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Journal ArticleDOI: 10.1080/16843703.2020.1753295

New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic

04 Mar 2021-Quality Technology and Quantitative Management (Taylor & Francis)-Vol. 18, Iss: 2, pp 135-155
Abstract: In this paper, a new distribution-free double exponentially weighted moving average (DEWMA) control chart based on the Wilcoxon rank-sum (WRS) test without any distributional assumption of the unde...

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Journal ArticleDOI: 10.1080/00207543.2020.1802079
Abstract: Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of th...

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Topics: Control chart (57%)

7 Citations


Journal ArticleDOI: 10.1080/03610918.2020.1811331
Abstract: The Mann–Whitney (MW) test is one of the most important nonparametric tests used in the comparison of the location parameters of two populations. Unlike the t-test, the MW test can be used when the...

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Topics: CUSUM (58%), Mann–Whitney U test (54%)

7 Citations



Open accessJournal Article
Abstract: Lucas and Saccucci showed that exponentially weighted moving average (EWMA) control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations. But a single EWMA chart cannot perform well for small and large shifts simultaneously. Furthermore, in the worst-case situation, this scheme requires a few observations to overcome its initial inertia. The main goal of this article is to suggest an adaptive EWMA (AEWMA) chart that weights the past observations of the monitored process using a suitable function of the current “error.” The resulting scheme can be viewed as a smooth combination of a Shewhart chart and an EWMA chart. A design procedure for the new control schemes is suggested. Comparisons of the standard and worst-case average run length profiles of the new scheme with those of different control charts show that AEWMA schemes offer a more balanced protection against shifts of different sizes.

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Topics: EWMA chart (79%), Control chart (60%), Chart (60%)

6 Citations


Open accessJournal ArticleDOI: 10.1177/0142331220973569
Abstract: Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA X¯¯¯ scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA X¯¯¯ scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) X¯¯¯ schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

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Topics: Moving average (57%), Observational error (54%), EWMA chart (54%) ... show more

5 Citations


References
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29 results found


Book ChapterDOI: 10.1007/978-1-4612-4380-9_16
Frank Wilcoxon1Institutions (1)
01 Dec 1945-Biometrics
Abstract: The comparison of two treatments generally falls into one of the following two categories: (a) we may have a number of replications for each of the two treatments, which are unpaired, or (b) we may have a number of paired comparisons leading to a series of differences, some of which may be positive and some negative. The appropriate methods for testing the significance of the differences of the means in these two cases are described in most of the textbooks on statistical methods.

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Topics: Ranking (51%)

11,355 Citations


Journal ArticleDOI: 10.1093/BIOMET/41.1-2.100
E. S. Page1Institutions (1)
01 Jun 1954-Biometrika

4,393 Citations


Open accessBook
01 Dec 1971-
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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Topics: Median test (66%), Normality test (65%), Sign test (65%) ... show more

2,863 Citations



Open accessJournal ArticleDOI: 10.1198/004017003000000023
Giovanna Capizzi1, Guido Masarotto1Institutions (1)
01 Aug 2003-Technometrics
Abstract: Lucas and Saccucci showed that exponentially weighted moving average (EWMA) control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations. But a single EWMA chart cannot perform well for small and large shifts simultaneously. Furthermore, in the worst-case situation, this scheme requires a few observations to overcome its initial inertia. The main goal of this article is to suggest an adaptive EWMA (AEWMA) chart that weights the past observations of the monitored process using a suitable function of the current “error.” The resulting scheme can be viewed as a smooth combination of a Shewhart chart and an EWMA chart. A design procedure for the new control schemes is suggested. Comparisons of the standard and worst-case average run length profiles of the new scheme with those of different control charts show that AEWMA schemes offer a more balanced protection against shifts of different sizes.

... read more

Topics: EWMA chart (79%), Control chart (60%), Chart (60%) ... show more

223 Citations


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20219
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20041