A Study on the Robustness of G-Chart to Non-Normality

Abstract

The G-chart is proposed by Riaz and Saghirr (2007) for monitoring the changes in the process variability more efficiently. This study investigates the influence of the parent population on the coefficients of the G-Chart. The appropriate values of the coefficients (b₂ and b₃) has been determined when the distributions of the processes are the normal, exponential, uniform, Laplace, and triangular. The false alarm rate and risk of type II error as performance measures of the G-chart are obtained. The robustness of the G-chart relative to Q- and R_Q-charts is studied. The efficiency of the G-chart relative to those of R-chart for detecting a shift in the process dispersion is examined. The results reveal that the proper attention to the parent population leads to the better performances of the G-chart. The G-chart is more robust than Q-chart and is slightly less efficient than R_Q-chart for detecting outliers. The G-chart is more efficient than R-chart to detect a shift for normal and non-normal processes.

Keywords:

• Exponential distribution
• False alarm rate
• G-chart
• R-chart
• Risk of type II error

Mathematical Subject Classification:

• Primary 62P30
• Secondary 62F10

Acknowledgments

The authors are very thankful to the Editor and referees for their constructive comments that lead to improvements in the structure and results of the paper. This work is financially supported by National Natural Science Foundation of China (11171303) and the specialized Research Fund for Doctor Programme of Higher Education of China (20090101110020).