Nonparametric (distribution-free) control charts: An updated overview and some results

Abstract

Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.

Keywords:

• CUSUM chart
• EWMA chart
• median
• multivariate
• Phase I
• Phase II
• precedence and exceedance statistics
• rank
• robust
• runlength
• Shewhart chart
• sign
• univariate

Acknowledgments

The authors thank the editor and two anonymous reviewers for their comments and suggestions that have improved clarity and presentation.

Additional information

Notes on contributors

S. Chakraborti

S. Chakraborti holds a PhD in Statistics from the State University of New York at Buffalo. He is Professor of Statistics and Robert C. and Rosa P. Morrow Faculty Excellence Fellow in the Department of Information Systems, Statistics and Management Science at the Culverhouse College of Commerce and Business Administration at the University of Alabama, Tuscaloosa. He is a Fellow of the American Statistical Association, an Elected member of the International Statistical Institute and a Fulbright Senior Scholar to South Africa. His specialty areas are Nonparametric and Robust Statistical Inference with applications in areas such as Statistical Process Control, Survival/Reliability Analysis, Econometrics, Statistical Computing, and Extreme Values. He has over one hundred publications in a variety of outlets, including national and international peer-review journals and is a co-author of the book Nonparametric Statistical Inference, fifth edition, published by Marcel Dekker. He has been a visiting professor at a great number of universities abroad, in India, Brazil, France, South Africa and Turkey and has won a number of teaching and research excellence awards. He has been serving as an Associate Editor of Communications in Statistics for over fifteen years. He is a member of the American Statistical Association and the International Statistical Institute. His e-mail address is [email protected].

M. A. Graham

M. A. Graham holds a PhD in Mathematical Statistics from the University of Pretoria, South Africa, and holds a Y1 rating from the National Research Foundation (NRF). She has published in several accredited peer-reviewed journals and has presented her research at national and international conferences. She has supervised over twenty Master's and Ph.D. students and her research interests are in Statistical Process Control and Nonparametric Statistics.