On Efficient Monitoring of Process Dispersion using Interquartile Range

Shabbir Ahmad, Zhengyan Lin, Saddam Akber Abbasi, Muhammad Riaz

Department of Mathematics, Institute of Statistics, Zhejiang University, 310027, Hangzhou, China.
Department of Statistics, Quaid-i-Azam University, Islamabad Pakistan Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia.
Department of Statistics, University of Auckland, New Zealand.

DOI: 10.4236/ojapps.2012.24B010                

Abstract

The presence of dispersion/variability in any process is understood and its careful monitoring may furnish the performance of any process. The interquartile range (IQR) is one of the dispersion measures based on lower and upper quartiles. For efficient monitoring of process dispersion, we have proposed auxiliary information based Shewhart-type IQR control charts (namely IQRr and IQRp charts) based on ratio and product estimators of lower and upper quartiles under bivariate normally distributed process. We have developed the control structures of proposed charts and compared their performances with the usual IQR chart in terms of detection ability of shift in process dispersion. For the said purpose power curves are constructed to demonstrate the performance of the three IQR charts under discussion in this article. We have also provided an illustrative example to justify theory and finally closed with concluding remarks.

Keywords

Auxiliary Information, Bivariate Normal Distribution, Control Carts, Interquartile Range, Lower and Upper Quartiles, Power Curves.

Conflicts of Interest

The authors declare no conflicts of interest.

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