A new adaptive control chart for monitoring process mean and variability

Traditionally, an $\bar{X}$ chart is used to control the process mean, and an R chart is used to control the variance. However, these charts are not sensitive to the small shifts in the processes. The adaptive charts might be considered if the aim is to detect process changes quickly. In this paper, we propose a new adaptive single control chart which integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistics for jointly monitoring both the process mean and variability. This new chart is effective in detecting the disturbances that shift the process mean, increase or decrease the process variance, or lead to a combination of both effects.

[1]  Shashibhushan B. Mahadik,et al.  A special variable sample size and sampling interval Hotelling’s T2 chart , 2011 .

[2]  Zhang Wu,et al.  A SYNTHETIC CONTROL CHART FOR MONITORING THE PROCESS MEAN OF SKEWED POPULATIONS BASED ON THE WEIGHTED VARIANCE METHOD , 2008 .

[3]  Eugenio K. Epprecht,et al.  Th e Non-Central Chi-Square Chart with Double Sampling , 2010 .

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

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

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

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

[8]  Changliang Zou,et al.  A control chart based on likelihood ratio test for monitoring process mean and variability , 2010, Qual. Reliab. Eng. Int..

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

[10]  Antonio Costa,et al.  Statistical design of variable sample size and sampling interval $$\bar X$$ control charts with run rulescontrol charts with run rules , 2006 .

[11]  Douglas M. Hawkins,et al.  Combined Charts for Mean and Variance Information , 2009 .

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

[13]  Antonio Fernando Branco Costa,et al.  Monitoring Process Mean and Variability with One Non-central Chi-square Chart , 2004 .

[14]  James M. Lucas.  Control Schemes for Low Count Levels , 1989 .

[15]  Zhang Wu,et al.  A CUSUM scheme with variable sample sizes for monitoring process shifts , 2007 .

[16]  Antonio Fernando Branco Costa,et al.  An adaptive chart for monitoring the process mean and variance , 2007, Qual. Reliab. Eng. Int..

[17]  Antonio Fernando Branco Costa,et al.  The non-central chi-square chart with two-stage samplings , 2004, Eur. J. Oper. Res..

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

[19]  William H. Woodall,et al.  CUSUM charts with variable sampling intervals , 1990 .

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

[21]  Shashibhushan B. Mahadik.  Charts with Variable Sampling interval and Warning limits , 2014 .

[22]  J Iu.  Combine Median and Range Charts with Variable Sample Sizes and Sampling Intervals , 2004 .

[23]  Raid W. Amin,et al.  A Robustness Study of Charts with Variable Sampling Intervals , 1993 .

[24]  Su-Fen Yang,et al.  Adaptive sampling interval cause-selecting control charts , 2007 .

[25]  Antonio Fernando Branco Costa,et al.  Joint X̄ and R charts with variable parameters , 1998 .

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

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

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

[29]  Changliang Zou,et al.  A New Chart for Detecting the Process Mean and Variability , 2011, Commun. Stat. Simul. Comput..

[30]  Corwin L. Atwood,et al.  Techniques for Uncertainty Analysis of Complex Measurement Processes , 1996 .

[31]  Li De.  Joint and R Chart with Variable Parameters , 2004 .

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

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

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

[35]  Zhang Wu,et al.  An SPRT control chart with variable sampling intervals , 2011 .

[36]  Eugenio K. Epprecht,et al.  A variable sampling interval EWMA chart for attributes , 2010 .

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

[38]  Afb Costa.  (X)OVER-BAR CHARTS WITH VARIABLE SAMPLE-SIZE , 1994 .

[39]  S. Albin,et al.  An X and EWMA chart for individual observations , 1997 .

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

[41]  A. A. Kalgonda.  Exponentially Weighted Moving Average Control Chart , 2013 .

[42]  James M. Lucas,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start , 2000, Technometrics.

[43]  Yan-Kwang Chen.  Economic design of X̄ control charts for non-normal data using variable sampling policy , 2004 .

[44]  Giovanni Celano,et al.  Statistical design of variable sample size and sampling interval , control charts with run rules , 2006 .

[45]  Ronald B. Crosier,et al.  Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start.: Give Your CUSUM A Head Start. , 2000 .