The Statistical Catastrophe Theory and Optimal Probability Based Design

Abstract

This paper deals with the statistical catastrophe theory method for the optimal design of machine components. A short introduction to the catastrophe theory is presented, the statement of optimal design problem is given in the first part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is focused on probability approach. Manage variables are viewed as random stationary processes, statistical linearization method and Pearson moment method are used for the reliability function evaluation.