Contributions to Stochastics pp 214-235 | Cite as
Nonparametric Selection Procedures in Complete Factorial Experiments
Summary
The behavior of many real-world systems depends on two or more factors which can be set at various levels. In such systems factorial experiments are usually conducted so that one can select or rank factor-level combinations, and study the performance of the system at those selected factor-level combinations. For the goal of selecting the best factor-level combination, all the existing theory in ranking and selection assumes normality of the observations. In this paper, we consider selection procedures for the above goal, in two-factor factorial experiments without relying on the assumption of normality. These procedures are then campared under no-interaction and interaction cases, and adaptive procedures are formulated.
Key words and phrases
Nonparametric selection complete factorial experiments indifference zone approach asymptotic efficiencyPreview
Unable to display preview. Download preview PDF.
References
- [1]Bawa, V.S. (1972). Asymptotic efficiency of one R-factor experiment relative to R one-factor experiments for selecting the best normal population. J. Amer. Statist. Assoc., 67, 660–661.CrossRefGoogle Scholar
- [2]Bechhofer, R.E. (1954). A single-sample multiple decision pro-ranking means of normal populations with known Ann. Math. Statist., 25, 16–39.MathSciNetMATHCrossRefGoogle Scholar
- [3]Bechhofer, R.E. (1977). Selection in factorial experiments. Proeeding of the 1977 Winter Simulation Conference, 65–70.Google Scholar
- [4]Bradley, J.V. (1979). A nonparametric test for interactions of any order. J. Quality Tech., 11, 177–184.Google Scholar
- [5]Dudewicz, E.J. (1977). New procedures for selection among (simulated) alternatives. Proceedings of the 1977 Winter Simulation Conference, 59–62.Google Scholar
- [6]Dudewicz, E.J. and Taneja, B.K. (1982). Ranking and selection in designed experiments: complete factorial experiments. J. Japan Statist. Soc., 12, 51–62.MathSciNetMATHGoogle Scholar
- [7]Lehmann, E.L. (1963). A class of selection procedures based on ranks. Math. Annalen., 150, 268–275.MathSciNetMATHCrossRefGoogle Scholar
- [8]Mehra, K.L. and Smith, G.E.J. (1970). On nonparametric estimation and testing for interactions in factorial experiments. J. Amer. Statist. Assoc., 65, 1283–1296.MathSciNetMATHCrossRefGoogle Scholar
- [9]Puri, M.L. (1964). Asymptotic efficiency of a class of c-sample tests. Ann. Math. Statist., 35, 102–121MathSciNetCrossRefGoogle Scholar
- [10]Puri, M.L. and Puri, P.S. (1969). Multiple decision procedures based on ranks for certain problems in analysis of variance. Ann. Math. Statist., 40, 619–632.MathSciNetMATHCrossRefGoogle Scholar
- [11]Taneja, B.K. (1986). Selection of best normal mean in complete factorial experiments with interaction and with common unknown variance. J. Japan Statist. Soc., 16, 53–65.MathSciNetMATHGoogle Scholar
- [12]Taneja, B.K. and Dudewicz, E.J. (1984). Selection of the best cell in 2 x 2 factorial experiments with interaction. Transactions of the Annual Quality Control Conference of the Rochester Section, American Society for Quality Control, 40, 305–350.Google Scholar
- [13]Taneja, B.K. and Dudewicz, E.J. (1984). Selection in factorial experiments with interaction, especially the 2 x 2 case. Preprint //84–2, Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 44106. Submitted for publication.Google Scholar