Multivariate Control charts such as Hotelling's T2 and X2 are commonly used for monitoring several related quality characteristics. These Control charts use correlation structure that exists between quality characteristics in an attempt to improve monitoring. The purpose of this article is to discuss some issues related to the G chart proposed by Levinson et al. [9] for detecting shifts in the process variance-covariance matrix. They use a G statistic which is distributed as a chi-square with p(p+1)/2 degrees of freedom where p denotes the number of variables under study. The authors show through simulation that the chi-square distribution only holds for certain cases. The results could be important to practitioners who use G chart for monitoring purposes.

The two most significant sources of uncertainty are randomness and incomplete information. In real systems, we wish to monitor processes in the presence of these two kinds of uncertainty. This paper aims to construct a fuzzy statistical Control chart that can explain existing fuzziness in data while considering the essential variability between observations. The proposed Control chart avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median. The out-of-Control states are determined based on a fuzzy in-Control region and a simple and precise graded exclusion measure that determines the degree to which fuzzy subgroups are excluded from the fuzzy in-Control region. The proposed chart is illustrated with a numerical example.

The Shewhart np Control chart is often used to monitor the quantity of nonconforming, but it is slow in detecting small deviations. This paper proposes an efficient approach to monitor the quantity of nonconforming. The novelty of the paper is utilization of an initial belief to construct an analytic variable limit np Control chart. The proposed method uses all gathered data, sequentially. This approach is significantly faster than some existent effective approaches in detecting small deviations. These charts are mainly used for evaluation of the initial setup in the process. The simulated results for the average run  length profiles demonstrate the superiority of the new approach against the standard np chart, binomial CUSUM, binomial EWMA and moving average approach.

Control charts are the most useful tools for Controlling the processes statistically. The construction of the Control charts requires the estimation of the process parameters using random sample data. Usually the classical estimators of the process parameters are used to construct the Control charts. The classical estimators of the parameters of the processes generating auto correlated data are sensitive to the presence of the outlier observations. Applying classical methods of estimation while outliers are present, introduce biased estimates of the model parameters which result in wrong interpretation of the Control chart. In this research a method called Iteratively Robust Filtered Fast Tau (IRFFT) which is insensitive to the presence of the outliers is proposed for estimating the parameters of the auto correlated models. The newly introduced estimators are used to construct robust Control chart for auto correlated data. The suggested robust Control chart is compared with the Control chart whose parameters are estimated using LS method. Results of the simulation study for the two methods indicate that the ARL for the suggested robust Control chart is much smaller under different scenarios. The findings may be extended to the other time series models.

R2R Controllers combine statistical process Control and engineering process Control. These techniques based on exponentially weighted moving average (EWMA) scheme and adjust input variable based on difference between forecasted and real output. This type of Control consist some cost as difference inventory or overtime and etc.In this paper we suggest that first output Controls by residual Control chart, and if there is out of Control case then the process is adjusted, also in this paper with considering cost parameters in adjustment of process, an economic model to optimum design of combination of R2R Control and residual Control chart is developed.

Acceptance Control charts (ACC), as an effective tool for monitoring highly capable processes, establish Control limits based on specification limits when the fluctuation of the process mean is permitted or inevitable. For designing these charts by minimizing economic costs subject to statistical constraints, an economic-statistical model is developed in this paper. However, the parameters of some processes are in practice uncertain. Such uncertainty could be an obstacle to getting the best design. Therefore, the parameters are investigated by a robust optimization approach. For this reason, a solution procedure utilizing a genetic algorithm (GA) is presented. The algorithm procedure is illustrated based on numerical studies. Additionally, sensitivity analysis and some comparisons are carried out for more investigations. The results indicate better performance of the proposed approach in designing ACC and more reliable solutions for practitioners.