Non-normal Response Robust Design Based On Generalized Linear Model And Bayesian Methods

Robust parameter design,as an important technology of continuous quality improvement,has been widely used in product development.The core ideology of robust parameter design is to minimize the fluctuation of the product quality characteristic value around the target on the basis of ensuring the mean value as close as possible to the target The method can adjust the level of controllable factors by utilizing the nonlinear relationship between the response variables and controllable factors and the interactions between controllable factors,so that the output of the product is not sensitive to the change of noise factors.Thus,the purpose of reducing the fluctuation of the quality characteristic can be achieved,and high quality products can be obtained at a lower cost.Most of previous researches on robust parameter design assume that quality response variables obey the normal distribution.However,a large amount of non-normal response cases also exist in the actual production process.For the problem of non-normal response quality design,generalized linear modeling method can be chosen to establish the functional relationship between response mean and variance by link function.Small sample experiments are usuallyimplemented in the actual production processes due to the expensive cost for full experiments.However,the limits of small sample experiment data may lead to high uncertainty of model parameters in the modeling process.On the contrast,Bayesian methods can make full use of prior information of parameters to solve the uncertainty problem of model parameters to some extent.Therefore,the problem of large uncertainty of model parameters caused by the limits of small sample data,the diversity problem of products from different batches in productions and the problems of noise factors in the non-normal response quality design are discussedin this paper.The robust parameter design of non normal response with generalized linear model and Bayesian method is studied systematically by using system modeling,simulation analysis and example verification.The detailed contents of this paper are as follows:(1)Robust parameter design for Bayesian generalized linear mixed model considering batches differences.In actual production,the quality of products from different production batches may have significant difference.For the non-normal response robust parameter design in batch production,the batches differences were set as random variables.A generalized linear mixed model based on the Bayesian inferences and MCMC methods was constructed in the paper under the framework of Bayesian method.In the batches production case,the mean square error is selected asthe optimization indicator to optimize the parameters using genetic algorithm and other optimization methods.(2)Robust parameter design for split-plot experiment based on the Bayesian generalized linear model.During the process of quality design in split-plot experiment,the split-plot factors were set as noise variables because split-plot factors are difficult to change.A Bayesian generalized linear model including response variables,significant parameters and noise factors was created based on the MCMC method.After obtaining large amount of sample data from the proposed model,parameter optimizations based on indicators of the mean square error and the rate of qualified products are implemented respectively.And the optimized results with or without considerations of the robustness of model were compared.(3)Robust parameter design for double hierarchical generalized linear model constructed considering noise factors.In order to further explore the influence of noise factorson the process,a double hierarchical generalized linear model was constructed including response variable,control factors and noise factors on the basis of Bayesian methods.And the mean square error was chosen as the optimization indicator based on the mean function and the variance function for the optimization of robust parameters.At last,after summarizing the research results,the future research directions are elaborated.