Robust Parameter Design For Mixed Response With Categorized Data

Robust parameter design is an important method for improving product quality.The purpose is to select a set of controllable factor combinations that can reduce product or process fluctuations to ensure more stable and reliable product performance.Most of the optimization targets of traditional robust parameter design methods are only focused on products with continuous response.However,in practice,the problem of designing robust response robust parameters with classified value data(classified response)is often encountered.Due to the different types of distributions of categorical and continuous responses,it is difficult to study mixed response problems under a unified joint distribution framework.In addition,the controllable factors in actual production are not completely invariable,and they will also be susceptible to variations due to various external uncertain factors.For this reason,this paper combines Copula function and robust optimization method on the basis of robust parameter design,and systematically studies the problem of robust parameter design with mixed response and controllable factor fluctuations.The main research contents include:(1)Mixed response robust parameter design based on Copula function.Aiming at the traditional robust parameter design methods,which usually only study continuous responses and ignore the mixed response problems of both categorical and continuous responses,a new method for constructing the joint probability density function of mixed variables is proposed by introducing the Copula function theory.Probabilistic optimization model for robust response design with mixed parameters.This method first fits the response surface model of each edge distribution parameter according to the existing experimental data,and then uses the Copula function method to build a joint probability density function with a marginal distribution as a mixed variable;and then combines the joint response density probability function with the mixed response.The consistency probability that each response meets the specification limit is obtained as the objective function.Finally,a hybrid genetic algorithm is used to obtain the optimal input parameter level in the parameter optimization stage.The case study shows that the proposed method can not only reasonably determine the joint density function of the mixed response,but also use the consistency probability index to effectively ensure the reliability of the optimal solution.(2)Design of robust response parameter considering the fluctuation of controllable factors.In view of the traditional robust parameter design method,the influence of controllable factor fluctuations on the robustness of the optimization results is ignored during the parameter optimization stage.Based on the previously mentioned probability optimization model based on the joint distribution of the Copula mixed response,the controllable factor fluctuations are also considered for the target.Influence of function sensitivity robustness and constraint feasible robustness,a hybrid response robust parameter design method considering the fluctuation of controllable factors is constructed.On the one hand,this method considers the position utility and divergence utility of the consistency probability within the fluctuation range of the controllable factors,and combines the entropy weight theory to construct a robust probability objective function.Robust Constraint Function with Maximum Factor Variation.Finally,a case study shows that the proposed method can not only reduce the sensitivity of the objective function to the controllable factor fluctuations,but also ensure that the optimal solution always falls in the feasible region,which is a true and feasible optimal solution in the true sense.The above research expands the research content on the existence of mixed response and controllable factor fluctuations in the traditional robust parameter design,and provides some new ideas and methods for the quality design of product / process parameter design.Based on this,it also points out the future Directions to be studied.