Catastrophe Theory as a Tool for Statistical Analysis of Systems

In the contemporary technology, science and industry the still more and more complicated and expensive systems are used. Their increasing complexity causes naturaly the still harder requirements on the respective system analysis and optimized synthesis. This leads to need to improve the conventional procedure of the system synthesis by the determination of allowable deviations and tolerances of the system parameters and system functions. Because for many systems the deterministic approach to this problem is not suitable, the methods of statistical analysis of system tolerances are used, often with very good results. However, there exist an interesting group of systems, expecially the systems with multivaluability and hysteresis, where the conventional statistical methods based on Monte Carlo approach are not advantageous. In this contribution there will be shown, how in such cases the problem of the tolerance analysis can be solved by modelling, based on some results from the catastrophe theory.