When there is a serious cause manifested in a Process and it makes the Process departs to an out-of-control condition, an effective root cause analysis could lead the Process management to identify and eliminate the serious cause. When a change takes place in a Multivariate Process, while several correlated variables exist, the root-cause analysis of the Process relatively is more challenging compared to the case of a univariate Process. Considering an out-of-control Multivariate Process, one can experience an effective root-cause analysis if only a comprehensive scheme allows detecting the out-of-control condition, identifying the change point, diagnosing the variable(s) contributing to the unnatural condition and distinguishing the shift direction all simultaneously. Although statistical approach has provided effective solution for the univariate Process, the approach has not provided a comprehensive solution in which a p-variate Process is considered. The Multivariate literature indicates that the solution based on the soft computing is illustrated more effectively in comparison with the statistical approach. This research approached practically shows only one of the scheme among the several schemes proposed in the Multivariate literature is able to trigger simultaneously all the required signals leading to an effective root-cause analysis. The extensive literature review on the Multivariate environment led the authors to represent the comprehensive scheme. The out-of-control ARL criterion is used to evaluate the performance of the scheme compared to the performance of a traditional scheme when the Monitoring of the correlated quality specifications in a real car body manufacturing Process has been investigated.

On-line high performance liquid chromatography (HPLC) was used to monitor steady state reactions in three reactors (K=3) over 48.0 h. Different numbers of chromatograms, with J=1981 retention time points, were recorded for each of the three reactors. Peaks for each chromatogram were baseline corrected and aligned using correlation optimized warping (COW). To make a complete three-way data set of I=266 chromatograms a cubic Hermite interpolation was performed. The applied bilinear Multivariate statistical Process control (MSPC) method included the unfolding PCA and the trilinear technique was PARAFAC.Unfolding in reactor (K) mode was the most informative. D-charts and Q-charts were applied to the data to determine samples which were out of control. Confidence limits were then applied to the D and Q-charts and variables with different behaviours from that encapsulated within the reference data set were located. Both bilinear and trilinear methods were found to be useful for Process analysis.

In this study, drought characteristics of Arak, Bandar Anzali, Tabriz, Tehran, Rasht, Zahedan, Shiraz and Kerman stations during the statistical period of 1956 to 2015 were studied by Reconnaissance Drought Index (RDI) and Standardized Precipitation Index. Precipitation and temperature data were needed to calculate RDI. Precipitation data was also required to estimate SPI. In this study, Drinc software was used to calculate RDI, SPI and potential evapotranspiration (PET). The software calculated PET by the Thornthwaite method. One of the main challenges in drought Monitoring is to determine the indicator that has a high reliability based on its Monitoring purpose. Therefore, in this research, two methods used for selecting the appropriate index based on the minimum rainfall and normal distribution were evaluated. The results of the evaluation of the minimum rainfall method for selecting the appropriate index showed that most drought indices with the occurrence of minimum rainfall level indicated severe or very severe drought situations; in most cases, it could not lead to selecting an exact and unique index. Based on the results of the normal distribution method for the stations of Arak, Tabriz, Rasht, Zahedan, Shiraz and Kerman, SPI index, and for the stations of Bandar Anzali and Tehran, RDI index were selected as the most appropriate ones.

Statistical variables are divided into two categories: nominal and ordinal, both of which have many uses. In some statistical Process Monitoring applications, the quality of a Process or product is described by multiple ordinal quality characteristics, which is called ordinal Multivariate Process. An ordinal contingency table is used to show the relationships between these variables and is modeled on an ordinal log-linear model. In our manuscript, two new statistics including simple ordinal categorical and Generalized-p are developed for Phase II Monitoring the ordinal log-linear model-based Processes. The performance of the proposed statistics will be evaluated using some simulation studies and real-world numerical examples. The results show the advantages of a simple ordinal category control card. In addition, the performance of these statistics is accessed through sensitivity analysis of the row and column sizes of the contingency table. Meanwhile, a sensitivity analysis with three and four categorical factors is performed and similar results are obtained.

Profile Monitoring in statistical quality control has attracted attention of many researchers recently. A profile is a function between response variables and one or more independent variables. There have been only a limited number of researches on Monitoring Multivariate linear profiles. Indeed, Monitoring correlated Multivariate profiles is a new subject in the filled of statistical Process control. In this paper, we investigate the effect of autocorrelations in Monitoring Multivariate linear profiles in phase II. The effect of three main models namely AR (1), MA (1), and ARMA (1, 1) on the methods of Multivariate linear profile Monitoring is evaluated and compared by using simulation study and average run length criteria. Results indicate that autocorrelation affects performance of the existing methods significantly.

In some statistical Processes Monitoring (SPM) applications, relationship between two or more ordinal factors is shown by an ordinal contingency table (OCT) and it is described by the ordinal Log-linear model (OLLM). Newton-Raphson algorithm methods have also been used to estimate the parameters of the log-linear model. In this paper, the OLLM based Processes is monitored using MR and likelihood ratio test (LRT) approaches in Phase I. Some simulation studies are applied to performance evaluation of the proposed approaches in terms of probability of signal under step shifts, drifts and the presence of outliers. Results show that, by imposing the small and moderate shifts in the ordinal log-linear model parameters, the MR statistic has better performance than LRT. In addition, a real case study in dissolution testing in pharmaceutical industry is employed to show the application of the proposed control charts in Phase I.

Nowadays in some manufacturing Processes, the quality of a product or Process is well expressed by both correlated attribute and variable quality characteristics. To best of our knowledge, there is no method for Monitoring the covariance matrix of Multivariate-attribute quality characteristics. In this paper, we propose a multi-layer perception artificial neural network to monitor Multivariate-attribute Processes as well as to diagnose the quality characteristic(s) responsible for out-of-control signals. The performance of the proposed method is evaluated through a numerical example from both detection and diagnosis perspectives. In addition, the performance of the proposed neural network in detecting shifts in the variance of quality characteristics is compared with two statistical methods first proposed for Monitoring the variability of Multivariate quality characteristics and developed in this paper for our problem. The results of numerical example show that the proposed artificial neural network outperforms the extended statistical methods in detecting different out-of-control shifts. The results also confirm that the performance of the proposed neural network in identifying the quality characteristic(s) responsible for out-of-control signal is satisfactory.

When a Process shifts to an out-of-control condition, a search should be initiated to identify and eliminate the special cause (s) manifested to the technical specification (s) of the Process. In the case of a Process (or a product) involving several correlated technical specifications, analyzing the joint e effects of the correlated specifications is more complicated compared to a Process involving only one technical specification.Most real cases refer to Processes involving more than one variable. The complexity of a solution to monitor the condition of these Processes, estimate the change point and identify further knowledge leading to root-cause analysis motivated researchers to develop solutions based on Artificial Neural Networks (ANN). This paper provides, analytically, a comprehensive literature review on Monitoring Multivariate Processes approaching artificial neural networks. Analysis of the strength and weakness of the proposed schemes, along with comparing their capabilities and properties,, are also considered. Some opportunities for new researches into Monitoring Multivariate environments are provided in this paper.