Economic-statistical design of multivariate control charts for monitoring the mean vector and covariance matrix |
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| Institution: | 1. Department of Industrial Engineering and Management, National Yunlin University of Science and Technology, Touliu 640, Taiwan, ROC;2. Department of Industrial Management, Southern Taiwan University of Technology, Yung-Kang 710, Taiwan, ROC;3. Department of Food and Nutrition, Hung-Kuang Institute of Technology, Shalu 433, Taiwan, ROC;1. Faculty of Engineering Technology, University of Twente, The Netherlands;2. VDL Enabling Technologies Group Almelo, The Netherlands;1. Research Unity of Geo-systems, Geo-resources and Geo-environments (UR3G), Department of Earth Sciences, Faculty of Sciences of Gabes, City Campus Erriadh-Zirig, 6072, Gabes, Tunisia;2. International Association of Water Resources in the Southern Mediterranean Basin, Gafsa, Tunisia;3. Water Researches and Technologies Center Borj-Cedria (CERTE), BP 273, 8020, Soliman, Tunisia;4. Faculty of Sciences of Bizerte, University of Carthage, Tunis, Tunisia;5. Department of Earth Sciences, Faculty of Sciences of Gafsa, Gafsa, Tunisia;1. Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, P.O. Box 5003-IMT, 1432 Aas, Norway;2. Department of Water Supply and Sewerage, Drammen Municipality, Engene 1, 3008 Drammen, Norway;1. Department of Water Production and Transmission, Metropolitan Waterworks Authority, Bangkok 10210, Thailand;2. Department of Electrical Engineering, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand |
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| Abstract: | When a control chart is used to monitor a process, three test parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits or critical region of the chart. In this paper, we present the procedure to conduct the economic-statistical design of multivariate control charts for monitoring the process mean vector and covariance matrix simultaneously; i.e. to economically determine the optimum values of the three test parameters such that the statistical constraints (including the type I error probability and power) of the control chart can be satisfied. The test statistic −2ℓnL is applied to develop this procedure and the cost model is established based on the function given by Montgomery and Klatt. A numerical example is provided to illustrate the solution procedure of the design and then the effects of cost parameters on the optimal design are examined. |
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