In this paper, a Control method based on binomial distribution is proposed in which, by analyzing the cumulated data for a uni-Variate quality characteristic, the possible mean shift is detected. In this method, the domain of observations is first divided into some specified intervals and then the number of observations in each interval is counted. Control statistics are next defined using the counted values based on the approximation methods. Necessary adaptations are made to form an appropriate statistic for the process monitoring. Using a simulation technique, the performance of the proposed method is compared with the ones of the optimal EWMA, GEWMA, CUSUM and GLR Control charts. The results show that with an equal in-Control average run length, the cumulative Binomial Control method performs better than Control charts in detecting a mean shift of any size less than 3s. The analysis is also carried out for auto correlated data, showing that the proposed method performs better than other methods for small to moderate values of autocorrelation coefficients.

We propose a new approach to monitor an overall mean shift of a bi-Variate quality Control system. To do this, we first define beliefs on deciding whether the quality characteristics are in out-of-Control state. Then, by taking new observations, in an iterative approach we update the belief of each quality characteristics being out-of-Control. This task is performed using a recursive method and prior beliefs. Finally, we introduce a statistics in combination with BiVariate Exponentially Weighted Moving Average (BEWMA) statistics to improve the performance of the proposed method. In order to understand the proposed methodology and to evaluate its performance, we perform a simulation study. Moreover, we compare in- and out-of-Control average run lengths of the proposed method with the ones from the well-known MCUSUM and MEWMA procedures in different scenarios of mean shifts. The results of the simulation study show that the proposed methodology performs better than the other methods for small shifts of the process mean.

In this research, the decision on belief (DOB) approach was employed for fault detection in uni-Variate process Control. The concept of DOB and its application in decision making problems were introduced, and then methodology of modeling fault detection in statistical process Control by DOB approach was discussed. In this iterative approach, the belief of being a fault in the process was updated by taking new observations on a quality characteristic using Bayesian rule and prior beliefs. If the beliefs are more than a specific threshold, then the system will be classified as an out-of-Control condition. Finally, a numerical example and simulation study were provided for elaborating the application of the proposed methodology and evaluating the performance of the proposed method.

This paper investigates a single-stage and two-stage production systems where specification limits are designed for inspection. When quality characteristics fall below a lower specification limit (LSL) or above an upper specification limit (USL), a decision is made to scrap or rework the item. The purpose is to determine the optimum mean for a process based on rework or scrap costs. In contrast to previous studies, costs are not assumed to be constant. In addition, this paper provides a Markovian model for multiVariate Normal process. Numerical examples are performed to illustrate the application of the proposed method.

In this paper, by conditioning on the matrix Variate normal distribution (MVND) the construction of the matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance matrix S of MVND is derived under Kullback Leibler divergence loss (KLDL). Further an application of the proposed result is given in the Bayesian context of the multiVariate linear model. It is illustrated that the Bayes estimators of coefficient matrix under both SEL and KLDL are identical.