An Interactive Framework for The Parameter Design Problem

Abstract

We propose an interactive framework for solving the Parameter Design Problem. In this context we consider a response function

Y=h(x1,...,xn), where x1,...,xn are random variables with known probability distribution functions, and h is a continuous and differentiable function. Given the distribution functions of x1 through xn and the function h, we use a family of Johnson distributions to approximate the probability density function of Y by using its first four moments as input. This density function can be displayed graphically and compared with the given specification limit of Y. Using this approach we develop a computer program that would allow the user to modify the set points of x1 through xn manually, and immediately observe the impact of this adjustment on the probability density function of Y. The user can then interactively search for and determine a satisfactory set of values for these set points. We also present two case studies and solve them by this method. The framework that we propose also provides a platform for employing other techniques such as nonlinear programming or statistical design of experiment in order to assist the user in determining a satisfactory solution for the parameter design problem.