A nonparametric exponentially weighted moving average control scheme

A common assumption when evaluating the properties of Exponentially Weighted Moving Average (EWMA) control procedures for controlling the process mean is the observations are normal with known variance. In this article we propose a nonparametric control procedure that can be used when the underlying distribution is not know there is not enough information on the variance or shape of the distribution. Its average run length properties are less affected than the corresponding parametric EWMA procedure when autocorrelation between the observations is present. The procedure nonparametric EWMA procedure is based on Wilcoxon signed-rank statistics ranking is within groups. Our simulation results show that the proposed control procedure is less efficient than the parametric -EWMA procedure when the distribution is not and it can be considerably more efficient than the parametric procedure for heavy- distributions. The proposed procedure is insensitive to misspecification of the van and its ARL properties of the ...

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

[2]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[3]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[4]  W. Shewhart.  The Economic Control of Quality of Manufactured Product. , 1932 .

[5]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[6]  S. Crowder.  A simple method for studying run-length distribution of exponentially weighted moving average charts , 1987 .

[7]  M. R. Reynolds,et al.  Nonparametric procedures for monitoring a location parameter based on linear placement statistics , 1987 .

[8]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[9]  James M. Lucas,et al.  Exponentially weighted moving average control schemes with variable sampling intervals , 1992 .

[10]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[11]  N. L. Johnson,et al.  A Simple Theoretical Approach to Cumulative Sum Control Charts , 1961 .

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

[13]  G. E. Noether.  Introduction to Wilcoxon (1945) Individual Comparisons by Ranking Methods , 1992 .

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

[15]  J. Lucas,et al.  Robust cusum: a robustness study for cusum quality control schemes , 1982 .

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

[17]  Elias Alphonse Parent,et al.  Sequential ranking procedures , 1965 .

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

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

[20]  Ralph A. Bradley,et al.  TWO SEQUENTIAL TWO-SAMPLE GROUPED RANK TESTS WITH APPLICATIONS TO SCREENING EXPERIMENTS. Technical Report No. 3 , 1962 .

[21]  Ralph A. Bradley,et al.  Sequential One-Sample Grouped Signed Rank Tests for Symmetry: Basic Procedures , 1971 .

[22]  H. Toutenburg,et al.  Lehmann, E. L., Nonparametrics: Statistical Methods Based on Ranks, San Francisco. Holden‐Day, Inc., 1975. 480 S., $ 22.95 . , 1977 .

[23]  Small Sample Power of the One Sample Wilcoxon Test for Non-Normal Shift Alternatives , 1965 .

[24]  C. A. McGilchrist,et al.  Note on a Distribution-free CUSUM Technique , 1975 .

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

[26]  Marion R. Reynolds,et al.  A Nonparametric Procedure for Process Control Based on Within-Group Ranking , 1979 .

[27]  Raid W. Amin,et al.  Improved switching rules in control procedures using variable sampling intervals , 1991 .