Control charts based on dependent count data with deflation or inflation of zeros |
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| Authors: | Cong Li Jianguo Sun |
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| Institution: | 1. Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, People's Republic of China;2. Center for Applied Statistical Research, School of Mathematics, Jilin University, Changchun, People's Republic of China;3. Department of Statistics, University of Missouri, Columbia, MO, USA |
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| Abstract: | The process of serially dependent counts with deflation or inflation of zeros is commonly observed in many applications. This paper investigates the monitoring of such a process, the first-order zero-modified geometric integer-valued autoregressive process (ZMGINAR(1)). In particular, two control charts, the upper-sided and lower-sided CUSUM charts, are developed to detect the shifts in the mean process of the ZMGINAR(1). Both the average run length performance and the standard deviation of the run length performance of these two charts are investigated by using Markov chain approaches. Also, an extensive simulation is conducted to assess the effectiveness or performance of the charts, and the presented methods are applied to two sets of real data arising from a study on the drug use. |
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| Keywords: | Cumulative control chart forecasting integer-valued autoregressive process statistical process control zero-modified distribution |
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