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Modified Tukey's Control Chart
Authors:Victor Tercero-Gomez  Jose Ramirez-Galindo  Alavarado Cordero-Franco  Milton Smith  Mario Beruvides
Institution:1. Department of Industrial Engineering , Texas Tech University , Lubbock , Texas , USA victor.tercero@ttu.edu;3. Department of Industrial Engineering , Texas Tech University , Lubbock , Texas , USA;4. Facultad de Ciencias Fisico Mathematics , Universidad Autonoma de Nuevo Leon, San Nicolas de los Garza , Nuevo Leon , Mexico
Abstract:Phase I of control analysis requires large amount of data to fit a distribution and estimate the corresponding parameters of the process under study. However, when only individual observations are available, and no a priori knowledge exists, the presence of outliers can bias the analysis. A relatively recent and successful approach to address this situation is Tukey's Control Chart (TCC), a charting method that applies the Box Plot technique to estimate the control limits. This procedure has proven to be effective for symmetric distributions. However, when skewness is present the average run length performance diminishes significantly. This article proposes a modified version of TCC to consider skewness with minimum assumptions on the underlying distribution of observations. Using theoretical results and Monte Carlo simulation, the modified TCC is tested over several distributions proving a better representation of skewed populations, even in cases when only a limited number of observations are available.
Keywords:Average run length  Box plot  Skewness  Tukey's control chart
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