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The Use of Hodges-Lehmann Estimator in Multiple Response Optimization with Replication

Ch'ng C.K., and Quah S.H., and Low H.C., (2004) The Use of Hodges-Lehmann Estimator in Multiple Response Optimization with Replication. Matematika, 20 (2). pp. 101-110. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/200420203.pdf

Affiliations

Universiti Sains Malaysia, School of Mathematical Sciences
Universiti Sains Malaysia, School of Mathematical Sciences
Universiti Sains Malaysia, School of Mathematical Sciences

Abstract

The development of an approximation model for the true response surface is needed in Response Surface Methodology. In multiple response optimization (with replication), the sample mean is widely used to calculate the mean value at each design point of every quality characteristic before the model fitting. However, the existence of outliers may have certain effects on the sample mean. Thus, the Hodges-Lehmann estimator, a robust estimator, is proposed in place of the sample mean in this paper. A summary of the properties and advantages of the Hodges-Lehmann estimator will be given together with an example from the literature to illustrate the computation of this proposal.

Item Type:Journal
Keywords:Response surface methodology; Hodges-Lehmann estimator; Optimization; Generalized reduced gradient
Subjects:Q Science, Computer Science
ID Code:5749

[1] E.D. Castillo,D.C. Montgomery and D.R. McCarville, Modified Desirability Functions for Multiple Response Optimization, Journal of Quality Technology, 1996, 28 (3), 337– 345.

[2] G. Derringer and R. Suich, Simultaneous Optimization of Several Response Variables, Journal of Quality Technology, 1980, 12 (4), 214–219.

[3] F.S. Fogliatto and S.L. Albin, Variance Of Predicted Response As An Optimization Criterion In Multiresponse Experiments, Quality Engineering, 2000, 12 (4), 523–533.

[4] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics: The Approach Based on Influence Functions, New York: John Wiley & Sons. Inc., 1986.

[5] M.O. Abu-Shawiesh and M.B. Abdullah, New Robust Statistical Process Control Chart for Location, Quality Engineering, 1999-2000, 12 (2), 149-159.

[6] J.A. JR. Alloway and M. Raghavachari, Control Chart Based on the Hodges-Lehmann Estimator, Journal of Quality Technology, 1991, 23 (4), 336-347.

[7] J.L. JR. Hodges and E.L. Lehmann, Estimates of Location Based on Rank Tests, Annals of Mathematical Statistics, 1963, 34, 598-611.

[8] E.L. Lehmann, Theory of Point Estimation, New York: John Wiley & Sons, Inc., 1983.

[9] J.L. JR. Hodges, Efficiency in Normal Samples and Tolerance of Extreme Values for Some Estimates of Location, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability Volume 1, edited by L.M. Le Cam and J. Neyman, University of California Press, Berkeley, 1967, pp.163-186.

[10] F.R. Hampel, The Robustness of Some Nonparametric Procedures, in A Festschrift for Erich L. Lehmann, edited by P.J. Bickel, K.A. Doksum and J.L. Hodges, Wadsworth International Group, Belmont, CA, 1983, pp.209-238.

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