A class of distribution‐free control charts

A class of Shewhart-type distribution-free control charts is considered. A key advantage of these charts is that the in-control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart "X" -chart. A numerical illustration is given. Copyright 2004 Royal Statistical Society.

[1]  Karen A. F. Copeland.  Cumulative Sum Charts and Charting for Quality Improvement , 1999 .

[2]  Stephen Wolfram,et al.  The Mathematica book (3rd ed.) , 1996 .

[3]  S. Chakraborti,et al.  Precedence tests for right-censored data : an overview and some results , 1996 .

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

[5]  G. J. Janacek,et al.  Control charts based on medians , 1997 .

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

[7]  M. R. Reynolds,et al.  Nonparametric quality control charts based on the sign statistic , 1995 .

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

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

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

[11]  Harold C. Mathisen.  A Method of Testing the Hypothesis that Two Samples are from the Same Population , 1943 .

[12]  M. C. Jones,et al.  3. Nonparametric Statistical Inference , 1993 .

[13]  Subhabrata Chakraborti.  Run length, average run length and false alarm rate of shewhart x-bar chart: exact derivations by conditioning , 2000 .

[14]  S. Chakraborti,et al.  An Overview of Precedence‐Type Tests for Censored Data , 1997 .

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

[16]  Lloyd S. Nelson,et al.  Tests on early failures: the precedence life test , 1993 .

[17]  Erich L. Lehmann,et al.  The Power of Rank Tests , 1953 .

[18]  Connie M. Borror,et al.  Robustness of the EWMA Control Chart to Non-Normality , 1999 .

[19]  Lloyd S. Nelson,et al.  Tables for a Precedence Life Test , 1963 .

[20]  P Laanvander,et al.  Precedence tests and confidence bounds for complete data : an overview and some results , 1994 .