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Dealing with several variables simultaneously is not a simple task for quality engineers because the interpretation of out-of-control signals involves the examination of the data from a multivariate perspective. In this paper, a graphical technique for interpreting out-of-control signals in multivariate control charts is proposed. This approach consists of a typical Hotelling’s chart with warning labels indicating:1) the univariate out-of-control points often masked by the T-squared statistic; 2) the plane of the biplot that should be investigated to identify the cause of the signal. The idea of using biplots as a complementary tool is to provide a broader view of the data without adding much complexity to the analysis. Finally, the benefits of this are shown through a case example of an automotive body assembly process.

Regression analysis is perhaps one of the most widely used statistical tools in six-sigma projects. The reason for its popularity is that it provides a formal evaluation of the relationship between one dependent variable and one or more predictors. The ordinary least squares (OLS), which is a method for estimating the parameters of the linear regression model, has some numerical properties that can be easily understood by looking at them in a geometric manner. In this paper, we discuss the fundamentals of both simple and multiple regression analysis from a geometric perspective. This approach offers an intuitive understanding of some concepts that otherwise would require a background in statistical mathematics and differential calculus. One of the topics covered in this paper is multicollinearity, whose consequences are not well understood by many practitioners.

A vehicle is a product that encloses high levels of complexity. Assessing its quality requires taking into account several variables simultaneously. Usually, this kind of analysis is made over one variable at a time, ignoring the multidimensional nature of the quality. This is even more critical when two or more vehicles are included in the analysis (e.g. for benchmarking purposes), or when the aim of the analysis is to evaluate the performance of more than one variable over time. This study presents an overview of the biplot, which is a low-dimensional representation of observations and variables, and the possibility to use it in monitoring multiple quality variables. We show a case study demonstrating that Principal Components Analysis (PCA) allows us to summarize in a two-dimensional biplot the information that would require a correlation matrix, several conventional plots and further analysis when comparing eight variables measured on two vehicles over the last four years.