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

Area of Science:

• Statistical quality control
• Industrial engineering
• Process monitoring

Background:

• Control charts are essential for monitoring production and manufacturing processes.
• Shewhart charts are sensitive to large shifts but assume normality.
• Cumulative Sum (CUSUM) charts excel at detecting smaller shifts and special causes.

Purpose of the Study:

• To evaluate the performance of robust dispersion parameters within a CUSUM control chart framework.
• To investigate novel robust scale estimators using trimming and winsorization.
• To compare the effectiveness of different estimators in detecting process variations.

Main Methods:

• Utilized a CUSUM control chart structure to assess robust dispersion parameters.
• Introduced Median Absolute Deviation (MAD) estimators incorporating trimming (MADTM) and winsorization (MADWM).
• Conducted a simulation study to evaluate Average Run Length (ARL) and Standard Deviation of Run Length (SDRL).

Main Results:

• CUSUM charts demonstrated robustness in detecting small process changes.
• The proposed robust estimators (MADTM, MADWM) showed superior performance across various scenarios.
• Effectiveness was confirmed for both normal and contaminated data distributions.

Conclusions:

• Robust estimators significantly enhance the sensitivity of CUSUM control charts.
• MADTM and MADWM offer improved performance in statistical quality control applications.
• CUSUM charts with robust estimators are highly effective for monitoring manufacturing processes.