Robust Control Charts based on Modified Trimmed Standard Deviation and Gini’s Mean Difference

M.R. SINDHUMOL
M.R. SRINIVASAN
Michele GALLO

Keywords

Control chart, Trimmed mean, Modified Trimmed Standard deviation, Gini’s Mean Deviation, Outlier, Average Run Length, Operation Characteristic Curve

Abstract

Control Charts are process control techniques widely used to observe and control deviations and to enhance the quality of the product. Traditional control charts are based on the assumption that process data are independent in nature. Shewhart control charts are well known and are based on the basic assumption of normality. If process parameters are used to construct control limits based on preliminary samples, stability of the limits needs to be established as presence of outliers may affect the setting of control limits. In this paper an attempt has been made to first develop robust control charts based on trimmed mean and modified trimmed standard deviation. Secondly, an estimate of process standard deviation using Gini’s Mean Difference (G) is also considered to modify the mean chart. Lastly, a comparative study is carried out to evaluate the performance of these two proposed robust charts with existing robust -MAD chart and two classical control charts namely -s chart and its modified -sv chart, based on simulated data. Simulation study is also considered for performance evaluation of the proposed charts with other charts based on Average Run Length (ARL) and Operation Characteristic (OC) curves. In addition to the simulation, real data set is also used for setting up of robust control limits.