Optimization of multi-response problems with continuous functional responses by considering dispersion effects

In some processes, quality of a product should be characterized by functional relationships between response variables and a signal factor. Hence the traditional methods cannot be used to find the optimum solution. In this paper, we propose a method which considers two different dispersion effects, i.e. in domain and between replicates variations in the functional responses. Besides, we propose an integral based measure to find the deviation from target function. A probabilistic method is applied to consider the correlation structure of functional responses. Three numerical examples and a real case from literature are studied to show the efficiency of the proposed method.