Hotelling’s T2 control chart with double warning lines

Recent studies have shown that the T2 control chart with variable sampling intervals (VSI) and/or variable sample sizes (VSS) detects process shifts faster than the traditional T2 chart. This article extends these studies for processes that are monitored with VSI and VSS using double warning lines (T2—DWL). It is assumed that the length of time the process remains in control has exponential distribution. The properties of T2—DWL chart are obtained using Markov chains. The results show that the T2—DWL chart is quicker than VSI and/or VSS charts in detecting almost all shifts in the process mean.

[1]  J. E. Jackson.  Multivariate quality control , 1985 .

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

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

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

[5]  James W. Liddy,et al.  A note on multivariate capability indices , 1993 .

[6]  George C. Runger,et al.  Comparison of multivariate CUSUM charts , 1990 .

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

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

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

[10]  J. B. Keats,et al.  X¯ chart with adaptive sample sizes , 1993 .

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

[12]  D. Montgomery,et al.  A Combined Adaptive Sample Size and Sampling Interval X Control Scheme , 1994 .

[13]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[14]  Marion R. Reynolds,et al.  Variable-sampling-interval control charts with sampling at fixed times , 1996 .

[15]  Francis Bernard Alt.  Aspects of multivariate control charts , 1973 .

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

[17]  Marion R. Reynolds,et al.  Variable Sampling Interval X Charts in the Presence of Correlation , 1996 .

[18]  Antonio Fernando Branco Costa,et al.  X̄ Chart with Variable Sample Size and Sampling Intervals , 1997 .

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

[20]  이경택,et al.  Variable Sampling Interval x Control Charts with An Improved Switching Rule , 1997 .

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

[22]  Marion R. Reynolds,et al.  EWMA control charts with variable sample sizes and variable sampling intervals , 2001 .

[23]  Wang Min.  Defective unit control chart with variable sampling intervals , 2003 .

[24]  Francisco Aparisi,et al.  Hotelling's T2 control chart with adaptive sample sizes , 1996 .

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

[26]  Changsoon Park,et al.  Economic Design of a Variable Sampling Rate X-bar Chart , 1999 .

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

[28]  F. Aparisi.  SAMPLING PLANS FOR THE MULTIVARIATE T 2 CONTROL CHART , 1997 .

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

[30]  J. Edward Jackson,et al.  Quality Control Methods for Several Related Variables , 1959 .

[31]  Irving W. Burr,et al.  Control Charts for Measurements with Varying Sample Sizes , 1969 .

[32]  George C. Runger,et al.  A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart , 1996 .

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

[34]  Douglas C. Montgomery,et al.  Evaluation of a three-state adaptive sample size X control chart , 1998 .