Abstract:
This research study of average run length (ARL) of controlling charts for Zero-inflated
binomial when the underlying distribution is ratio of two Poisson means (ZIBpoi). The proposal
of this research is to find ARL by deriving explicit formulas (EF) for Moving Average (MA)
and Double Moving Average (DMA) control charts for ZIBpoi process. Next, to represent the
ARL by using the Markov Chain Approach (MCA) of Exponentially Weighted Moving Average
(EWMA) and Cumulative· Sum (CUSUM) control charts for ZIBpoi process, comparing the
estimates of ARL obtained from the MCA with the results from the Monte Carlo Simulation
(MC). Furthermore, the performance of MA, DMA, EWMA and CUSUM control charts, are
compared when ZIBpoi process is not under control, we consider the value of ARL1 to be the
measure of the effective comparison. The ARL by EF of MA and DMA control charts is very
effective in detecting the process change. It is simple and easy to implement. The value of
the ARL by using the MCA are closed from the MC, but the MCA is more timesaving to
evaluate than MC. The results show that the DMA control charts are the most effective for
detecting very small processing change and the MA control chart has performance is the
second.