Hoteling T^2 Control Charts Multivariable statistics is an aspect of statistics that involves analysis of more than one variables. In other words, the multivariable analysis is concerned with the statistical analysis of more than one variables how they are related to one another. Some problems involve using the multivariable data using multiple regression or linear regression, and one of the aspects of the multivariable analysis is an area that involves analysis of quality control using the linear regression. Contrary to the univariable analysis that uses two variables, the multivariable analysis uses two or more independent variables or dependent variables. The concept independent variables are the variables manipulated by the researcher to carry out the analysis. With this control, the researcher will be able to correlate the dependent and independent variables. However, the manufacturing companies are increasingly using the multivariable statistics to enhance product quality. In the contemporary manufacturing environment, increasing number of manufacturing companies are moving towards the global drive to increase their productivity as well as meeting global demand with lowest possible costs. More importantly, quality control through metal machining remains the most important aspect of the manufacturing process. Particularly, in the automated manufacturing company, the automated inspection is critical in enhancing quality control and quality management to minimize consumer and producer risks. However, the multivariable statistical analysis is the technique to enhance quality control in the manufacturing sector. The multivariable analysis uses both the descriptive statistics and inferential statistics to summarize and present the results of the data. The inferential statistics assists in answering the questions related to the data as well as assisting in testing the null hypothesis or alternative hypothesis. Moreover, the analyses assist in estimating the measure of association or correlation between two or more variables. Multivariable regression also uses the p-value to compute the significant level where 0.05 is referred as confidence level and 95% of repetition produces a true parameter. One of the important aspects of multivariable analysis is to use the regression analysis is to establish the relationships between X and Y variables. The linear regression is able to predict the out if Y variables are based on the values of X variables. Thus, the multivariable analysis is able to use the linear regression to produce estimates using the linear equation to make the independent variables to predict the dependent variables. In the regression analysis, the scatter plot assists in determining the model to be used as the dependent variable. Moreover,...

An effective method to measure the fitness of the model is to use the R Square in the multivariate regression. For example, if there is no relationship between the variables the R Square will be very close to zero. However, if the R-square is very close one, there is a linear relationship between variables.
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The Hoteling Control chart is a statistical data analysis technique to determine if a univariate process has been out of the statistical control. An effective approach to carrying out the measurement process is the Hoteling control that employs the multivariate extension that takes into account the correlational analysis. In the process control chart, the multivariable analysis applies the process using the manufacturing data to enhance a better control of the manufacturing processes. For example, the control charting is increasingly being used in the automated industry to enhance quality control. Haris, et al. (2016) reveal that full automation in the metal cutting process is one of the goals of the manufacturing sector, and one of the vital obstacles against this objective is an inability to monitor the condition of the cutting tools completely in a real time since a premature damage of the tools can lead to substantial costs to the organization.

Moreover, the goal to enhance competitive market advantages has pushed increasing number of manufacturing companies to move in monitoring the performances of the cutting metal machine Haris, et al. (2016) believe that SPC (statistical process control) is an effective tool to automate decision. The authors use the multivariate analysis to correlate the tool wears using the multivariate control charts. To achieve this objective, the authors use the multivariate autoregressive model to control the process.

Bersimis, et al. (2005) support the argument of the previous authors by pointing out that the process control charting using multivariable analysis is the technique of enhancing the quality control in the contemporary manufacturing environment. Typically, the multivariable SPC is an advanced statistical technique to assist in controlling and monitoring the operating performances using the continuous and batch processes. Specifically, the multivariate SPC approach helps to reduce the information within the process variables using the statistical modeling.

Harris et al. (2016) use the case study of the metal cutting process to demonstrate how the SPC multivariate approach implements the tool conditioning process. In the manufacturing sector, it is critical to monitor the tool wear since the…