Monitoring the Coefficient of Variation Using a Variable Sampling Interval Control Chart

The coefficient of variation (CV) is a quality characteristic that has several applications in applied statistics and is receiving increasing attention in quality control. Few papers have proposed control charts that monitor this normalized measure of dispersion. In this paper, an adaptive Shewhart control chart implementing a variable sampling interval (VSI) strategy is proposed to monitor the CV. Tables are provided for the statistical properties of the VSI CV chart, and a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV. An example illustrates the use of these charts on real data gathered from a casting process. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  W. G. Warren.  On the adequacy of the chi-squared approximation for the coefficient of variation , 1982 .

[2]  Marion R. Reynolds,et al.  Chart with runs and variable sampling intervals , 1988 .

[3]  Philippe Castagliola,et al.  The variable sampling interval X̄ chart with estimated parameters , 2012, Qual. Reliab. Eng. Int..

[4]  Marion R. Reynolds,et al.  Variable sampling intervals for multiparameter shewhart charts , 1989 .

[5]  S. Fichera,et al.  Evaluation of the Statistical Performance of a Variable Sampling Interval R EWMA Control Chart , 2006 .

[6]  Giovanni Celano,et al.  Monitoring the Coefficient of Variation Using EWMA Charts , 2011 .

[7]  James M. Lucas,et al.  Exponentially weighted moving average control schemes with variable sampling intervals , 1992 .

[8]  A. T. McKay,et al.  Distribution of the Coefficient of Variation and the Extended “T” Distribution , 1932 .

[9]  Boris Iglewicz,et al.  Comparisons of Approximations to the Percentage Points of the Sample Coeffcient of Variation , 1970 .

[10]  Maria E. Calzada,et al.  A synthetic control chart for the coefficient of variation , 2013 .

[11]  Walter A. Hendricks,et al.  The Sampling Distribution of the Coefficient of Variation , 1936 .

[12]  Lili Tian,et al.  Inferences on the common coefficient of variation , 2005, Statistics in medicine.

[13]  William H. Woodall,et al.  CUSUM charts with variable sampling intervals , 1990 .

[14]  Douglas C. Montgomery,et al.  ADAPTIVE SAMPLING ENHANCEMENTS FOR SHEWHART CONTROL CHARTS , 1993 .

[15]  George C. Runger,et al.  Adaptative sampling for process control , 1991 .

[16]  Marion R. Reynolds.  Shewhart and EWMA Variable Sampling Interval Control Charts with Sampling at Fixed Times , 1996 .

[17]  Raymond H. Myers,et al.  On the percentage points of the sample coefficient of variation , 1968 .

[18]  Raid W. Amin,et al.  A Robustness Study of Charts with Variable Sampling Intervals , 1993 .

[19]  J. A. Nachlas,et al.  X charts with variable sampling intervals , 1988 .

[20]  Wolfgang Reh,et al.  Significance tests and confidence intervals for coefficients of variation , 1996 .

[21]  Douglas M. Hawkins,et al.  A Control Chart for the Coefficient of Variation , 2007 .

[22]  Marion R. Reynolds,et al.  Optimal one-sided shewhart control charts with variable sampling intervals , 1989 .

[23]  P. Castagliola,et al.  A variable sampling interval S2-EWMA control chart for monitoring the process variance , 2007, Int. J. Technol. Manag..

[24]  George F. Reed,et al.  Use of Coefficient of Variation in Assessing Variability of Quantitative Assays , 2002, Clinical and Vaccine Immunology.

[25]  Amal K. Shamma,et al.  A double exponentially weigiited moving average control procedure with variable sampling intervals , 1991 .

[26]  George Tagaras.  A Survey of Recent Developments in the Design of Adaptive Control Charts , 1998 .

[27]  Francisco Aparisi,et al.  Hotelling's T2 control chart with variable sampling intervals , 2001 .

[28]  Steve P. Verrill,et al.  Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation , 2007 .

[29]  Rahim Mahmoudvand,et al.  Two new confidence intervals for the coefficient of variation in a normal distribution , 2009 .

[30]  W. Sharpe.  The Sharpe Ratio , 1994 .