About The Run Length Properties for ( Cumulative Sum(Cusum) and The Exponentially Weighted Moving Average (EWMA)) control charts for Poisson Distribution

Abstract

In this study, we investigate about the run length properties of cumulative sum (Cusum) and The exponentially weighted moving average (EWMA) control charts, to detect positive shifts in the mean of the process for the poisson distribution with unknown mean. We used markov chain approach to compute the average and the standard deviation for run length for Cusum and EWMA control charts, when the variable under control follows poisson distribution. Also, we used the Cusum and the EWMA control charts for monitoring a process mean when the observations (products are selected from Al_Mamun Factory ) are identically and independently distributed (iid) from poisson distribution in continuous manufacturing .We assumed several values for the parameters of the poisson Cusum and the poisson EWMA control charts, and several state numbers for markov chain. The results were obtained by using Programs written using matlab-R2018a program .The results shown that poisson Cusum and poisson EWMA control charts control charts for poisson distribution were more sensitive at certain values for the parameters of the Cusum and the EWMA control charts. at certain values for the state number of markov chain.