A catastrophic phenomenon should not be considered a sudden and causeless event, but as a process whose characteristics are continuously changing throughout the entire previous period. This process manifests itself in the form of a trajectory of changes in time of the controlled parameter. This trajectory contains the information necessary for making decisions, both about the current degree of criticality of the system’s state and about the moment it reaches its limit state. This monograph discusses the method of searching for such a moment for a controlled system. The methodology consists of two complementary and therefore mutually validating forecasting methods. The first method analyzes the trend of a time series compiled from the results of monitoring the behavior of a controlled object, and the second method analyzes the periodic component, which together with the trend forms the original time series. The monograph considers the following processes as such processes: wear of the cutting tool, leading to defects in the workpiece; development of a manufacturing defect leading to an accident under operating conditions or catastrophe of products that differ in the volume of their production; preparation for earthquakes and volcanic eruptions.