Study For Multiple Response Optimization Based On Robust Parameter Design

With the rapid development of global economy and the continuous progress of science and technology, product quality has become the focus of competition among the enterprises around the world and even has been the key factor to win customers in the global market. Hence, the continuous quality improvement has been the eternal pursuit of goal for each enterprise. Robust parameter design is an important supporting technology in the continuous quality improvement activities. Because the technology is mainly used in the design stage of product or process, it can reduce and control the variation of product or process at the beginning. Hence, the technology can further improve product quality. With the more and more complex for the product design and manufacturing process, quality engineers often encounter the problems which there are multiple responses (quality characteristics) in product/process design. Because there are often different units or dimensions for multiple responses and exists correlation among multiple responses, it is difficult to obtain the optimal solution of a set of controllable factors combination when optimizing the multiple response. Therefore, the problems for multi-response robust parameter design have been more and more important in the process of the continuous quality improvement.The research object is the problem of multi-response optimization based on the robust parameter design in the paper. The concerned problems in static multi-response optimization and dynamic multi-response optimization are systematically studied by means of the systematic modeling, simulation experiment and empirical research. These techniques and methods are synthetically utilized in research process, and more specifically they include response surface methodology, ordinary least squares regression, seemingly unrelated regression, principal component analysis, desirability function and quality loss function. The main contents are summarized as follows:(1) Study for static multi-response optimization based on robust parameter design considering the correlation among variables. Most of studies in existing literature in multi-response optimization assume that multiple responses are independent. However, the assumption may be not appropriate since correlation among multiple responses is not unusual in many practical situations. Meanwhile, most of studies ignore correlation among covariates for correlated multi-response optimization. How to account for the correlation among covariates for correlated multi-response is discussed in this paper. A new desirability function approach based on principal component analysis and seemingly unrelated regression is proposed to achieve optimum and robustness for correlated multi-response optimization. The specific example is used to illustrate the effectiveness of the proposed approach.(2) Study for static multi-response robust parameter design when the proposed mean-variance response is regarded as the new modeling objective. In existing approaches of multi-response optimization, two empirical models (the mean and variance as separate responses) are built based on the dual response surface methodology, respectively. Through optimizing the two empirical models based on different schemes, the robust and optimal solution can be obtained for the predicted response. On the basis of existing studies, the mean-variance response is developed from a particular combination of the mean and variance for each response in this paper. The mean-variance response is regarded as the new modeling objective, which is an extended approach for the dual response surface methodology. Model uncertainty associated with the fitted response surface model is considered through making confidence intervals of the predictions to be contained in the specification limits. The illustrated example is utilized to show that the proposed approach can deal with the robustness problem for multi-response optimization.(3) Study for static multi-response optimization based on robust parameter design considering the weight determination method. Existing approaches for multi-response optimization only consider the subjective preference information of a decision-maker to determine the weights of multiple responses. The optimization results are greatly influenced by subjective preference information of the decision-maker, which leads to reduce the credibility of the optimization results. To solve the problem for weight determination method, a new desirability function approach is proposed to make more reasonable decisions for correlated multi-response optimization problems. For the proposed approach, the objective information from the experimental data is also considered when subjective information of the decision-maker has been considered. Two specific examples are illustrated to verify the effectiveness of the proposed method. The results show that the proposed method can achieve reliable optimal operating condition under model uncertainty.(4) Study for dynamic multi-response optimization based on robust parameter design considering the correlation characteristic between response and signal factor. Most of studies in existing literature assume that the correlation characteristic between response and signal factor is the first-order linear correlation. However, the assumption may be not appropriate because there are relatively complex nonlinear relationships in many dynamic multi-response systems. In such a case, if the first-order linear correlation is still utilized to depict the correlation in actual systems, it makes deviation greater for dynamic multi-response systems. To solve the problem, a new robust optimization model based on response surface methodology is proposed after analyzing the correlation characteristic between response and signal factor. A global optimal and robust solution can be obtained and the acquired correlation can also reflect the actual correlation between response and signal factor.(5) Study for dynamic multi-response optimization based on robust parameter design considering the skewness characteristics of multiple responses. Most of studies in existing literature assume that response variables obey normal distribution. However, the assumption may be not appropriate because response does not often obey normal distribution. In such a case, if the normal distribution is still utilized to depict the actual response distribution, it makes deviation greater for dynamic multi-response systems. How to resolve the robust parameter design problem for dynamic multi-response optimization with the skewness characteristics are discussed in this paper. A new approach based on the multivariate skew normal distribution and response surface methodology is proposed to deal with the robust parameter design for dynamic multi-response. The proposed approach can consider the correlation among multiple responses, and also consider the great influence on the optimization and robustness of responses from the scale and skewness. The specific example is illustrated to verify the effectiveness of the proposed method.Finally, we also discuss some challenging topics which deserve further research in the future based on the above research results.