Ch. 13. Control chart schemes for monitoring the mean and variance of processes subject to sustained shifts and drifts

We consider control chart schemes for detecting sustained shifts and drifts in the process mean μ and process standard deviation σ, when individual observations are sampled from the process. The standard Shewhart X chart and moving range (MR) chart are contrasted with several types of exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts and with combinations of charts involving the EWMA charts or the CUSUM charts. The combinations involving the EWMA charts or the CUSUM charts are convenient to implement on-line and can detect small shifts and slow-rate drifts in μ and/or σ much faster than the traditional Shewhart X and MR charts.

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

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

[3]  E. Yashchin.  Statistical Control Schemes: Methods, Applications and Generalizations , 1993 .

[4]  Douglas C. Montgomery,et al.  A Discussion on Statistically-Based Process Monitoring and Control , 1997 .

[5]  G. Geoffrey Vining,et al.  Statistical process monitoring and optimization , 2000 .

[6]  Marion R. Reynolds,et al.  The Robustness and Performance of CUSUM Control Charts Based on the Double-Exponential and Normal Distributions , 2004 .

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

[8]  Marion R. Reynolds,et al.  Some Recent Developments in Control Charts for Monitoring a Proportion , 1999 .

[9]  Marion R. Reynolds,et al.  Individuals control schemes for monitoring the mean and variance of processes subject to drifts , 2001 .

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

[11]  Marion R. Reynolds,et al.  The SPRT control chart for the process mean with samples starting at fixed times , 2001 .

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

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

[14]  Raid W. Amin,et al.  An EWMA Quality Control Procedure for Jointly Monitoring the Mean and Variance , 1993 .

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

[16]  S. Chakraborti,et al.  Nonparametric Control Charts: An Overview and Some Results , 2001 .

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

[18]  Ronald J. M. M. Does,et al.  Shewhart-Type Control Charts for Individual Observations , 1993 .

[19]  William H. Woodall,et al.  Control Charts Based on Attribute Data: Bibliography and Review , 1997 .

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

[21]  Fah Fatt Gan,et al.  Ewma control chart under linear drift , 1991 .

[22]  Dulal K. Bhaumik,et al.  Statistical Methods for Groundwater Monitoring , 1994 .

[23]  J. Macgregor,et al.  The exponentially weighted moving variance , 1993 .

[24]  Douglas C. Montgomery,et al.  Research Issues and Ideas in Statistical Process Control , 1999 .

[25]  Charles W. Champ,et al.  Design Strategies for Individuals and Moving Range Control Charts , 1994 .

[26]  Andrew C. Gross,et al.  Statistics in the 21st Century , 1996 .

[27]  William H. Woodall,et al.  The State of Statistical Process Control as We Proceed into the 21st Century , 2000 .

[28]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[29]  George C. Runger,et al.  Steady-state-optimal adaptive control charts based on variable sampling intervals , 2001 .

[30]  Charles W. Champ,et al.  Evaluation of control charts under linear trend , 1991 .

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

[32]  A. F. Bissell,et al.  The Performance of Control Charts and Cusums Under Linear Trend , 1984 .

[33]  H. Lenz,et al.  Frontiers in Statistical Quality Control 2. , 1984 .

[34]  Raid W. Amin,et al.  A Note on Individual and Moving Range Control Charts , 1998 .

[35]  Marion R. Reynolds,et al.  Robustness to non-normality and autocorrelation of individuals control charts , 2000 .

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

[37]  Zachary G. Stoumbos.  Control charts applying a sequential test at fixed sampling intervals with optional sampling at fixed times , 1993 .

[38]  Thomas P. Ryan,et al.  Statistical methods for quality improvement , 1989 .

[39]  Lloyd S. Nelson,et al.  Control Charts for Individual Measurements , 1982 .

[40]  William H. Woodall,et al.  Controversies and Contradictions in Statistical Process Control , 2000 .