Conference Agenda

Control statistics are widely used to monitor the quality of processes in various fields such as industry, healthcare, and machine learning. These statistics give an alarm when observed data exceed a threshold, traditionally set as a constant value to maintain a desired false alarm rate. Now we want to focus on a new setting: When monitoring a sequence of observations, there may be additional information that potentially affects the law of the observations, and we would like to change the design by using adapted thresholds, which are functions of the additional information.
So far, we have considered several classes of adaptive threshold functions for continuous observations, including constant, proportional, and dominated classes. Our focus is on the proportional class threshold, which adjusts the sensitivity automatically based on the external information, making it particularly effective in detecting rare but critical cases. We derive an estimator for this threshold function using kernel density estimation and establish its consistency, asymptotic normality and some further asymptotic properties. Additionally, we demonstrate the application of this method for real car engine data, where we monitor the engine revolutions per minute (RPM) using lubrication pressure as external information to assess the performance of this method.