A robust cusum control chart for median absolute deviation based on trimming and winsorization.

Abstract

Statistical quality control is concerned with the analysis of production and manufacturing processes. Control charts are process control techniques, commonly applied to observe and control deviations. Shewhart control charts are very sensitive and used for large shifts based on the basic assumption of normality. Cumulative Sum (CUSUM) control charts are effective for identifying that may have special causes, such as outliers or excessive variability in subgroup means. This study uses a CUSUM control chart problems structure to evaluate the performance of robust dispersion parameters. We investigated the design structure features of various control charts, based on currently defined estimators and some new robust scale estimators using trimming and winsorization in different scenarios. The Median Absolute Deviation based on trimming and winsorization is introduced. The effectiveness of CUSUM control charts based on these estimators is evaluated in terms of average run length (ARL) and Standard Deviation of the Run Length (SDRL) using a simulation study. The results show the robustness of the CUSUM chart in observing small changes in magnitude for both normal and contaminated data. In general, robust estimators MADTM and MADWM based on CUSUM charts outperform in all environments.