基于响应曲面方法的乘用车市场研究
|
摘要
本文详细介绍了将响应曲面方法应用到乘用车市场分析的过程步骤,并以2008年的中国乘用车市场的数据作为实证研究,证明了该方法的可行性。将响应曲面方法应用到该领域不仅是对响应曲面方法应用领域的扩展,同时对乘用车市场分析方法的拓展方面也有重要意义。本文提出应用响应曲面方法分析乘用车市场的销售数据,确定不同因子的权重及因子的交互作用,并解析乘用车市场的量化规律。影响乘用车市场销售量的因素有很多,本文主要分析的是乘用车价格,以及不同车型间交互影响的作用对乘用车销售量的影响。
响应曲面方法是数学方法和统计技术相结合的产物,是用来对所感兴趣的问题进行建模和分析的一种方法,目的是找到被众多因素所影响的响应的最优值。响应曲面方法一直在工程领域中应用,但在市场分析等经济领域并没有得到过很好地运用。正是基于此,本文提出将响应曲面方法扩展到经济分析应用领域,以乘用车市场为研究对象,通过深入解析其市场销售数据,从而对乘用车市场的变化规律产生深刻的量化认知。
本文介绍了响应曲面近几年的方面的发展,作为对响应曲面方法理论方面的归纳总结。在第三章中,详细介绍了应用响应曲面方法分析乘用车市场的具体步骤,包括:对乘用车市场的建模、回归模型的参数估计、回归模型参数估计的计算过程和回归模型的诊断。通过建模、参数估计、计算、误差分析等过程,完整的介绍了响应曲面应用于乘用车市场的具体方法,为后面的分析奠定了坚实的理论基础。
乘用车市场中的汽车种类繁多,关系复杂。数据非常分散、无规律。为了能够更好对数据进行分析,更清晰的量化出乘用车市场,需要对乘用车市场进行价值分类。本文对2008年中国主要乘用车市场中127款车型进行了分类研究。各型主要乘用车的销售量和价格完全是由市场决定的,根据市场数据对主要乘用车进行价值分类是实证研究,其结果具有客观公正性。通过市场细分得到不同市场的价值,五类市场的价值分别为1.35亿元、6.87亿元、28.03亿元、58.58亿元和87.04亿元。因此,中国主要乘用车总体市场价值不低于180亿元。
确定了价值分类之后,本文对五类细分市场分别用响应曲面方法进行建模、计算、分析和归纳,得到了五类细分市场对应的响应曲面函数以及车型的影响权重和车型间的相互影响权重。通过本文的分析,可以帮助厂商明确各自市场竞争的对手,精确制定市场营销策略和整体经营战略。因此本文的研究具有一定的实际意义。
This paper introduces the response surface method, which is applied to the car market analysis. The process steps of vehicle market analysis using response surface is given in this paper. Then we set an example of 2008 China vehicle market data as empirical research, which can prove the feasibility of this method. Using Response surface method to the fields is not only to extend application of Response surface method, but also have great significance to the car market analysis development.
In volatile external environment, how to maintain its normal production and sales now becomes a major concern of the main problems. Hoping enterprises have better development must have a profound understanding of the market law. In this paper response surface method was used in analysis of the car market sales data. Then we defined different factor weights and factor interactions and analyzed the passenger car market quantization rule.
Response surface method (RSM) is mathematics method and the outcome of the combination of statistical techniques. RSM is used for interested problem of modeling and analysis, which is a new method for purpose to find out the optimal value of the response among influence factors. Response surface method has been applied in engineering field, but in the market analysis and economic fields have received very good use. Based on this, the paper puts forward the response surface method will be expanded to economic analysis on passenger cars, the market as the research object, by analyzing its market sales data deeply, so as to change rules of passenger car market profound quantification.
This paper introduces the response surface in recent years, as the development and summary of response surface method. After that we is put forward using the response surface method in passenger car market analysis. In the third chapter, we detailed introduced the specific steps of the response surface method analysis application of the passenger car market, including modeling and parameter estimation, the calculation and error analysis, etc. this paper complete introduced the specific methods about that response surface applied in passenger car market through steps above. The introduction about specific steps laid a solid theoretical foundation for the analysis below.
The car passenger market is variety because of the complex relationship. In order to better data analysis, a clear measure of a car market, we need to take the car market value for classification. This paper studied on the classification of market value about China's major passenger car for 127 classification model in 2008. It is empirical research that the value classification for main vehicle is obtained according to the market data. Each major car sales and prices is completely determined by the market. As a result that the classification of market value we got is objective. China main passenger car market can be divided into five types of market segmentation according to the market value. Different market segments can be got through the market value. market value of five segmentations is respectively 1.35 billion Yuan, 6.87 billion Yuan, 28.03 billion Yuan, 58.58 billion and 87.04 billion Yuan Therefore, main passenger car market value in China is more than general 180 million Yuan.
