A method is proposed to detect incidents that occur in two interdependent time series in real-time, estimating the incident time point from the profiles of the linear trend test statistics, computed on consecutive overlapping data window. The method is based on Slope Statistics Profile (SSP) utilizing adaptive data windowing, estimating real-time classifications of the linear trend profiles, according to two different linear trend scenarios, suitably adapted to the conditions of the problem. The method is applied on real datasets from a chemical process system that is situated at the premises of CERTH / CPERI, suggesting the occurrence of incidents, during experiments.