Comparisons were also made between the Shewhart and CUSUM charts for the ZIPINAR(1) and ZIPINARCH(1) processes. Our analysis
revealed that when correlated counts come from a ZIPINAR(1) process, the CUSUM chart is the most sensitive scheme in the detection
of small and moderate shifts in process mean, especially for small and moderate IC values of the first-order autocorrelation ˛0 and the
zero-inflation parameter 0. As the values of ˛0, 0 increase, the performance of the ZIPINAR(1) CUSUM chart is highly affected and
becomes comparable, if not worse, with the performance of the ZIPINAR(1) Shewhart chart. Similar conclusions were derived for the
ZIPINARCH(1) case.
Comparisons were also made between the Shewhart and CUSUM charts for the ZIPINAR(1) and ZIPINARCH(1) processes. Our analysisrevealed that when correlated counts come from a ZIPINAR(1) process, the CUSUM chart is the most sensitive scheme in the detectionof small and moderate shifts in process mean, especially for small and moderate IC values of the first-order autocorrelation ˛0 and thezero-inflation parameter 0. As the values of ˛0, 0 increase, the performance of the ZIPINAR(1) CUSUM chart is highly affected andbecomes comparable, if not worse, with the performance of the ZIPINAR(1) Shewhart chart. Similar conclusions were derived for theZIPINARCH(1) case.
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