After determining the value about the classification, this paper did modeling, calculation, analysis and induction respectively with five kinds of market segmentation using response surface method, and got the weight of five kinds of market segmentation and models of mutual influence weight among the corresponding response surface function models. Through analysis of this paper, we can define manufacturers’respective market competition, and help manufacturers accurate formulate marketing strategy and overall business strategy.
响应曲面方法是数学方法和统计技术相结合的产物,是用来对所感兴趣的问题进行建模和分析的一种方法,目的是找到被众多因素所影响的响应的最优值。响应曲面方法一直在工程领域中应用,但在市场分析等经济领域并没有得到过很好地运用。正是基于此,本文提出将响应曲面方法扩展到经济分析应用领域,以乘用车市场为研究对象,通过深入解析其市场销售数据,从而对乘用车市场的变化规律产生深刻的量化认知。
本文介绍了响应曲面近几年的方面的发展,作为对响应曲面方法理论方面的归纳总结。在第三章中,详细介绍了应用响应曲面方法分析乘用车市场的具体步骤,包括:对乘用车市场的建模、回归模型的参数估计、回归模型参数估计的计算过程和回归模型的诊断。通过建模、参数估计、计算、误差分析等过程,完整的介绍了响应曲面应用于乘用车市场的具体方法,为后面的分析奠定了坚实的理论基础。
乘用车市场中的汽车种类繁多,关系复杂。数据非常分散、无规律。为了能够更好对数据进行分析,更清晰的量化出乘用车市场,需要对乘用车市场进行价值分类。本文对2008年中国主要乘用车市场中127款车型进行了分类研究。各型主要乘用车的销售量和价格完全是由市场决定的,根据市场数据对主要乘用车进行价值分类是实证研究,其结果具有客观公正性。通过市场细分得到不同市场的价值,五类市场的价值分别为1.35亿元、6.87亿元、28.03亿元、58.58亿元和87.04亿元。因此,中国主要乘用车总体市场价值不低于180亿元。
确定了价值分类之后,本文对五类细分市场分别用响应曲面方法进行建模、计算、分析和归纳,得到了五类细分市场对应的响应曲面函数以及车型的影响权重和车型间的相互影响权重。通过本文的分析,可以帮助厂商明确各自市场竞争的对手,精确制定市场营销策略和整体经营战略。因此本文的研究具有一定的实际意义。
This paper introduces the response surface method, which is applied to the car market analysis. The process steps of vehicle market analysis using response surface is given in this paper. Then we set an example of 2008 China vehicle market data as empirical research, which can prove the feasibility of this method. Using Response surface method to the fields is not only to extend application of Response surface method, but also have great significance to the car market analysis development.
In volatile external environment, how to maintain its normal production and sales now becomes a major concern of the main problems. Hoping enterprises have better development must have a profound understanding of the market law. In this paper response surface method was used in analysis of the car market sales data. Then we defined different factor weights and factor interactions and analyzed the passenger car market quantization rule.
Response surface method (RSM) is mathematics method and the outcome of the combination of statistical techniques. RSM is used for interested problem of modeling and analysis, which is a new method for purpose to find out the optimal value of the response among influence factors. Response surface method has been applied in engineering field, but in the market analysis and economic fields have received very good use. Based on this, the paper puts forward the response surface method will be expanded to economic analysis on passenger cars, the market as the research object, by analyzing its market sales data deeply, so as to change rules of passenger car market profound quantification.
This paper introduces the response surface in recent years, as the development and summary of response surface method. After that we is put forward using the response surface method in passenger car market analysis. In the third chapter, we detailed introduced the specific steps of the response surface method analysis application of the passenger car market, including modeling and parameter estimation, the calculation and error analysis, etc. this paper complete introduced the specific methods about that response surface applied in passenger car market through steps above. The introduction about specific steps laid a solid theoretical foundation for the analysis below.
The car passenger market is variety because of the complex relationship. In order to better data analysis, a clear measure of a car market, we need to take the car market value for classification. This paper studied on the classification of market value about China's major passenger car for 127 classification model in 2008. It is empirical research that the value classification for main vehicle is obtained according to the market data. Each major car sales and prices is completely determined by the market. As a result that the classification of market value we got is objective. China main passenger car market can be divided into five types of market segmentation according to the market value. Different market segments can be got through the market value. market value of five segmentations is respectively 1.35 billion Yuan, 6.87 billion Yuan, 28.03 billion Yuan, 58.58 billion and 87.04 billion Yuan Therefore, main passenger car market value in China is more than general 180 million Yuan.
After determining the value about the classification, this paper did modeling, calculation, analysis and induction respectively with five kinds of market segmentation using response surface method, and got the weight of five kinds of market segmentation and models of mutual influence weight among the corresponding response surface function models. Through analysis of this paper, we can define manufacturers’respective market competition, and help manufacturers accurate formulate marketing strategy and overall business strategy.
引文
1 Montgomery D C. Design and Analysis of Experiment(6th Edition英文版).北京:人民邮电出版社, 2007.
2肖粤翔.非参数响应曲面方法研究及应用.天津大学硕士学位论文,2004:4-5
3 R. Coetzer, R. F. Rossouw and D. Lin. