Correlated Multi-response Robust Optimization Considering Control Factors Fluctuations

Traditional robust parameter design deals with the single response problem and usually focuses on the impact of the noise factors. This dissertation expands the research to the correlated multi-response problems considering other uncertain factors, such as control factors fluctuations, parameter estimate errors, etc. Different approaches for multi-response robust optimization are proposed according to the specific characteristics of the problems in reality.Firstly, comparative analysis is done for different estimate methods, including ordinary least squares(OLS), seemingly unrelated regression(SUR) and Bayesian estimate. It is found that SUR often gives overall better estimate than OLS in case that the responses are correlated and there are sufficient samples. While Bayesian estimate can take into account the errors uncertainty in parameters through posterior analysis.Secondly, a hierarchical optimization approach based on Bayesian analysis and desirability functions method is proposed for the unrelated responses optimization problems considering model and prediction uncertainties. The hierarchical strategy allows a quality engineer to make balance between optimality and robustness. It can reduce the complexity of the algorithm and improve the efficiency of optimization procedures. For the case that current robust optimal solution has a poor reliability, simulation data are generated through two different ways. The effects of future remedial measures are accessed quantitatively by the pre-posterior analysis, which can provide some guidance for subsequent improvement experiments.Thirdly, a robust loss function method based on SUR is proposed for multiple correlated responses optimization considering control factors fluctuations. The correlations among responses are considered through employing the SUR to model fitting and process optimization. The Jacobi matrix of the predicted responses at given points is used to estimate the changes of the responses caused by the control factors fluctuations. Different cost matrices are selected according to whether or not the predicted responses meet their specification limits. Then, the process robustness measure is constructed using a quality loss term. The major advantage of the proposed approach is its ability to incorporate the correlations among responses, target optimization, prediction quality and process robustness into a single loss function framework. The adaptable strategy for the choices of the cost matrices can ensure the optimal solutions being in the feasible region.Finally, a Monte Carlo approach for multiple response robust optimization is proposed, which further takes into account the noise factors and model uncertainties. Statistical simulation is used to describe the fluctuations of the factors quantitatively. And then the expectation and variance of the predicted response are estimated by Monte Carlo method. The loss function is used to account for both the optimality and the variability of the process. The proposed approach can overcome the drawbacks of the probabilistic method, which is based on Bayes and cannot realize each response further optimization in the feasible region.The study extends the research range of parameter robust design. It is helpful for engineering design personnel to learning about the process. Furthermore, the results can provide some references for process improving or process design.