Probabilistic design of systems with general distributions of parameters

This paper presents a new method for finding optimal solutions of systems with design parameters which are random variables distributed with various general and possibly non‐symmetrical distributions. A double‐bounded density function is used to approximate the distributions. Specifications may require tracking constraints in time domain and stability conditions in frequency domain. Using sensitivity information, the proposed method first finds a linearized feasible region. Afterwards it attempts to place a tolerance box of the design parameters such that the region with higher yield lies in the feasible region. The yield is estimated by the joint cumulative density function over a portion of the tolerance box contained in the feasible region. Optimal designs are found for a fourth‐order servomechanism and actual yields are evaluated by Monte‐Carlo simulation.