On Efficient Monitoring of Process Dispersion using Interquartile Range

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.

[1]  Muhammad Riaz,et al.  A mean deviation-based approach to monitor process variability , 2009 .

[2]  Antonio Arcos,et al.  Difference estimators of quantiles in finite populations , 2003 .

[3]  Aamir Saghir,et al.  The Use of Probability Limits of COM–Poisson Charts and their Applications , 2013, Qual. Reliab. Eng. Int..

[4]  Ronald J. M. M. Does,et al.  Variables control chart limits and tests for special causes , 1992 .

[5]  H. A. David.  Early sample measures of variability , 1998 .

[6]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[7]  Muhammad Riaz,et al.  A Dispersion Control Chart , 2008, Commun. Stat. Simul. Comput..

[8]  David M. Rocke.  Robust control charts , 1989 .

[9]  Michael B. C. Khoo,et al.  Design of Runs Rules Schemes , 2003 .

[10]  David M. Rocke.  Xq and Rq charts: Robust control charts , 1992 .

[11]  Saddam Akber Abbasi,et al.  On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes , 2012, Qual. Reliab. Eng. Int..

[12]  Sarjinder Singh,et al.  Quantile estimation in two-phase sampling , 2007, Comput. Stat. Data Anal..

[13]  Petros E. Maravelakis,et al.  Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules , 2007 .

[14]  I. Olkin,et al.  Sampling theory of surveys, with applications , 1955 .

[15]  M. D. Martínez-Miranda,et al.  Looking for optimal auxiliary variables in sample survey quantile estimation , 2007 .

[16]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[17]  Lawrence G. Tatum.  Robust estimation of the process standard deviation for control charts , 1997 .

[18]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.