The synthetic control chart based on two sample variances for monitoring the covariance matrix

In this article, we propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance |S| are its faster detection of process changes and its better diagnostic feature, that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the synthetic chart based on the VMAX statistic. The proposed chart is always more efficient than the chart based on the generalized variance |S|. An example is presented to illustrate the application of the proposed chart. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  R. Crosier.  Multivariate generalizations of cumulative sum quality-control schemes , 1988 .

[2]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[3]  Francisco Aparisi,et al.  A comparison of T 2 control charts with variable sampling schemes as opposed to MEWMA chart , 2003 .

[4]  Antonio Fernando Branco Costa,et al.  X̄ charts with variable sample size , 1994 .

[5]  F. Aparisi,et al.  Statistical properties of the lsi multivariate control chart , 1999 .

[6]  H.-J. Huang,et al.  A synthetic control chart for monitoring process dispersion with sample range , 2005 .

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

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

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

[10]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals , 1999 .

[11]  J. B. Keats,et al.  Improving the performance of the multivariate exponentially weighted moving average control chart , 1999 .

[12]  D. He,et al.  Multivariate multiple sampling charts , 2005 .

[13]  R. N. Rattihalli,et al.  Unit and Group-Runs Chart to Identify Increases in Fraction Nonconforming , 2005 .

[14]  George C. Runger,et al.  Designing a Multivariate EWMA Control Chart , 1997 .

[15]  Zhang Wu,et al.  Implementing Synthetic Control Charts for Attributes , 2001 .

[16]  Antonio Fernando Branco Costa,et al.  A Single EWMA Chart for Monitoring Process Mean and Process Variance , 2006 .

[17]  Trevor A Spedding,et al.  A Synthetic Control Chart for Detecting Fraction Nonconforming Increases , 2001 .

[18]  G. Runger,et al.  Multivariate control charts for process dispersion , 2004 .

[19]  W. Woodall,et al.  Multivariate CUSUM Quality- Control Procedures , 1985 .

[20]  H. Moskowitz,et al.  Univariate X¯ control charts for individual characteristics in a multinormal model , 2000 .

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

[22]  Jean-Jacques Daudin,et al.  Double sampling X charts , 1992 .

[23]  Chien-Wei Wu,et al.  A multivariate EWMA control chart for monitoring process variability with individual observations , 2005 .

[24]  Antonio Fernando Branco Costa,et al.  Adaptive control charts: A Markovian approach for processes subject to independent disturbances , 2006 .

[25]  Trevor A Spedding,et al.  Implementing Synthetic Control Charts , 2000 .

[26]  A. Grigoryan,et al.  Multivariate double sampling |S| charts for controlling process variability , 2005 .

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

[28]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[29]  Francisco Aparisi,et al.  Double sampling hotelling's T2 charts , 2008, Qual. Reliab. Eng. Int..

[30]  F. Aparisi,et al.  GENERALIZED VARIANCE CHART DESIGN WITH ADAPTIVE SAMPLE SIZES. THE BIVARIATE CASE , 2001 .

[31]  Zachary G. Stoumbos,et al.  Should Exponentially Weighted Moving Average and Cumulative Sum Charts Be Used With Shewhart Limits? , 2005, Technometrics.

[32]  Elvira N. Loredo,et al.  A Program for ARL Calculation for Multivariate EWMA Charts , 2001 .

[33]  H. J. Huang,et al.  A synthetic control chart for monitoring process dispersion with sample standard deviation , 2005, Comput. Ind. Eng..

[34]  Michael B. C. Khoo,et al.  Optimal Statistical Design of a Multivariate EWMA Chart Based on ARL and MRL , 2006 .