A Two-Phase Robust Estimation of Process Dispersion Using M-estimator

Document Type : Research Paper


Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


Parameter estimation is the first step in constructing any control chart. Most estimators of mean and dispersion are sensitive to the presence of outliers. The data may be contaminated by outliers either locally or globally. The exciting robust estimators deal only with global contamination. In this paper a robust estimator for dispersion is proposed to reduce the effect of local contamination when estimating the parameters. The results have shown that the introduced estimator is more precise in estimating the dispersion when there are outliers within the subgroups. Simulation results indicate that robustness and efficiency of the proposed dispersion estimator is considerably high and its sensitivity to the changes in mean and standard deviation of any subgroup is roughly lower than the other estimators being compared.


Main Subjects

[1] Huber P.J. (1981), Robust Statistics; John Wiley; New York.
[2] Langenberg P., Iglewicz B. (1986), Trimmed mean X and R charts; Journal of Quality Technology
18; 152-161.
[3] Maronna A.R. (2006), Robust statistics theory and methods; John Wiley; New York.
[4] Montgomery D.C. (2005), Introduction to statistical quality control; 5th Edition, Wiley; New York.
[5] Omar M. (2008), A simple robust control chart based on MAD; Journal of Mathematics and Statistics
4(2); 102-107.
[6] Rocke D.M. (1989), Robust control charts; Technometrics 31;173–184.
[7] Rocke D.M. (1992), X Q and Q R charts: robust control charts; The Statistician 41; 97-104.
[8] Shahriari H., Maddahi A., Shokouhi A.H. (2009), A robust dispersion control chart based on Mestimate;
Journal of Industrial and system engineering 2; 297-307.
[9] Tatum L.G. (1997), Robust estimation of the process standard deviation for control charts;
Technometrics 39; 127–141.