Variable Selection And Robust Parameter Design Based On Generalized Linear Models

Quality design is an important supporting technology in the continuous quality improvement activities, which mainly is used in the design stage of products or processes, so it can reduce and control the variation of products or processes at the beginning. With the widespread application of experimental design, quality engineers have frequently encountered non-normal responses such as Poisson responses (number of defects), binomial responses (proportion defective data), or exponential responses (time to failure data). In industrial experiments, non-normal responses usually satisfy the characteristics of the exponential family distribution, that is, the response variance is the function of the response mean. Generalized linear models (GLM) not only are suitable for extensive exponential family distribution, but only can establish the function relationship between the response mean and variance. Therefore, some researchers had paid much more attention to quality design based on GLM.In the paper, taking the quality design of non-normal responses as the subject of the research, we systematically study the problems of variable selection and robust parameter design based on GLM by means of the systematic modeling, simulation experiment and empirical research, which synthetically use the techniques and methods of GLM, Bayesian statistics, stochastic search technique and heuristic approach. Some main results are summarized as follows.(1) Bayesian estimation and analysis of screening experiments based on GLM. As for some special experimental data such as over-dispersion and zero-inflation, we firstly carry out the Bayesian estimation of model parameters based on GLM by using MCMC simulation technique and SAS statistical software, and then propose a new approach of identifying significant factors through the posterior probabilities of these parameters which are larger than zero or less than zero. Finally, the effectiveness of the proposed method is verified by the wave soldering experiment and simulated fractional factorial design.(2) Two-stage Bayesian variable and model selection based on GLM. As for fractional factorial experiment design with non-normal responses, taking the deviance information criterion (DIC) as the assessment criterion of Bayesian models, we propose an approach of two-stage Bayesian variable and model selection by using MCMC method and stepwise iterative optimization technique. a practical example is analyzed by the proposed approach. The results reveal that the proposed approach can deal with the problems of variable and model selection when the number of experimental factors is large, and can effectively extend the method of variable selection and modeling techniques for the fractional factorial experiment with non-normal responses.(3) Bayesian variable and model selection based on GLM and stochastic search technique. The number of model under consideration is very large when the number of factors in screening experiments is large. In such cases, it is necessary to seek an efficient algorithm which can search the whole model space (the model set consisting of different candidate variables) and identify significant factors and select the best model by means of the posterior probabilities of the candidate variables and models. In view of the difference of information which the experimenters can obtain, we propose two approaches of Bayesian variable and model selection based on GLM by using the stochastic search technique. The effectiveness of the proposed approach is demonstrated by a practical industrial example and a simulation experiment. In some cases, the experimenters can learn about the important interaction effects based on past experience and prior information. In such case, an approach of Bayesian variable and model selection is proposed by using the stochastic search technique based on GLM. However, the experimenters often lack some prior information and experience knowledge about the experiments under consideration. Therefore, we further consider three basic factorial effect principles (effect sparsity principle, effect hierarchical principle and effect heredity principle) on the basis of the above study, and propose a multi-stage approach of Bayesian variable and model selection which combines the factorial effect principles with GLM. Compared with the previous methods, the proposed approach considering three basic factorial effect principles can effectively reduce the model space under consideration. Furthermore, The best model considering the factorial effect principles usually conforms to the basic idea of experimental design, so it can avoid gaining a good fitting but nonsensical model.(4) Dual response surface methodology and robust parameter design based on GLM. As for the robust parameter design with non-normal responses, we propose a dual response surface model for GLM based on the jointed generalized linear models of mean and dispersion. Then, in view of the very complicated nonlinear functions of dual response surface models, the hybrid function based on genetic algorithm and pattern search is used to realize the robust parameter design of products or processes in the experimental region and obtain the optimum parameter values of the control factors. A resistivity experiment is analyzed by the proposed approach in the paper. The results reveal that the proposed approach not only can reduce the deviate degree between the process mean and the target, but also can reduce the variation of the whole process.(5) Robust parameter design with dynamic responses based on GLM. As for the robust parameter design with dynamic response, we propose an approach of dynamic robust parameter design based on the jointed generalized linear model and response model. As for the system with dynamic responses, we firstly fit the mean model and dispersion model based on GLM respectively, and minimize the variation by selecting the suitable level of dispersion and location factors, and then adjust the intercept and slope of the new model to the target value. An example of push-pull cable actuator is analyzed by the proposed approach in the paper. The results reveal that the new approach not only can effectively distinguish the different influences of the variation between the explicit noise and the hidden noise in the whole process, but also can flexibly adjust the intercept and slope of the model so that it can satisfy the different design goals.Finally, the thesis also discusses some challenging topics which deserve further research in the future based on the above research results.