appropriate places. Also, a brief discussion of the general approach of Bechhofer, Kiefer, and Sobel is presented in §6.8.6.2 SELECTION OF THE LARGEST NORMAL MEANStein (1948) considered the following problem. Let Xij , i=1,…,k ; j=1,2,… , be independent random variables where Xij is distributed normally with mean ξi+ηj and variance σj2 .