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

doi:10.1080/08982112.2018.1549330

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

Journal Article•DOI•

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

Subhabrata Chakraborti¹, Marien Alet Graham²•Institutions (2)

University of Alabama¹, University of Pretoria²

03 May 2019-Quality Engineering (Taylor & Francis)-Vol. 31, Iss: 4, pp 523-544

TL;DR: Both univariate and multivariate nonparametric control charts are reviewed, unlike the past reviews, which did not include the multivariate charts, here they are reviewed.

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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 the...

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Journal Article•DOI•

Big Data? Statistical Process Control Can Help!

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Peihua Qiu¹•Institutions (1)

University of Florida¹

03 Jan 2020-The American Statistician

TL;DR: It is believed that SPC can become a powerful tool for handling many big data applications that are beyond the production line monitoring, and some recent SPC methods are introduced and their potential to solve some big data problems are discussed.

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Abstract: “Big data” is a buzzword these days due to an enormous amount of data-rich applications in different industries and research projects. In practice, big data often take the form of data streams in t...

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32 citations

Cites background from "Nonparametric (distribution-free) c..."

...For recent overviews on this topic, see Chakraborti and Graham (2019) and Qiu (2018)....
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Journal Article•

Nonparametric monitoring of data strems for changes in location and scale

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Gordon J. Ross, Dimitris K. Tasoulis, Niall M. Adams

01 Jan 2013-Quality Engineering

TL;DR: In this paper, a framework for detecting changes in data streams when the distributional form of the stream variables is unknown is developed, based on hypothesis tests which involve ranking data points and a method for calculating these ranks online in a manner which respects the constraints of data stream analysis.

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Abstract: The analysis of data streams requires methods which can cope with a very high volume of data points. Under the requirement that algorithms must have constant computational complexity and a fixed amount of memory, we develop a framework for detecting changes in data streams when the distributional form of the stream variables is unknown. We consider the general problem of detecting a change in the location and/or scale parameter of a stream of random variables, and adapt several nonparametric hypothesis tests to create a streaming change detection algorithm. This algorithm uses a test statistic with a null distribution independent of the data. This allows a desired rate of false alarms to be maintained for any stream even when its distribution is unknown. Our method is based on hypothesis tests which involve ranking data points, and we propose a method for calculating these ranks online in a manner which respects the constraints of data stream analysis.

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23 citations

Journal Article•DOI•

An overview of synthetic-type control charts : techniques and methodology

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Athanasios C. Rakitzis¹, Subhabrata Chakraborti², Subhabrata Chakraborti³, Sandile Charles Shongwe³, Marien Alet Graham³, Michael B. C. Khoo⁴ - Show less +2 more•Institutions (4)

University of the Aegean¹, University of Alabama², University of Pretoria³, Universiti Sains Malaysia⁴

01 Nov 2019-Quality and Reliability Engineering International

TL;DR: The South African Researchers Chair Initiative (SARCHI) as discussed by the authors is the South African Research Chair Chair at the University of Pretoria, South Africa, which was established in 2003.

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Abstract: The South African Researchers Chair Initiative (SARCHI) Chair at the University of Pretoria.

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23 citations

Journal Article•DOI•

A nonparametric triple exponentially weighted moving average sign control chart

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Vasileios Alevizakos¹, Kashinath Chatterjee², Christos Koukouvinos¹•Institutions (2)

National Technical University of Athens¹, Visva-Bharati University²

01 Jun 2021-Quality and Reliability Engineering International

22 citations

Journal Article•DOI•

Generally weighted moving average monitoring schemes: Overview and perspectives

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Kutele Mabude¹, Jean-Claude Malela-Majika¹, Philippe Castagliola², Sandile Charles Shongwe¹•Institutions (2)

University of South Africa¹, University of Nantes²

01 Mar 2021-Quality and Reliability Engineering International

TL;DR: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided in this article, where a number of possible future GWMA-related schemes are documented and categorized in such a manner that it is easy to identify research gaps.

