تكوين لوحات MEWMA متعددة المتغيرات باستخدام عوامل بيز

Abstract EN

This research discusses the formation of four multivariate quality control charts to control the mean vector and variance matrix in two cases of multivariate t distribution and two cases of Generalized Multivariate Modified Bessel Distribution (GMMBD).

This process is performed using Bayesian sequential method with State Space Model (SSM) through applying Bayes Factors (BF) to determine the points that provide information about the process is in control or not.

In the theoretical part of this research, predictive error was obtained, which considered the nominator of Bayes factor, through Kalman filter after finding the estimation of parameters for each case.

Also, target distribution was assumed, which considered the denominator of Bayes factor.

It was appeared that the Bayes factors are considered as correlated sequence and failed to have normality condition, for this reason, it was important to take these two facts into consideration.

Therefore, EWMA chart had been modified through assuming that the sequence of Bayes factors are time series of type ARMA (1, 1) and it is named (MEWMA), and providing determined values for the parameter of initiated chart in order to make it as a base of drawing Bayes factors.

In the practical part, MATLAB Language were used to generate simulated data for each of the assumed two distributions, and then applying what have been obtained in the theoretical part for the different cases using written programs through MATLAB language, Minitab and E-Views software packages.

It was founded that, it could be use these charts to control the mean and variance together for data that possess heavy-tailed distributions.