Multiresponse optimisation of powder metals via probabilistic loss functions

Abstract

Quadratic loss functions have been used extensively within the context of quality engineering and experimental design for process and product optimisation and robust design. In general, this approach determines optimal parameter settings based on minimising the sum of individual or mean loss of the associated response(s) of interest in a defined response surface. While the method is neat and handy, it totally neglects the effect of deviations on the desirable value of loss function. This paper utilises variance and probability distribution of loss functions for developing an in depth optimisation scheme that balances mean and variance of loss in a Pareto optimal manner. Since losses are usually defined in financial terms, this model then further improved to handle the user determined risk levels so that financial losses are being restricted within a certain region of interest. Application of the model is illustrated on a multiresponse optimisation problem from powder metallurgy industry.