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Nonparametric Selection Procedures in Complete Factorial Experiments

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Contributions to Stochastics
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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.

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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.

    Article  Google 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.

    Article  MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google Scholar 

  7. Lehmann, E.L. (1963). A class of selection procedures based on ranks. Math. Annalen., 150, 268–275.

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

  9. Puri, M.L. (1964). Asymptotic efficiency of a class of c-sample tests. Ann. Math. Statist., 35, 102–121

    Article  MathSciNet  Google 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.

    Article  MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google 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 

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© 1987 Physica-Verlag Heidelberg

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Taneja, B.K. (1987). Nonparametric Selection Procedures in Complete Factorial Experiments. In: Sendler, W. (eds) Contributions to Stochastics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46893-3_22

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  • DOI: https://doi.org/10.1007/978-3-642-46893-3_22

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-642-46895-7

  • Online ISBN: 978-3-642-46893-3

  • eBook Packages: Springer Book Archive

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