On Efficient Monitoring of Process Dispersion using Interquartile Range Shabbir Ahmad 1 , Zhengyan Lin 1 , Saddam Akber Abbasi 2 , Muhammad Riaz 3,4 1 Department of Mathematics, Institute of Statistics, Zhejiang University, 310027, Hangzhou, China 2 Department of Statistics, University of Auckland, New Zealand 3 Department of Statistics, Quaid-i-Azam University, Islamabad Pakistan 4 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia Email: 1 shabbirahmad786@yahoo.com 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 IQR r and IQR p 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. 1. Introduction Statistical Process Control (SPC) is a collection of fundamental tools which are used to monitor process behavior. In the early 1920s Walter A. Shewhart developed control charting as a useful tool of Statistical Process Control (SPC) to monitor process parameters such as location, dispersion etc. The existence of variability is unavoidable in any process and its careful monitoring is necessary to improve the performance of any process. The variability in a process can be classified in two parts namely natural and unnatural. Natural/normal variation has a consistent pattern while unnatural/unusual variation has an unpredictable behavior over the time. The presence of natural variation in a process ensures that the process is in- control state, otherwise out-of-control. Control charts assist differentiating between natural and unnatural variations and hence declaring the process to be in-control or out-of- control. To monitor process variability [1] proposed usual range and standard deviation charts (namely R and S charts). The efficiency of R chart is affected with the increment in sample size where as the performance of S chart becomes poor due to existence of outliers in data (cf. [2]). Later on different estimators of interquartile range (IQR) have been used to establish design structures of dispersion charts such as: [3] and [4] have used interquartile range by restricting the position of lower and upper quartiles as integer, which become cause of some uneven patterns in design structure of control chart. Rocke [5] proposed IQR based R q chart which out performs the R chart for detecting shifts in process dispersion in outlier scenario. To avoid some irregularities of R q chart, [2] proposed a new method of usual IQR chart based on the definition of [6]. Abbasi & Miller [7] compared the performances of different dispersion charts under normally and non-normally distributed environments and concluded that for small sample size the IQR chart exhibits reasonable performance while the performances of R and S charts are significantly influenced for highly skewed process environments. Much of the work related to dispersion control charts may be seen in the bibliographies of the above authors. In this article we have proposed IQR control charts namely IQR r and IQR p charts to monitor the process dispersion in Shewhart setup. These charts are based on ratio and product estimators of lower and upper quartiles of study variable Y using one auxiliary variable X under bivariate normally distributed process. The rest of the article is organized as: Section II provides the design structure of IQR charts based on different quantile estimators considered here. In Section III the performance of IQR charts are investigated under the assumption of normality. An illustrative example is provided in Section IV to justify our proposal and finally the study is concluded with some recommendation in Section V. 2. Quantile Estimators and IQR Charting Structures Let the quality characteristic of interest is Y (e.g. inner diameter of shaft) and X be an auxiliary characteristic (e.g. Open Journal of Applied Sciences Supplement：2012 world Congress on Engineering and Technology Copyright © 2012 SciRes. 39