Adaptive EWMA control charts with time-varying smoothing parameter

Time-weighted charts like EWMA or CUSUM are designed to be optimal to detect a specific shift. This feature, however, can make the chart suboptimal for some other shifts.If, for instance, the charts are designed to detect a small shift, then, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to circumvent this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper aims to propose new adaptive EWMA control charts (AEWMA) based on the assessment of a potential misadjustment, which is translated into a time-varying smoothing parameter. The resulting control charts can be seen as a smooth combination between Shewhart and EWMA control charts, which could be efficient for a wide range of shifts. Markov chain procedures are established to analyse and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of our proposals.

[1]  Zhonghua Li,et al.  A new adaptive control chart for monitoring process mean and variability , 2012 .

[2]  Giovanni Celano,et al.  Monitoring the coefficient of variation using a variable sample size control chart , 2015, The International Journal of Advanced Manufacturing Technology.

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

[4]  William H. Woodall,et al.  THE STATISTICAL DESIGN OF CUSUM CHARTS , 1993 .

[5]  William H. Woodall,et al.  Performance of the Control Chart Trend Rule under Linear Shift , 1988 .

[6]  Michael B. C. Khoo,et al.  Two Improved Runs Rules for the Shewhart X¯ Control Chart , 2006 .

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

[8]  J. Stuart Hunter,et al.  The exponentially weighted moving average , 1986 .

[9]  Marion R. Reynolds,et al.  Corrected diffusion theory approximations in evaluating properties of SPRT charts for monitoring a process mean , 1997 .

[10]  Douglas M. Hawkins.  A fast accurate approximation for average run lengths of CUSUM control charts , 1992 .

[11]  Stefan H. Steiner.  Exponentially Weighted Moving Average Control Charts with Time-Varying Control Limits and Fast Initial Response , 1998 .

[12]  Stephen V. Crowder,et al.  Design of Exponentially Weighted Moving Average Schemes , 1989 .

[13]  Robert V. Baxley,et al.  An Application of Variable Sampling Interval Control Charts , 1995 .

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

[15]  Ross Sparks,et al.  CUSUM Charts for Signalling Varying Location Shifts , 2000 .

[16]  E. S. Page.  A test for a change in a parameter occurring at an unknown point , 1955 .

[17]  P. Robinson,et al.  Average Run Lengths of Geometric Moving Average Charts by Numerical Methods , 1978 .

[18]  J. Everett.  The exponentially weighted moving average applied to the control and monitoring of varying sample sizes , 2011 .

[19]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[20]  Wei Jiang,et al.  Adaptive CUSUM procedures with Markovian mean estimation , 2008, Comput. Stat. Data Anal..

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

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

[23]  Emmanuel Yashchin,et al.  Some aspects of the theory of statistical control schemes , 1987 .

[24]  E. S. Page.  CONTROL CHARTS WITH WARNING LINES , 1955 .

[25]  Wei Jiang,et al.  Adaptive CUSUM procedures with EWMA-based shift estimators , 2008 .

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

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

[28]  J. Bert Keats,et al.  Statistical Process Control Scheme Design , 1995 .

[29]  S. Crowder.  Average Run Lengths of Exponentially Weighted Moving Average Control Charts , 1987 .

[30]  Ying Zhang,et al.  The Variable Sample Size X¯ Chart with Estimated Parameters , 2012, Qual. Reliab. Eng. Int..

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

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

[33]  Stelios Psarakis,et al.  Adaptive Control Charts: Recent Developments and Extensions , 2015, Qual. Reliab. Eng. Int..

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

[35]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[36]  John H . Reynolds,et al.  The Run Sum Control Chart Procedure , 1971 .

[37]  Marion R. Reynolds,et al.  Control charts applying a general sequential test at each sampling point , 1996 .

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

[39]  C. A. Acosta-Mejia,et al.  Two Sets of Runs Rules for the Chart , 2007 .

[40]  Sheldon M. Ross,et al.  Statistical Aspects of Quality Control , 1996 .

[41]  Petros E. Maravelakis,et al.  Statistical Process Control using Shewhart Control Charts with Supplementary Runs Rules , 2007 .

[42]  Dong Han,et al.  A CUSUM CHART WITH LOCAL SIGNAL AMPLIFICATION FOR DETECTING A RANGE OF UNKNOWN SHIFTS , 2007 .

[43]  J. Tukey,et al.  The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data , 1974 .

[44]  Morton Klein,et al.  Two Alternatives to the Shewhart X̄ Control Chart , 2000 .

[45]  Douglas M. Hawkins.  CUMULATIVE SUM CONTROL CHARTING: AN UNDERUTILIZED SPC TOOL , 1993 .

[46]  Shaomin Wu.  Optimal inspection policy for three-state systems monitored by variable sample size control charts , 2011 .

[47]  W Zhang.  Variable Sampling Interval Control Charts with Sampling at Fixed Times , 2002 .

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

[49]  Gyo-Young Cho,et al.  CUSUM charts with variable sampling intervals , 2009 .

[50]  S. W. Roberts,et al.  Control Chart Tests Based on Geometric Moving Averages , 2000, Technometrics.

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

[52]  Athanasios C. Rakitzis,et al.  The Revised m-of-k Runs Rule , 2007 .

[53]  K. Waldmann,et al.  Bounds for the Distribution of the Run Length of Geometric Moving Average Charts , 1986 .

[54]  S. W. Roberts.  Control chart tests based on geometric moving averages , 2000 .

[55]  Chun-ping Wang.  Control charts with warning lines for dynamic baseline and its appllication in birth defects monitoring. , 2000 .

[56]  Fugee Tsung,et al.  A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes , 2003 .

[57]  Amirhossein Amiri,et al.  A New Adaptive Variable Sample Size Approach in EWMA Control Chart , 2014, Commun. Stat. Simul. Comput..

[58]  Wei Jiang,et al.  A Markov Chain Model for the Adaptive CUSUM Control Chart , 2006 .

[59]  William H. Woodall,et al.  A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated , 2015, Qual. Reliab. Eng. Int..

[60]  Khalifa N. Al-Khalifa,et al.  Adaptive cumulative sum charts with the adaptive runs rule , 2013 .

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

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

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

[64]  Marion R. Reynolds,et al.  Evaluating properties of variable sampling interval control charts , 1995 .

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

[66]  Robert B. Davis,et al.  Performance of the zone control chart , 1990 .

[67]  Abdel-Salam G. Abdel-Salam,et al.  The Performance of the Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters , 2013, Qual. Reliab. Eng. Int..

[68]  D. C. Montgomery,et al.  Statistical Process Control Methods for Detecting Small Process Shifts , 1987 .

[69]  Shashibhushan B. Mahadik.  X¯ Charts with Variable Sample Size, Sampling Interval, and Warning Limits , 2013, Qual. Reliab. Eng. Int..

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

[71]  Dja Shin Wang,et al.  Variable sample size control chart for monitoring process capability index Cpm , 2016, International Journal of Industrial and Systems Engineering.

[72]  Lianjie Shu,et al.  An adaptive exponentially weighted moving average control chart for monitoring process variances , 2008 .

[73]  Charles W. Champ,et al.  Exact results for shewhart control charts with supplementary runs rules , 1987 .

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

[75]  Lonnie C. Vance.  Computer Programs: Average Run Lengths of Cumulative Sum Control Charts for Controlling Normal Means , 1986 .

[76]  Ying Liu,et al.  An enhanced adaptive CUSUM control chart , 2009 .