A linear approximation model for the parameter design problem

We consider the problem of minimizing the variance of a nonlinear function of several random variables, where the decision variables are the mean values of these random variables. This problem arises in the context of robust design of manufactured products and/or manufacturing processes, where the decision variables are the set points for various design components. A nonlinear programming (NLP) model is developed to obtain approximate solutions for this problem. This model is based on a Taylor series expansion of the given function, up to its linear term. A case study pertaining to the design of a coil spring is discussed, and its corresponding NLP model is developed. Using this model, a non-inferior frontier curve is obtained that shows the trade-off between the minimum mass of the coil spring and the minimum variance of its performance characteristic. Results of applying the model to three other case studies are also presented.