A synthetic control chart for monitoring process dispersion with sample standard deviation

Some factors in manufacturing such as faulty raw material, unskilled/careless operators, and loosening of machine settings may lead to a change in process dispersion without necessarily influencing the level of the process mean. This paper proposes a synthetic control chart for monitoring the changes in the standard deviation of a normally distributed process. The synthetic chart is a combination of the sample standard deviation (S) chart and the conforming run length (CRL) chart. The S chart can be regarded as a special case of the synthetic chart. The operation, design, and performance of this chart are described. Average run length comparisons between other procedures and the synthetic chart are presented. It indicates that the synthetic chart is a good alternative for monitoring process dispersion. The variable sampling interval (VSI) schemes as an enhancement to the synthetic chart are discussed to further improve the chart performance. An example is presented to illustrate the application of synthetic chart and its VSI scheme.

[1]  Song Huat Yeo,et al.  A comparative study of the CRL-type control charts , 2000 .

[2]  Muni S. Srivastava.  Cusum procedure for monitoring variability , 1997 .

[3]  Joseph J. Pignatiello,et al.  Monitoring Process Dispersion without Subgrouping , 2000 .

[4]  Maria E. Calzada,et al.  A Note on the Lower-Sided Synthetic Chart for Exponentials , 2003 .

[5]  Morton Klein,et al.  Modified S-charts for controlling process variability , 2000 .

[6]  J. Sheil,et al.  An approach to controlling process variability , 1989 .

[7]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Small Shifts in the Process Mean , 2000 .

[8]  Charles W. Champ,et al.  The Performance of Control Charts for Monitoring Process Variation , 1995 .

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

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

[11]  Thong Ngee Goh,et al.  A COMPARATIVE STUDY OF CCC AND CUSUM CHARTS , 1998 .

[12]  H. Hotelling,et al.  Multivariate Quality Control , 1947 .

[13]  Fah Fatt Gan,et al.  A CUMULATIVE SUM CONTROL CHART FOR MONITORING PROCESS VARIANCE , 1995 .

[14]  Frank B. Alt.  Multivariate Quality Control , 1984 .

[15]  Lloyd S. Nelson,et al.  Column: Technical Aids: Monitoring Reduction in Variation with a Range Chart , 1990 .

[16]  Fah Fatt Gan,et al.  Optimal designs of one-sided ewma charts for monitoring a process variance , 1994 .

[17]  E. S. Page.  Controlling the Standard Deviation by Cusums and Warning Lines , 1963 .

[18]  Patrick D. Bourke,et al.  Detecting a shift in fraction nonconforming using runlength control charts with 100% inspection , 1991 .

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

[20]  William H. Woodall,et al.  Evaluating and Improving the Synthetic Control Chart , 2002 .

[21]  James C. Benneyan,et al.  Statistical Control Charts Based on a Geometric Distribution , 1992 .

[22]  Lloyd S. Nelson,et al.  Control Charts for Individual Measurements , 1982 .

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

[24]  Cesar A. Acosta-Mejia.  Monitoring reduction in variability with the range , 1998 .

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

[26]  Matoteng M. Ncube,et al.  A Comparison of dispersion quality control charts , 1987 .

[27]  CESAR A. Acosta-Mejia,et al.  A comparison of control charting procedures for monitoring process dispersion , 1999 .

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

[29]  G. Jasso.  Review of "International Encyclopedia of Statistical Sciences, edited by Samuel Kotz, Norman L. Johnson, and Campbell B. Read, New York, Wiley, 1982-1988" , 1989 .

[30]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

[31]  Maria E. Calzada,et al.  THE ROBUSTNESS OF THE SYNTHETIC CONTROL CHART TO NON-NORMALITY , 2001 .