Optimization of filter designs with dependent and asymmetrically distributed parameters

This paper presents a new statistical design method for maximizing the manufacturing yield of engineering systems for which the realizations of design parameters are assumed to be dependent random variables. Like in many practical situations, the method assumes that the joint distribution of design parameters is unknown and their marginal distributions can be estimated but are not necessarily symmetrical. This is a difficult problem to which little research has been devoted, other than using some brute force search methods. We use a Frank copula to construct the joint distribution of correlated random variables. Kumaraswamy density function is used to approximate their marginal distributions because of its flexibility and simplicity. The proposed method is based on the approximation of the yield integral over the largest rectangular hypercube (n-box) that is contained in the feasible region. It tries to maximize the yield by relocating and rescaling the box so that higher portion of the manufacturing yield is captured by this box. No integration is necessary since the yield of any given design is approximated by evaluating the cumulative distribution of the copula at the endpoints of the associated n-box. Finally, the actual yield of the optimal design is tested using Monte-Carlo simulation. This requires generating correlated random samples from the chosen copula distribution. One tutorial example and two practical design problems demonstrate the applications of the proposed method. Computational results show that the optimal designs significantly increase the manufacturing yield and this observation is verified using Monte-Carlo simulation.