The effect of autocorrelation on the ewma maxmin tolerance limits

Amin et al. (1999) developed an exponentially weighted moving average (EWMA) control chart, based on the smallest and largest observations in each sample. The resulting plot of the extremes suggests that the MaxMin EWMA may also be viewed as smoothed tolerance limits. Tolerance limits are limits that include a specific proportion of the population at a given confidence level. In the context of process control, they are used to make sure that production will not be outside specifications. Amin and Li (2000) provided the coverages of the MaxMin EWMA tolerance limits for independent data. In this article, it is shown how autocorrelation affects the confidence level of MaxMin tolerance limits, for a specified level of coverage of the population, and modified smoothed tolerance limits are suggested for autocorrelated processes.

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

[2]  Douglas C. Montgomery,et al.  Some Statistical Process Control Methods for Autocorrelated Data , 1991 .

[3]  David J. Groggel,et al.  Practical Nonparametric Statistics , 2000, Technometrics.

[4]  Raid W. Amin,et al.  The MaxMin EWMA tolerance limits , 2000 .

[5]  Fred A. Spiring.  Process capability: A total quality management tool , 1995 .

[6]  S. J. Lee,et al.  The Effects of Autocorrelation and Outliers on Two-Sided Tolerance Limits , 1999 .

[7]  Roger M. Sauter,et al.  Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[8]  Edward J. Dudewicz,et al.  Modern Statistical Systems and Gpss Simulation: The First Course , 1990 .

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

[10]  Ronald W. Golland,et al.  Principles of Random Variate Generation , 1990 .

[11]  Layth C. Alwan,et al.  Time-Series Modeling for Statistical Process Control , 1988 .

[12]  William G. Hunter,et al.  Monitoring Sewage Treatment Plants: Some Quality Control Aspects , 1978 .

[13]  Stephen V. Crowder,et al.  An EWMA for Monitoring a Process Standard Deviation , 1992 .

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

[15]  E. Ziegel.  Juran's Quality Control Handbook , 1988 .

[16]  Doan T. Modianos,et al.  Random Number Generation on Microcomputers , 1984 .

[17]  T. Harris,et al.  Statistical process control procedures for correlated observations , 1991 .

[18]  R. Amin,et al.  Process tolerance limits , 2000 .

[19]  Gerald J. Hahn,et al.  Tables for Normal Tolerance Limits, Sampling Plans and Screening , 1981 .

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

[21]  Wolfgang Schmid,et al.  On EWMA Charts for Time Series , 1997 .

[22]  T. W. Anderson,et al.  Statistical analysis of time series , 1972 .

[23]  John M. Howell,et al.  Control Chart for Largest and Smallest Values , 1949 .

[24]  Richard A. Johnson,et al.  The Effect of Serial Correlation on the Performance of CUSUM Tests II , 1974 .

[25]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[26]  A. Vasilopoulos,et al.  Modification of Control Chart Limits in the Presence of Data Correlation , 1978 .

[27]  Wolfgang Schmid,et al.  The influence of parameter estimation on the ARL of Shewhart type charts for time series , 2000 .

[28]  Wolfgang Schmid,et al.  On the run length of a Shewhart chart for correlated data , 1995 .

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

[30]  Emmanuel Yashchin,et al.  Performance of CUSUM control schemes for serially correlated observations , 1993 .

[31]  J. D. T. Oliveira,et al.  The Asymptotic Theory of Extreme Order Statistics , 1979 .