### تقريب المعدل والانحراف المعياري لأطوال التشغيل باستعمال أسلوب سلسلة ماركوف للوحتي سيطرة (المجموع المتراكم (Binomial Cusum) والمتوسط المتحرك الموزون اسيا (Binomial EWMA))

#### Abstract

In this study, the average and the standard deviation for run lengths approximated by markov chain approach 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 binomial distribution with unknown mean. We depend on average Run Length (ARL), Standard Deviation Run Length (SDRL) as comparative between control charts, when the variable under control follows Binomial Distribution. Also, we used the Cusum and the EWMA control charts for monitoring a process mean when the observations (product is Binomial Distribution) in continuous manufacturing. We assumed several values for the parameters of the Binomial Cusum and the Binomial 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 Binomial Cusum and Binomial EWMA control charts control charts for Binomial Distribution were more sensitive at certain values for the parameters of the Binomial Cusum and the Binomial EWMA control charts. at certain values for the state number of markov chain.

#### Keywords

control charts, cumulative sum, Cusum, the Exponentially Weighted Moving Average, EWMA, markov chains, the Binomial Distribution, Average Run Length, ARL, Standard Deviation Run Length, SDRL.#### Metrics