Data driven choice of control charts |
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| Affiliation: | 1. LERSTAD, Gaston Berger University, Saint Louis, Senegal;2. IRMAR, National Institute of Applied Sciences, Rennes, France;1. LERSTAD, CEA-MITIC, Gaston Berger University, Saint Louis, Senegal;2. IRMAR-INSA, Rennes, France;1. GEPSI–PSE Group, CIEPQPF, Department of Chemical Engineering, University of Coimbra, Pólo II, R. Sílvio Lima, 3030-790 Coimbra, Portugal;2. Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199 Coimbra, Portugal;3. Department of Biostatistics, Fielding School of Public Health, UCLA, 10833 Le Conte Ave., Los Angeles, CA 90095-1772, USA;4. Department of Statistics, London School of Economics, London WC2A 2AE, United Kingdom;1. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China;2. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China;3. Beijing Key Lab of Traffic Data Analysis and Mining, Beijing, China;4. School of Mathematics and Statistics, Tianshui Normal University, Gansu, China |
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| Abstract: | Standard control charts are often seriously in error when the distributional form of the observations differs from normality. Recently, control charts have been developed for larger parametric families. A third possibility is to apply a suitable (modified version of a) nonparametric control chart. This paper deals with the question when to switch from the control chart based on normality to a parametric control chart, or even to a nonparametric one. This model selection problem is solved by using the estimated model error as yardstick. It is shown that the new combined control chart asymptotically behaves as each of the specific control charts in their own domain. Simulations exhibit that the combined control chart performs very well under a great variety of distributions and hence it is recommended as an omnibus control chart, nicely adapted to the distribution at hand. The combined control chart is illustrated by an application on real data. The new modified nonparametric control chart is an attractive alternative and can be recommended as well. |
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