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Abstract: The most popular multivariate control chart for monitoring the mean of a distribution is probably the Hotelling T 2 rule. Unfortunately, this rule relies on the assumption that the distribution under control is Gaussian, which is rarely true in practice. The objective of this paper is to propose a new approach for the non-normal multivariate case. It consists in the construction of a tolerance region obtained from a density level set estimation. The method follows a “plug-in” approach in which the density of the observations is previously estimated. This estimation is conducted using copulas modeling, an increasingly popular tool in multivariate modeling. [Copyright &y& Elsevier]

In recent years, fault detection has become a crucial issue in semiconductor manufacturing. Indeed, it is necessary to constantly improve equipment productivity. Rapid detection of abnormal behavior is one of the primary objectives. Statistical methods such as control charts are the most widely used approaches for fault detection. Due to the number of variables and the possible correlations between them, these control charts need to be multivariate. Among them, the most popular is probably the Hotelling T^2 rule. However, this rule only makes sense when the variables are Gaussian, which is rarely true in practice. A possible alternative is to use nonparametric control charts, such as the k-nearest neighbor detection rule by He and Wang, in 2007, only constructed from the learning sample and without assumption on the variables distribution. This approach consists in evaluating the distance of an observation to its nearest neighbors in the learning sample constituted of observations under control. A fault is declared if this distance is too large. In this paper, a new adaptive Mahalanobis distance, which takes into account the local structure of dependence of the variables, is proposed. Simulation trials are performed to study the benefit of the new distance against the Euclidean distance. The method is applied on the photolithography step of the manufacture of an integrated circuit. [ABSTRACT FROM AUTHOR]