Quality loss functions for optimization across multiple response surfaces

Most manufactured products must conform to multiple "fitness for use" criteria. The manufacturing design must balance these different needs and find settings of design parameters that maximize product quality. This paper proposes the use of quadratic quality loss functions applied to response surface models to solve this multiple criterion problem. The discussion concentrates on the premanufacturing phase, when off-target losses predominate over losses due to random variability, but the methodology is equally applicable to situations in which both sources contribute appreciably to quality losses. It is shown that operating a process at the minimum of the loss function has the additional benefit of minimizing sensitivity of the product to noise variation in the design parameter settings, leading to robust designs automatically.