Skewed and Heavy-Tailed Hidden Random Walk Models with Applications in Automated Production Testing

摘要

We present a new approximate stochastic filter for single-output state-space models with skewed Student-t measurement noise. The Student-t assumption provides robustness to outliers, while the skewness property allows for better adaption to unsymmetric measurement noise distributions than the traditional Kalman filter. The new filter is compared to an existing one, which uses another type of skew Student-t distribution. Our motivating application is fault detection during automatic testing in industrial production. Estimation of noise parameters and test limits in combination with outlier-robustness of the filters leads to a practical procedure for automatic generation of dynamic test limits. Using data from a large-scale car engine manufacturing line, we demonstrate the relevance of skewness in datasets and the feasibility of our approach.