A Nonparametric Shewhart-Type Signed-Rank Control Chart Based on Runs |
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Authors: | S. Chakraborti |
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Affiliation: | Department of Information Systems, Statistics and Management Science , University of Alabama , Tuscaloosa, Alabama, USA |
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Abstract: | Measures of distributional symmetry based on quantiles, L-moments, and trimmed L-moments are briefly reviewed, and (asymptotic) sampling properties of commonly used estimators considered. Standard errors are estimated using both analytical and computer-intensive methods. Simulation is used to assess results when sampling from some known distributions; bootstrapping is used on sample data to estimate standard errors, construct confidence intervals, and test a hypothesis of distributional symmetry. Symmetry measures based on 2- or 3-trimmed L-moments have some advantages over other measures in terms of their existence. Their estimators are generally well behaved, even in relatively small samples. |
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Keywords: | Average run-length (ARL) Distribution-free False alarm rate (FAR) Median run-length (MRL) Median Process control Quartiles Run-length Symmetry |
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