Average Run Length of Cumulative Sum Control Chart by Markov Chain Approach for Zero-Inflated Poisson Processes
Keywords:
Zero-Inflated Poisson, CUSUM, EWMA, Average Run Length, Markov Chain Approach.Abstract
A Cumulative Sum (CUSUM) chart is an alternatives effective to standard control such Shewhart control chart in order to monitor a small shift in process but limited to normality assumption. Therefore, the objectives in this paper are to propose closed form expression of the Average Run Length (ARL) based on Markov Chain Approach (MCA) underlying Zero-Inflated Poisson (ZIP) processes. Furthermore, performance of the CUSUM chart is compared with an Exponentially Weighted Moving Average (EWMA) chart by studying the effect of the probability of extra zeros in ZIP models and the magnitudes of shifts in parameter of the ZIP process for both of the control charts. The numerical results are obtained from the MCA which the performance of EWMA and CUSUM charts are in the same manner for the smallest magnitude of shifts However, the CUSUM shows the poor performance for moderate to large shifts when compared with the EWMA chart.
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