A Robust Dispersion Control Chart based on Modified Trimmed Standard Deviation
Control Chart is a widely used on-line process control techniques to control variability. This paper focuses on variability due to dispersion of a quality characteristic. Classical methods of estimating parameters of the distribu- tion of quality characteristic may be affected by the presence of outliers. In order to overcome such situation, robust estimators, which are less affected by the extreme values or small departures from the model assumptions, are introduced in industrial application. This article introduced a modification to trimmed standard deviation to increase its efficiency, and is used in con- trolling process dispersion. Authors constructed a phase-I control chart de- rived from standard deviation of trimmed mean, which is robust. Simulation study is conducted to assess its performance at phase-II. This robust control chart is compared with s-chart in terms of its efficiency to detect outliers or assignable causes of variation as well as its Average Run Length.
Abu-Shawiesh, M. O. (2008). A simple robust control chart based on MAD. Journal of Mathematics and Statistics, 4(2), 102.
Adekeye, K. S. (2012). Modified Simple Robust Control Chart Based on Median Absolute Deviation. International Journal of Statistics and Probability, 1(2), p91.
Adekeye, K. S., Azubuike, P. I. (2012). Derivation of the limits for control chart using the median absolute deviation for monitoring non-normal process. Journal of Mathematics and Statistics, 8(1), 37-41.
Capéràa,P., Rivest,L.P.(1995).Onthevarianceofthetrimmedmean.Statistics probability letters, 22(1), 79-85.
Das, N. (2011). Control charts for controlling variability of non-normal processes. Eco- nomic Quality Control, 26(2), 121-131.
Dixon, W. J., Yuen, K. K. (1974). Trimming and winsorization: A review. Statistische Hefte, 15(2-3), 157-170.
Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69(346), 383-393.
Huber, P. J. (1981). Robust Statistics John.
Iglewicz, B., Langenberg, P. (1986). Trimmed mean X-bar and R charts. Journal of Quality Technology, 18(3).
Riaz, M., Saghir, A. (2007). Monitoring process variability using Ginis mean difference. Quality Technology and Quantitative Management, 4(4), 439-454.
Rocke, D. M. (1989). Robust control charts. Technometrics, 31(2), 173-184.
Schoonhoven, M., Does, R. J. (2012). A robust standard deviation control chart. Tech- nometrics, 54(1), 73-82.
Shahriari, H., Maddahi, A., Shokouhi, A. H. (2009). A robust dispersion control chart based on M-estimate. Journal of Industrial and Systems Engineering, 2(4), 297-307.
Sindhumol, M.R., Srinivasan, M.R. (2015). A simple robust dispersion chart based on MMLE, Journal of Mathematics, 11(4), (Accepted for publishing).
Wilcox, R. R. (2012). Introduction to robust estimation and hypothesis testing. Aca- demic Press.
Tukey, J. W. (1948). Some elementary problems of importance to small sample practice. Human Biology, 205-214.
Full Text: pdf