Single Continuously Differentiable Desirability Functions for Multiple Response Optimization

摘要

The quality of a product, process or system is seldom defined by a single characteristic. Several quality characteristics are often interrelated according to various design parameters in a variety of competing ways. The quality to the consumer is a combination of the characteristics. The need to find an appropriate balance of the parameters to make the optimal decision on the multiple characteristics has been addressed by the introduction of desirability functions. Recently, gradient-based optimization has been invoked to help find the best combination of parameters by introducing differentiable desirability functions that are defined over piecewise intervals and connected by polynomials. Herein we take this approach a step further by providing single, differentiable, desirability functions and a new, more robust system desirability function. Examples that arise from network models, neural networks and response surface methods illustrate the method.