A mean deviation-based approach to monitor process variability

The study proposes a Shewhart-type control chart, namely an MD chart, based on average absolute deviations taken from the median, for monitoring changes (especially moderate and large changes – a major concern of Shewhart control charts) in process dispersion assuming normality of the quality characteristic to be monitored. The design structure of the proposed MD chart is developed and its comparison is made with those of two well-known dispersion control charts, namely the R and S charts. Using power curves as a performance measure, it has been observed that the design structure of the proposed MD chart is more powerful than that of the R chart and is very close competitor to that of the S chart, in terms of discriminatory power for detecting shifts in the process dispersion. The non-normality effect is also examined on design structures of the three charts, and it has been observed that the design structure of the proposed MD chart is least affected by departure from normality.

[1]  G. B. Wetherill,et al.  A Simplified Scheme for the Economic Design of X̄-Charts , 1974 .

[2]  M. F. Ramalhoto,et al.  Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals , 1999 .

[3]  G. B. Wetherill,et al.  A Simplified Scheme for the Economic Design of X-Bar Charts , 1974 .

[4]  J. Tukey.  A survey of sampling from contaminated distributions , 1960 .

[5]  R. Fisher.  A mathematical Examination of the Methods of determining the Accuracy of Observation by the Mean Error, and by the Mean Square Error , 1920 .

[6]  Arthur B. Yeh,et al.  A multivariate exponentially weighted moving average control chart for monitoring process variability , 2003 .

[7]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[8]  Frederick S. Hillier,et al.  X-Bar- and R-Chart Control Limits Based on A Small Number of Subgroups , 1969 .

[9]  Douglas C. Montgomery,et al.  Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[10]  David M. Rocke.  Xq and Rq charts: Robust control charts , 1992 .

[11]  W. K. Chiu,et al.  The Economic Design of Cusum Charts for Controlling Normal Means , 1974 .

[12]  R. F.,et al.  Statistical Method from the Viewpoint of Quality Control , 1940, Nature.

[13]  William H. Woodall,et al.  The Performance of Bootstrap Control Charts , 1998 .

[14]  Egon S. Pearson,et al.  THE PERCENTAGE LIMITS FOR THE DISTRIBUTION OF RANGE IN SAMPLES FROM A NORMAL POPULATION. (n ≤ 100.) , 1932 .

[15]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[16]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[17]  W. Hoeffding,et al.  Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. , 1962 .

[18]  Benjamin M. Adams,et al.  Advanced Topics in Statistical Process Control : The Power of Shewhart's Charts , 1995 .

[19]  The L-Chart for Non-Normal Processes , 2005 .

[20]  H. P.,et al.  Stellar Movements and the Structure of the Universe , 1915, Nature.

[21]  Zhaojun Wang,et al.  THE MEDIAN ABSOLUTE DEVIATIONS AND THEIR APPLICATIONS TO SHEWHART CONTROL CHARTS , 2002 .

[22]  Peter R. Nelson,et al.  Power Curves for the Analysis of Means , 1985 .

[23]  Fah Fatt Gan,et al.  Shewhart Charts for Monitoring the Variance Components , 2004 .

[24]  Enrique del Castillo,et al.  SPC Methods for Quality Improvement , 1999, Technometrics.

[25]  S. Gorard.  REVISITING A 90-YEAR-OLD DEBATE: THE ADVANTAGES OF THE MEAN DEVIATION , 2005 .

[26]  Michael B. C. Khoo,et al.  Alternatives to the Multivariate Control Chart for Process Dispersion , 2004 .

[27]  Eamonn Mullins,et al.  STATISTICAL QUALITY CONTROL AND IMPROVEMENT , 1996 .

[28]  Frank R. Hampel,et al.  Is statistics too difficult? , 1998 .

[29]  Kwok-Leung Tsui,et al.  Run-Length Performance of Regression Control Charts with Estimated Parameters , 2004 .

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

[31]  Sheldon M. Ross,et al.  A Course in Simulation , 1990 .

[32]  Erno Lehtinen,et al.  Difficulties Experienced by Education and Sociology Students in Quantitative Methods Courses , 2003 .

[33]  Glenn J. Battaglia.  Regression-Based Statistical Process Control , 1996 .

[34]  A. Goel,et al.  Determination of A.R.L. and a Contour Nomogram for Cusum Charts to Control Normal Mean , 1971 .

[35]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[36]  Frederick S. Hillier,et al.  Mean and Variance Control Chart Limits Based on a Small Number of Subgroups , 1970 .

[37]  A. Zients.  Andy , 2003 .

[38]  W. A. Shewhart,et al.  Statistical method from the viewpoint of quality control , 1939 .

[39]  Roger G. Schroeder,et al.  A Simultaneous Control Chart , 1987 .

[40]  Lawrence G. Tatum.  Robust estimation of the process standard deviation for control charts , 1997 .

[41]  Steven A. Yourstone,et al.  Non‐Normality and the Design of Control Charts for Averages* , 1992 .

[42]  Nancy Belunis,et al.  Statistical Process Analysis , 2001, Technometrics.

[43]  Benjamin M. Adams,et al.  Alternative Designs of the Hodges-Lehmann Control Chart , 1996 .

[44]  Arthur B. Yeh,et al.  Multivariate Control Charts for Monitoring Covariance Matrix: A Review , 2006 .

[45]  David M. Rocke.  Robust control charts , 1989 .

[46]  L. K. Chan,et al.  Robustness of mean E(X) and R charts , 1988 .

[47]  Lloyd S. Nelson,et al.  Standardization of Shewhart Control Charts , 1989 .

[48]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[49]  Matoteng M. Ncube,et al.  A Comparison of dispersion quality control charts , 1987 .

[50]  CESAR A. Acosta-Mejia,et al.  A comparison of control charting procedures for monitoring process dispersion , 1999 .

[51]  Lloyd S. Nelson,et al.  Column: Technical Aids: The Shewhart Control Chart--Tests for Special Causes , 1984 .

[52]  E. Viles,et al.  Design of R control Chart Assuming a Gamma Distribution , 2001 .

[53]  W. R. Buckland,et al.  Outliers in Statistical Data , 1979 .

[54]  H. Leon Harter,et al.  Tables of Range and Studentized Range , 1960 .

[55]  Yu Ding,et al.  A comparison of process variation estimators for in-process dimensional measurements and control , 2005 .

[56]  Peter R. Nelson,et al.  The Effect of Non-Normality on the Control Limits of X-Bar Charts , 1976 .