Optimization of Multiple Response Surfaces with Secondary Constraints for Improving a Radiography Inspection Process

The quality and reliability measures of products and processes are frequently multidimensional, and the goal of various statistical studies and experiments is to find settings of design or process variables that optimize such products or processes. In many such situations, these measures of interest are further restricted by some physical secondary constraints of the process. These constraints may cause interdependencies among the factors. Moreover, the operability region imposed by the constraints is often unknown a priori, and hence, standard experimental strategy is not always feasible. In this paper, we study a radiography inspection process with dual conflicting radiograph quality measures, contrast sensitivity and spatial resolution, and an image density constraint. The paper presents a sequential approach to tackle this constrained optimization problem. We use and initial experiment to estimate the constraints, and then to account for the interdependencies between the factors more accurately, we use a sliding level design with sliding factors nested within multiple factors. We propose to use a nested effects modeling approach to analyze the experimental data and illustrate its benefits for this example. To optimize conflicting multiple responses, a goal optimization formulation based on this modeling approach is presented.