Search

The well-known cumulative sum (CUSUM) sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step. This paper shows how to build an asymptotically optimal detection rule under the common average run length (ARL) constraint when these densities are not available but can be consistently estimated. This is the case for nonlinear state--space systems observed through output variables: for such systems, a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities, leading to an optimal CUSUM-like filter detection rule (FDR). Index Terms--Average run length (ARL) constraint, convolution kernel filter, cumulative sum (CUSUM) rule, model change detection, particle filter, state--space systems.

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]