Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals

Recent research has shown that adaptive control charts and the CUmulative SUM (CUSUM) schemes are quicker in detecting process shifts than traditional static Shewhart charts. This article proposes a weighted loss function CUSUM (WLC) scheme with Variable Sampling Intervals (VSI). It simultaneously monitors both mean shifts and an increasing variance shift by manipulating a single CUSUM chart. Most importantly, this VSI WLC scheme is much easier to operate and design than a VSI CCC scheme which comprises of three CUSUM charts (two of them monitoring the increasing and decreasing mean shifts and one monitoring the increasing variance shift). In terms of detection efficiency, the VSI WLC scheme is a much more powerful tool than the static X&S chart, the VSI X&S chart and the static WLC scheme. It is even more powerful than the VSI CCC scheme for many different combinations of mean and increasing variance shifts.

[1]  Marion R. Reynolds,et al.  CUSUM Control Charts with Variable Sample Sizes and Sampling Intervals , 2001 .

[2]  Marion R. Reynolds,et al.  Control Charts and the Efficient Allocation of Sampling Resources , 2004, Technometrics.

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

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

[5]  Smiley W. Cheng,et al.  Monitoring Process Mean and Variability with One EWMA Chart , 2001 .

[6]  Dov Ingman,et al.  Adaptive Control Limits for Bivariate Process Monitoring , 1996 .

[7]  Marion R. Reynolds,et al.  Should Observations Be Grouped for Effective Process Monitoring? , 2004 .

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

[9]  Robert V. Baxley,et al.  EWMA Control Charts for the Smallest and Largest Observations , 1999 .

[10]  Zhang Wu,et al.  Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart , 2004 .

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

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

[13]  Robert O'donnell,et al.  Statistical Aspects of Quality Control , 1996 .

[14]  Yu Tian,et al.  Optimization design of the charts for monitoring process capability , 2002 .

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

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

[17]  Yu Tian,et al.  Weighted-loss-function CUSUM chart for monitoring mean and variance of a production process , 2005 .

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

[19]  Wu Zhang,et al.  Optimization of joint X and S control charts with asymmetric control limits , 1997 .

[20]  Ken Nishina,et al.  A comparison of control charts from the viewpoint of change‐point estimation , 1992 .

[21]  Yu Tian,et al.  Adjusted-loss-function charts with variable sample sizes and sampling intervals , 2005 .

[22]  F. Gan.  Joint monitoring of process mean and variance using exponentially weighted moving average control charts , 1995 .

[23]  William H. Woodall,et al.  A Control Chart for Preliminary Analysis of Individual Observations , 1996 .

[24]  Rickie J. Domangue,et al.  Some omnibus exponentially weighted moving average statistical process monitoring schemes , 1991 .

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