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 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.