Fault detection with an adaptive distance for the k-Nearest neighbors rule

In recent years, fault detection has become a crucial issue for many industrial fields, notably the semiconductor manufacturing where process control engineers constantly try to improve the equipment productivity by detecting as quickly as possible an abnormal behavior. Due to the number of variables and the correlations between them in this type of applications, statistical methods dealing with fault detection need to be multivariate. Usually, the multivariate control chart procedures used in the industry derived from the Hotelling T². However, this rule can only be used when the observations are generated by a Gaussian distribution, an assumption rarely satisfied in practice. An alternative consists to apply nonparametric control charts for which there is no assumption needed on the distribution. A nonparametric rule, the k-Nearest Neighbors Detection rule is studied in this paper. The approach consists in evaluating the distance of an observation to its nearest neighbors and declaring a fault if this distance is too large. In this paper, a new adaptive Mahalanobis distance is proposed. It takes into account the local correlation structure of the data and then improves the number of faults detected for a fixed false alarm rate, compared to a classic distance such as the Euclidean distance.