Comparison of Robust Estimators of Standard Deviation in Normal Distributions Within the Context of Quality Control

Abstract

Pitman criterion is used in simulation to determine the “closer” estimator of the standard deviation among selected choices. The initial simulation utilizes a standard normal distribution from which samples are taken of specific sizes. Popular and commonly used estimators of standard deviation are compared with the known population standard deviation in this study. Closeness criterion is calculated for each comparison and sample size. A secondary simulation applies the findings to variables control charts, in order to verify the ability of each estimator to identify out-of-control conditions.

Keywords:

• Closeness
• Estimation
• Quality control
• Range
• Standard deviation

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62P30

Acknowledgments

The authors would like to thank the reviewers and editors for their suggestions and recommendations which have greatly enhanced the quality of this article, and Dr. William Woodall for his review of an early draft and helpful suggestions.

Notes

†Passed away while working on project.