An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location
01 Apr 2017-Quality and Reliability Engineering International (John Wiley & Sons, Ltd)-Vol. 33, Iss: 3, pp 669-685
TL;DR: A nonparametric exponentially weighted moving average (EWMA) control chart is developed based on Wilcoxon signed-rank statistic using ranked set sampling and shows better detection ability than some of the competing counterparts including EWMA sign chart, EWMAsigned-rank chart, and the usual EWMA control chart using simple random sampling scheme.
Abstract: The statistical performance of traditional control charts for monitoring the process shifts is doubtful if the underlying process will not follow a normal distribution. So, in this situation, the use of a nonparametric control charts is considered to be an efficient alternative. In this paper, a nonparametric exponentially weighted moving average (EWMA) control chart is developed based on Wilcoxon signed-rank statistic using ranked set sampling. The average run length and some other associated characteristics were used as the performance evaluation of the proposed chart. A major advantage of the proposed nonparametric EWMA signed-rank chart is the robustness of its in-control run length distribution. Moreover, it has been observed that the proposed version of the EWMA signed-rank chart using ranked set sampling shows better detection ability than some of the competing counterparts including EWMA sign chart, EWMA signed-rank chart, and the usual EWMA control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright © 2016 John Wiley & Sons, Ltd.
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...By substituting the value of (11) in (12), we get...
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TL;DR: The methodology to compute the exact run length properties of the proposed chart and the algorithms to obtain the optimal chart parameters through the minimization of the out-of-control average run length are provided.
Abstract: In this paper, a new phase II EWMA-type chart for count data, based on the sign statistic, is proposed and applied to the monitoring of the location of an unknown continuous distribution. The most ...
36 citations
TL;DR: A new nonparametric AEWMA-type chart for count data, based on the sign statistic (denoted as the CAEWMA SN chart), is proposed without requiring any parametric probability distribution for the underlying process.
32 citations
TL;DR: RSS and its variation, extreme RSS, median RSS and neoteric RSS are employed to construct new memory type homogeneously weighted moving average (HWMA) control charts to monitor the process location to establish the better shift detection ability of the proposed charts.
Abstract: The process monitoring and construction of control charts involves the measurement of the quality characteristic under certain time and cost constraints. Ranked set sampling (RSS) is a very useful ...
30 citations
TL;DR: Comparison results based on Monte-Carlo simulation show that the proposed chart is quite robust to non-normally distributed data, and moreover, it shows satisfactory performance in detecting various process shifts in terms of the average run length and standard deviation of run length.
30 citations
References
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TL;DR: There are valuable points here; they are, however, generally too hard to find and some of them are undercut by the author’s misguided attempt to be “fair.”
Abstract: (2007). Introduction to Statistical Quality Control. Technometrics: Vol. 49, No. 1, pp. 108-109.
3,358 citations
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...Then, the SR test statistic based on SRS is given by: SRSRSl 1⁄4 Xn k1⁄41 sign X lk θ0 ð ÞR þ lk (1) where l= 1, 2, 3,....
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TL;DR: No associations with mortality were found with any circulating miRNAs studied and these results cast doubt onto the effectiveness of circulating miRNA as early predictors of mortality or the major underlying diseases that contribute to mortality in participants treated for HIV-1 infection.
Abstract: Introduction
The use of anti-retroviral therapy (ART) has dramatically reduced HIV-1 associated morbidity and mortality. However, HIV-1 infected individuals have increased rates of morbidity and mortality compared to the non-HIV-1 infected population and this appears to be related to end-organ diseases collectively referred to as Serious Non-AIDS Events (SNAEs). Circulating miRNAs are reported as promising biomarkers for a number of human disease conditions including those that constitute SNAEs. Our study sought to investigate the potential of selected miRNAs in predicting mortality in HIV-1 infected ART treated individuals.
Materials and Methods
A set of miRNAs was chosen based on published associations with human disease conditions that constitute SNAEs. This case: control study compared 126 cases (individuals who died whilst on therapy), and 247 matched controls (individuals who remained alive). Cases and controls were ART treated participants of two pivotal HIV-1 trials. The relative abundance of each miRNA in serum was measured, by RTqPCR. Associations with mortality (all-cause, cardiovascular and malignancy) were assessed by logistic regression analysis. Correlations between miRNAs and CD4+ T cell count, hs-CRP, IL-6 and D-dimer were also assessed.
Results
None of the selected miRNAs was associated with all-cause, cardiovascular or malignancy mortality. The levels of three miRNAs (miRs -21, -122 and -200a) correlated with IL-6 while miR-21 also correlated with D-dimer. Additionally, the abundance of miRs -31, -150 and -223, correlated with baseline CD4+ T cell count while the same three miRNAs plus miR-145 correlated with nadir CD4+ T cell count.
Discussion
No associations with mortality were found with any circulating miRNA studied. These results cast doubt onto the effectiveness of circulating miRNA as early predictors of mortality or the major underlying diseases that contribute to mortality in participants treated for HIV-1 infection.
3,094 citations
Book•
01 Dec 1971
TL;DR: Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data.
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.
2,988 citations
1,264 citations
TL;DR: The application of the ranked sample method to pasture measurement is discussed and the means of such a sample is slightly less than (n + 1)/2 times more efficient than the mean of n items taken at random.
Abstract: A new method of sampling is described Take the largest in the first of n sets, each of n random items, the second largest in the second set, and so on to the smallest in the nth set The sample of n items selected in this way is an unbiased sample of the population For typical unimodal distributions the mean of such a sample is slightly less than (n + 1)/2 times more efficient than the mean of n items taken at random The application of the ranked sample method to pasture measurement is discussed
1,158 citations