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Abstract: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution-free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (i.e. double GWMA, composite Shewhart-GWMA, mixed GWMA-CUSUM and mixed CUSUM-GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA-related schemes (i.e. 61 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

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20 citations

Cites background from "Nonparametric (distribution-free) c..."

...Hence, a standalone paper on the latter is required addressing a variety of issues; for instance (1) the effect of phase I sample size on the performance of the phase II scheme, (2) the extent of the negative effect of estimating parameters as compared to when they are assumed known, and so on....
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...Next, for ease in identifying the different types of GWMA-related schemes or their enhancements, in Table 3, these have been categorized with respect to: (1) the statistic of interest (ie, location, variability or the joint location and variability), (2) whether the underlying parameters are known or unknown (ie, Case K or Case U), (3) whether the observations are assumed to follow some parametric distribution or they are distribution-free, (4) whether the observations are i....
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...E (Gt) = μ0 and σ (Gt) = σ0 √ n √ Qt, (2)...
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Journal Article•DOI•

Controlling the false discovery rate: a practical and powerful approach to multiple testing

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Yoav Benjamini, Yosef Hochberg

01 Jan 1995-Journal of the royal statistical society series b-methodological

TL;DR: In this paper, a different approach to problems of multiple significance testing is presented, which calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate, which is equivalent to the FWER when all hypotheses are true but is smaller otherwise.

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Abstract: SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.

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83,420 citations

"Nonparametric (distribution-free) c..." refers methods in this paper

...The BH-procedure (see Benjamini and Hochberg 1995) is used to control the FDR of the abovementioned multiple testing as close to target level q as possible....
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Book•

Nonparametric Statistical Inference

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Jean D. Gibbons, Subhabrata Chakraborti

01 Dec 1971

TL;DR: Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data.

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Abstract: Introduction and Fundamentals Introduction Fundamental Statistical Concepts Order Statistics, Quantiles, and Coverages Introduction Quantile Function Empirical Distribution Function Statistical Properties of Order Statistics Probability-Integral Transformation Joint Distribution of Order Statistics Distributions of the Median and Range Exact Moments of Order Statistics Large-Sample Approximations to the Moments of Order Statistics Asymptotic Distribution of Order Statistics Tolerance Limits for Distributions and Coverages Tests of Randomness Introduction Tests Based on the Total Number of Runs Tests Based on the Length of the Longest Run Runs Up and Down A Test Based on Ranks Tests of Goodness of Fit Introduction The Chi-Square Goodness-of-Fit Test The Kolmogorov-Smirnov One-Sample Statistic Applications of the Kolmogorov-Smirnov One-Sample Statistics Lilliefors's Test for Normality Lilliefors's Test for the Exponential Distribution Anderson-Darling Test Visual Analysis of Goodness of Fit One-Sample and Paired-Sample Procedures Introduction Confidence Interval for a Population Quantile Hypothesis Testing for a Population Quantile The Sign Test and Confidence Interval for the Median Rank-Order Statistics Treatment of Ties in Rank Tests The Wilcoxon Signed-Rank Test and Confidence Interval The General Two-Sample Problem Introduction The Wald-Wolfowitz Runs Test The Kolmogorov-Smirnov Two-Sample Test The Median Test The Control Median Test The Mann-Whitney U Test and Confidence Interval Linear Rank Statistics and the General Two-Sample Problem Introduction Definition of Linear Rank Statistics Distribution Properties of Linear Rank Statistics Usefulness in Inference Linear Rank Tests for the Location Problem Introduction The Wilcoxon Rank-Sum Test and Confidence Interval Other Location Tests Linear Rank Tests for the Scale Problem Introduction The Mood Test The Freund-Ansari-Bradley-David-Barton Tests The Siegel-Tukey Test The Klotz Normal-Scores Test The Percentile Modified Rank Tests for Scale The Sukhatme Test Confidence-Interval Procedures Other Tests for the Scale Problem Applications Tests of the Equality of k Independent Samples Introduction Extension of the Median Test Extension of the Control Median Test The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons Other Rank-Test Statistics Tests against Ordered Alternatives Comparisons with a Control Measures of Association for Bivariate Samples Introduction: Definition of Measures of Association in a Bivariate Population Kendall's Tau Coefficient Spearman's Coefficient of Rank Correlation The Relations between R and T E(R), tau, and rho Another Measure of Association Applications Measures of Association in Multiple Classifications Introduction Friedman's Two-Way Analysis of Variance by Ranks in a k x n Table and Multiple Comparisons Page's Test for Ordered Alternatives The Coefficient of Concordance for k Sets of Rankings of n Objects The Coefficient of Concordance for k Sets of Incomplete Rankings Kendall's Tau Coefficient for Partial Correlation Asymptotic Relative Efficiency Introduction Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data Introduction Contingency Tables Some Special Results for k x 2 Contingency Tables Fisher's Exact Test McNemar's Test Analysis of Multinomial Data Summary Appendix of Tables Answers to Problems References Index A Summary and Problems appear at the end of each chapter.

