集美麻豆

Sains Malaysiana 30: 87-106 (2001)                                                                                                    Pengajian Kuantitatif/

Quantitative Studies

A Modified Nonparametric Univariate Control Chart for

Location Based on the Trimmed Mean

Moustafa O, Abu-Shawiesh

Department of Staistics

College of Management Sciences and Planning

King Faisal University, P.O. Box 1760

Al-Ahsa 31982, Kingdom of Arab Saudi

Mokhtar B. Abdullah

School of Mathematical Sciences

Faculty Science and Technology

Universiti Kebangsaan Malaysia

43600 集美麻豆 Bangi

Selangor D.E. Malaysia

ABSTRAK

Rencana ini mengemukakan ubahsuaian kepada had kawalan dan garis tengah Carta Kawalan Hodges-Lehmann yang dicadangkan oleh Alloway dan Raghavachari (1991).  Ubahsuaian ini dilakukan dengan menggantikan median purata Walsh dengan min terpangkas-a dalam penganggar Hodges-Lehmann.  Contoh berangka ditunjukkan bagi menerangkan kaedah baru ini. Prestasinya dibandingkan dengan prestasi kaedah Alloway & Raghavachari (1991) menerusi kajian simulasi.

ABSTRACT

This paper develops a modified approach to the computation of control limits and central line for the Hodges-Lehmann control chart proposed by Alloway & Raghavachari (1991).  The modified approach is based on replacing the median of the Walsh averages by the a-trimmed mean, in the Hodges-Lehmann estimator. A numerical example is given to illustrate the use of the modified approach. It is performance is compared with that of Alloway & Raghavachari (1991) using some simulation studies.

RUJUKAN/REFERENCES

Alloway, J.A, Jr. & Raghavachari, M. 1991. Control charts based on the Hodges­ Lehmann estimator. Journal of Quality Technology 23(4): 336-347.

Andrews, D.F., Bickel, P.J., F.R., Huber, P.J .. Rogers, W.H. & Tukey J.W. 1972. Robust estimators of location survey and advances. Princeton: Princeton University Press.

Amin, R.W. & Searcy, A.J. 1991. A nonparametric exponentially weightially moving average control scheme. Communication in Statistics-Simulation and Computation. 20(4): 1049-1072.

Arnold, B.F. 1985. The sign test in current control. Statistishe Hefte 26: 253-262. Arnold, B.F. 1986. Comparison of the approximate and exact optimum economic design of control charts basing on the sign test. Statistische Hefte 27: 239-241.

Bakir, S.T. & Reynold, M.R. 1979. A non parametric procedure for process control. Technometrics 21: 175-183.

Beightler, C.S. & Shamblin, J.E. 1965. Sequential process control. The Journal of Industrial Engineering 16(2): 101-108.

Bickel, P.J. 1965. On some robust estimates of location. The Annals of Mathematical Statistics 36: 847-858.

Bickel, PJ. & Lehmann, E.L. 1975. Descriptive statistics for non-parametric models. The Annals of Statistics 3(5): 1045-1069.

Bowker, A.H. & Liebermann, OJ. 1972. Engineering statistics, 2nd ed. New Jersey: Prentice-Hall, Inc.

Farnum, N.R. & Stanton, L.W. 1986. Using counts to monitor a process mean. Journal of Quality Technology 18: 22-28.

Ford Motor Company. 1987. Continuing process control and process capability improvement. Dearborn: Corporate Quality Education Quality and Training Center, Corporate Quality Office.

Gastwirth, J.L. & Cohen, M.L. 1970. Small sample behaviour of some robust linear estimators of location. Journal of the American Statistical Association-Theory and Methods Section 65(330): 946-973.

Hackl, P. & Ledolter, J. 1991. A control chart based on ranks. Journal of Quality Technology 23: 46-52.

Hackl, P. & Ledolter, J. 1992. A new non parametric quality control technique. Communication in Statistics-Simulation and Computation 21 (2): 423-443.

Hawkins, D.M. 1980. Identification of outliers. New York: Chapman and Hall, Ltd. Hogg, R.Y. 1974. Adaptive robust procedures: Parital review and some suggestions for future applications and theory. Journal of the American Statistical Association 69(348): 909-923.

Hoaglin, D.C., Mostteller, F. & Tukey, J.W. 1983. Understanding robust and exploratory data analysis. New York: John Wiley & Son.

Janacek, G.J & Meikle S.E. 1977. Control charts based on medians. The Statistician 46(1): 19-31.

Koopmans, L.H. 1987. Introduction to contemporary statistical methods. Boston: PWS-KENT.

Lehmann, E.L. 1983. Theory of point estimation. New York: John Wiley & Sons. Mehrotra, K., Jackson, P. & Schick, A. 1991. On choosing an optimally trimmed mean. Communication in Statistic-Simulation and Computation 20(1): 73-80.

Messina, W.S. 1985. Use of Trimmed means in manufacturing production. Proceedings of 14th Measurement Science Conference, pp. 101-105.

Nelson, L.S. 1982. Control charts for medians. Journal of Quality Technology 14(4): 226-227.

Pappanastos, E.A. & Adams, B.M. 1996. Alternative designs of the Hodges-Lehmann control chart. Journal of Quality Technology 28(2): 213-223.

Park, C. & Reynolds. M.R., Jr. 1987. Nonparametric procedures for monitoring a location parameter based on linear palacement statistics. Sequential Analysis 6(4): 303-323.

Reynolds, J.H. 1971. The rin sum control chart procedure. Journal of Quality Technology. 3(2): 23-27.

Rocke, D.M. 1989. Robust control charts. Technometrics 31(2): 173-184. Rosenberger, J.L. & Gasko, M. 1983. Comparing location estimators: trimmed means, medians and trimean. In Hoaglin, D.C., Mosteller, F. & Tukey, J.W. (Eds). Understanding Robust and Exploratory Data Analysis. New York: John Wiley & Sons, 297-338.

Siegel, A.F. 1988. Statistics and data analysis: an introduction. New York: John Wiley & Son.

Stigler, S.M. 1973. The asymptotic distribution of the trimmed mean. The Annals of Statistics, 1:472-477.

Stigler, S.M. 1977. Do robust estimators work with real data? The Annals of Statistics 5(6): 1055-1098.

Tukey, J.W. [960. A survey of sampling from contaminated distributions. In Otkin, I. et al. (Eds), Contributions to Probability and Statistics. Essays in Honor of Harold Hotelling. Stanford: Stanford University Press, 448-485.