Tutorial on indifference-zone normal means ranking and selection procedures

ABSTRACT

This tutorial concerns the ranking and selection problem of choosing that one of k normal populations (with common known variance) which has the largest mean. We discuss a number of procedures which guarantee a specified probability of selecting the correct population. We concentrate on so-called indifference-zone procedures.

REFERENCES

• 1: Bechhofer, R.E. (1954). "A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with Known Variances." Ann. llath. Sta~:., ~5, 16-39.
• 2: Bechhofer, R.E. and D. Golds~an (1986). Technical Report (in preparation), School of OR&IE, Cornell Univ., Ithaca, NY.
• 3: Bechhofer, R.E., J. Kiefer, and N. Sobel (1968). Sequential Identification and Ranking Procedures. The Univ. of Chicago Press, Chicago.
• 4: Fabian, V. (1974). "Note on Anderson's Sequential Procedures with Triangular Boundary." Annals of Statistics, ~, 170-175.
• 5: Gibbons, J.D., I. Olkin, and M. Sobel (1977). SeleetinE and Ordering Populations. John ~iley, New York.
• 6: David Goldsman, Ranking and selection in simulation, Proceedings of the 15th conference on Winter Simulation, p.387-394, December 12-14, 1983, Arlington, Virginia, United States
• 7: David Goldsman, Ranking and selection procedures using standardized time series, Proceedings of the 17th conference on Winter simulation, p.120-124, December 11-13, 1985, San Francisco, California, United States [doi>10.1145/21850.253094]
• 8: Gupta, S.S. (1956). On a Decision Rule for a Problem in Rankin# lleans. Ph.D. Dissertation (Mimeo Ser. No. 150). Inst. of Statist., Univ. of N. Carolina, Chapel {till.
• 9: Gupta, S.S. and S. Panchapakesan (1979). Multiple Decision Procedures. John ~iley, New York.
• 10: Hartmann, M. (1986). "An Improvement on Paulson's Sequential Procedure for Selecting the Largest Normal Mean." Technical Report, School of OR&IE, Cornell Univ., Ithaca, NY.
• 11: Paulson, E. (1964). "A Sequential Procedure for Selecting the Population with the Largest Mean from k Normal Populations." Ann. Math. Seat,, 35, 174-180.
• 12: Ramberg, J.S. ( 1966). A Comparison o{ the Performance Characteristics o{ Two Sequential Procedures for Ranking Means of Normal Populations. Master's Thesis, School of OR&IE, Cornell Univ., Ithaca, NY.
• 13: Tamhane, A.C. and R.E. Bechhofer (1977). "A Two- St age Minimax Procedure with Screening for Selecting the Largest Normal Mean." Comm. Stat. - Theor. Neth., A6, 1003-1033.
• 14: Tamhane, A.C. and R.E. Bechhofer (1979). "A Two- Stage Minimax Procedure with Screening for Selecting the Largest Normal Mean (II): An Improved PCS Lower Bound and Associated Tables." Comm. S(~at. -Theor. Meth., k8, 337-358.

INDEX TERMS

Primary Classification:
  A. General Literature

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Design, Performance, Theory