The optimisation of bi-signal multi-response systems with stochastic target profiles using goal programming

There are many real world applications consisting of finding optimal design variables that yields desirable values for stochastic responses. Finding the levels of controllable factors is an important process control stage to achieve desired specification of the output. On other hand, finding the optimal setting will be more important when there are more than one signal in dynamic systems. Also difficulties may arise particularly for multiple responses when there are stochastic target profiles in each level of signal factor. In this regard, linear regression models for response mean, variance and covariance of multiple responses in each level of signals are obtained. Then optimal settings of controllable factors are extracted by the goal programming applied in an example from the literature. Then optimal setting of controllable factors is determined by stochastic optimisation. Also, the sensitivity analysis is performed to show efficiency of the proposed approach in case of existing stochastic target profiles in multiple response optimisation.