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2,988 citations

"Nonparametric (distribution-free) c..." refers background or methods in this paper

...These charts are based on some well-known nonparametric goodnessof-fit statistics, such as the Cramer-von-Mises (CvM) and the Kolmogorov-Smirnov (KS) statistic (see Gibbons and Chakraborti 2010)....
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...This chart is based on the well-known Kruskal-Wallis nonparametric test (see Gibbons and Chakraborti 2010)....
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...To this end, note that the sign (SN) and the signed-rank (SR) tests are among the simplest and yet versatile one-sample distribution-free tests (see, for example, Gibbons and Chakraborti, 2010)....
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...The WRS test statistic, say T1, is defined as T1 ¼ XN k¼1 kZk (1) and the AB test statistic, say T2, is defined as T2 ¼ XN k¼1 k 1 2 N þ 1ð ÞZk: (2) For more details on the WRS and the AB tests the interested reader is referred to Gibbons and Chakraborti (2010)....
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...Interested readers can consult Gibbons and Chakraborti (2010) for a discussion on these three concepts which are not always the same and are not well understood....
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Journal Article•

Exponentially weighted moving average control schemes: Properties and enhancements

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James M. Lucas, Michael S. Saccucci

01 Jan 1991-Quality Engineering

TL;DR: The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done.

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1,624 citations

"Nonparametric (distribution-free) c..." refers methods in this paper

...…used when the EWMA chart has been running for several time periods) are based on the asymptotic standard deviation of the control statistic (Lucas and Saccucci, 1990) and are given by UCL=LCL ¼ 6L ffiffiffiffiffiffiffiffiffiffiffiffi kn 2 k r and CL ¼ 0: (13) If any of the charting…...
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Journal Article•DOI•

Exponentially weighted moving average control schemes: properties and enhancements

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James M. Lucas¹, Michael S. Saccucci², Robert V. Baxley, William H. Woodall, Hazem D. Maragh, Fedrick W. Faltin, Gerald J. Hahn, William T. Tucker, J. Stuart Hunter, John F. MacGregor, Thomas J. Harris - Show less +7 more•Institutions (2)

DuPont¹, Drexel University²

03 Jan 1990-Technometrics

TL;DR: In this article, the authors evaluate the properties of an exponentially weighted moving average (EWMA) control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value.

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Abstract: Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...

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1,380 citations

Book•

Nonparametric methods in multivariate analysis

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J. Ogawa, Madan L. Puri, Pranab Kumar Sen

01 Jan 1971

750 citations

"Nonparametric (distribution-free) c..." refers methods in this paper

...…nonparametric process monitoring: Phase II charts Shewhart-type control charts for location in Case K Das (2009) proposed a multivariate nonparametric control charting scheme based on the bivariate SN test (the reader is referred to Puri and Sen (1976) for more details on the bivariate SN test)....
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