A Robust Standard Deviation Control Chart

Abstract

This article studies the robustness of Phase I estimators for the standard deviation control chart. A Phase I estimator should be efficient in the absence of contaminations and resistant to disturbances. Most of the robust estimators proposed in the literature are robust against either diffuse disturbances, that is, outliers spread over the subgroups, or localized disturbances, which affect an entire subgroup. In this article, we compare various robust standard deviation estimators and propose an algorithm that is robust against both types of disturbances. The algorithm is intuitive and is the best estimator in terms of overall performance. We also study the effect of using robust estimators from Phase I on Phase II control chart performance. Additional results for this article are available online as Supplementary Material.

Keywords:

• Average run length
• Mean squared error
• Phase I
• Phase II
• Statistical process control.

Supplementary material

Figures S1– S4 and Tables S1– S3.

Acknowledgments

The authors are very grateful to the Editor, the Associate Editor, and a referee for their helpful comments, which led to improvements in this article.