Robustification of CUSUM control structure for monitoring location shift of skewed distributions based on modified one-step M-estimator

Abstract

Including three existing charts, a new approach employing a modified one-step M-estimator (MOM) with Cumulative Sum (CUSUM) control structure were evaluated and compared for their Phase II performances based on the average run length (ARL) under various skewed distributions. The primary focus was on the robustness of the CUSUM charts in two separate cases: (i) when the process parameters are known and (ii) when the process mean is unknown and estimated from an in-control Phase I sample. The simulation and real data analysis showed the proposed technique is comparable or sometimes better than the existing charts.

Keywords:

• CUSUM chart
• Average run length
• Skewed distributions
• Process location
• MOM

Acknowledgments

The authors would like to acknowledge the work that led to this paper is supported Fundamental Research Grant Scheme (S/0 CODE 13578) of the Utara Malaysia and Ministry of Higher Education, Malaysia. The authors are grateful for the reviewer’s careful reading of the manuscript and constructive comments for improvement.