Robust Individuals Control Chart for Exploratory Analysis

Abstract Apart from their uses in the context of statistical process control, control charts are also used as an exploratory tool in the context of exploratory data analysis. These two application situations are not similar and, as a consequence, control charting methodology should be adjusted to the exploratory context. In this article we make an inventory of the requirements for control charts that are used for exploratory analysis and we propose a procedure that meets these requirements. Robustness against assignable causes of variation appears to be important. The proposed methodology is illustrated from two real-life examples.

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

[2]  Douglas M. Hawkins Robustification of Cumulative Sum Charts by Winsorization , 1993 .

[3]  G. Box,et al.  Cumulative score charts , 1992 .

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

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

[6]  Ronald J. M. M. Does,et al.  Statistical process control in industry , 1998 .

[7]  A. M. Gross Confidence Interval Robustness with Long-Tailed Symmetric Distributions , 1976 .

[8]  Ronald J. M. M. Does,et al.  CUSUM Charts for Preliminary Analysis of Individual Observations , 2000 .

[9]  Michael Stuart,et al.  Understanding Robust and Exploratory Data Analysis , 1984 .

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

[11]  Lewis H. Shoemaker Robustness properties for a class of scale estimators , 1984 .

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

[13]  Amit Mitra,et al.  Statistical Quality Control , 2002, Technometrics.

[14]  Charles P. Quesenberry,et al.  The Effect of Sample Size on Estimated Limits for and X Control Charts , 1993 .

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

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

[17]  D. Lax Robust Estimators of Scale: Finite-Sample Performance in Long-Tailed Symmetric Distributions , 1985 .

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

[19]  D. Ruppert Robust Statistics: The Approach Based on Influence Functions , 1987 .

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

[21]  Russell A. Boyles ESTIMATING COMMON-CAUSE SIGMA IN THE PRESENCE OF SPECIAL CAUSES , 1997 .

[22]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

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

[24]  Marie A. Gaudard,et al.  ESTIMATING THE STANDARD DEVIATION FOR INDIVIDUALS CONTROL CHARTS , 1997 .

[25]  William H. Woodall,et al.  A Control Chart for Preliminary Analysis of Individual Observations , 1996 .