Adjusted-loss-function charts with variable sample sizes and sampling intervals

Recent research has shown that the control charts with adaptive features are quicker than the traditional static Shewhart charts in detecting process shifts. This article presents the design and implementation of a control chart based on Adjusted Loss Function (AL) with Variable Sample Sizes and Sampling Intervals (VSSI). This single chart (called the VSSI AL chart) is able to monitor the process shifts in mean and variance simultaneously. Our studies show that the VSSI AL chart is not only easier to design and implement than the VSSI X¯ & S (or X¯ & R) charts, but is also 10% more effective than the latter in detecting the process shifts from an overall viewpoint.

[1]  M. R. Reynolds,et al.  The SPRT chart for monitoring a proportion , 1998 .

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

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

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

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

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

[7]  TAPAS K. DAS,et al.  Economic design of dual-sampling-interval policies for X¯ charts with and without run rules , 1997 .

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

[9]  Fred A. Spiring,et al.  A General Class of Loss Functions with Industrial Applications , 1998 .

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

[11]  Marion R. Reynolds,et al.  Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals , 2001 .

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

[13]  Antonio Fernando Branco Costa,et al.  X̄ Charts with Variable Parameters , 1999 .

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

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

[16]  Joseph J. Pignatiello,et al.  Estimation of the Change Point of a Normal Process Mean in SPC Applications , 2001 .

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

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

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

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

[21]  Acheson J. Duncan,et al.  The Economic Design of X Charts Used to Maintain Current Control of a Process , 1956 .

[22]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals , 1995 .

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