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.

  Autorentext

  Anton Panda, prof. Ing., PhD.: University studies - Faculty of Mechanical Engineering TU KoSice (Ing.-1987); terminated doctoral studies -Faculty of manufacturing technologies TU KoSice (PhD.-2002), associate professor of study branch 4.7.51 manufacturing technologies, FMT TU KoSice (assoc. prof.-2008), professor of study branch 4.7.51 manufacturing technologies, FMT TU KoSice (prof.-2015). 29 - years of experience in the engineering company supplying the products for demanding automotive, also farm and agricultural industry (constructor of special purpose machinery and equipment, systems analyst, head the department of development and technical preparation of production, methodist of statistical methods, commercial and technical director, director of quality). In the present expertise and design activities in the area of development, production and verification of rolling bearings, in the areaof deposition with rolling bearings for various domestic and foreign customers. Since 2008 (since 1994 external) operates as pedagogue and scientist at the Faculty of manufacturing technologies TU KoSice with the seat in PreSov, as well as an expert - coordinator (auditor) of quality management systems. He is the author (co-author) of 20 monographs (14 foreign, 6 domestic) - of it 6 monographs in Springer publishing, 3 university textbooks (2 foreign, 1 domestic), 16 university lecture notes, author's certificates (14), patents and discoveries (14), catalogs of bearings (2), several domestic and foreign original scientific papers in the scientific and professional journals, in Current Content Connect journals in Web of Science (21), in impacted journals and publications led in the world renowned databases (Thomson Scientific Master Journal List - Web of Science (Web of Science - 123, Scopus - 173) and in proceedings from domestic and foreign scientific conferences from the following areas: Automobile production, manufacturing technologies, experimental methods in the manufacturing technologies, machining, development, manufacturing and verification of new products in accordance with the standards EN ISO 9001 and in accordance to the specific requirement of automobile manufacturers IATF 16 949 (ISO/TS 16 949), quality control, statistical methods and techniques of quality for the production of part, capability of machine, capability of manufacturing processes, capability of gauges and measuring equipment, technical preparation of production, product audit, system audit of quality management system, analysis of potential errors and their effect on construction (FMEA-K) and on manufacturing process/technology (FMEA-V), statistical regulation of manufacturing processes SPC, process of approval of part to the production PPAP, modern quality planning of product APQP,control plans and regulation, requirements the association of automobile manufacturers in Germany VDA 6.1, quality system requirements for suppliers of Ford, Chrysler, GM, specific requirements the using of EN ISO 9001:2015 in organizations ensuring the mass production in automotive industry ISO/TS 16949, method of Poka-Yoke, quality assurance before the mass production for suppliers of automobile manufacturers in Germany VDA 3.3, quality assurance of supplies for suppliers of automobile manufacturers in Germany VDA 2, product ability, method of Global 8D (8-step method for solving of problems), etc. At these works are registered the various domestic and foreign quotations and testimonials in the worldwide databases. Solver of several projects and grant projects for engineering companies at home and abroad, solver of research tasks, author of the directives, methodological guidelines, technical regulations and other technical documentation for domestic and foreign manufacturing companies. He is auditor of quality system management on Technical University in KoSice. Active collaboration with the university workplaces at home and abroad. He is recognized as an expert for the production of bearings in companies in Germany, Italy, China, Slovakia and Czech Republic. As the coordinator of research collective and co-author of documentation EFQM has won the Award for improvement of performance in the competition National award of Slovak Republic for quality in the year 2010 for the Technical University of KoSice. In the same competition, he has won the same award in year 2012, when the Technical University of KoSice has obtained the highest score in its category. Since 2014 he has a member of the Polish Academy of Sciences. Since 2014 he has a member of ASME, USA.

  Volodymyr Nahornyi, PhD.: University studies - Faculty of Electronics and Information Technologies, Department of Computer Science, Section of Information Technology of Design, Sumy State University, Sumy, Ukraine (2006 - 2011); Master's degree in Information Technology of Design (2011); Dynamics and strength (PhD. - 2015). Senior Lecturer in the Department of Computer Science, Section of Information Technology of Design in Sumy State University (2016 - 2022); Since 2022, Associate Professor in the Information Technology Department in Sumy State University. He is the developer (co-developer) courses such as Mobile programming, Frontend development of SPA Web applications, Software Product Development Technology. He is the author (co-author) of 2 monographs, author's certificates (3), patents and discoveries (8), 71 domestic and foreign original scientific papers in the scientific and professional journals, publications included in the world renowned databases (Thomson Scientific Master Journal List - Web of Science (Web of Science - 14, Scopus - 20)) and in proceedings from domestic and foreign scientific conferences from the following areas (26): Information technologies in production, the determination of the individual resource of technical systems, the control of the dynamic behavior of metal-processing technological systems and the forecasting of their working time, the determination of the technical state of the systems.