Detecting mean increases in Poisson INAR(1) processes with EWMA control charts
Processes of serially dependent Poisson counts are commonly observed in real-world applications and can often be modeled by the first-order integer-valued autoregressive (INAR) model. For detecting positive shifts in the mean of a Poisson INAR(1) process, we propose the one-sided s exponentially weighted moving average (EWMA) control chart, which is based on a new type of rounding operation. The s-EWMA chart allows computing average run length (ARLs) exactly and efficiently with a Markov chain approach. Using an implementation of this procedure for ARL computation, the s-EWMA chart is easily designed, which is demonstrated with a real-data example. Based on an extensive study of ARLs, the out-of-control performance of the chart is analyzed and compared with that of a <italic>c</italic> chart and a one-sided cumulative sum (CUSUM) chart. We also investigate the robustness of the chart against departures from the assumed Poisson marginal distribution.
Year of publication: |
2011
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Authors: | Weiß, Christian H. |
Published in: |
Journal of Applied Statistics. - Taylor & Francis Journals, ISSN 0266-4763. - Vol. 38.2011, 2, p. 383-398
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Publisher: |
Taylor & Francis Journals |
Saved in:
Saved in favorites
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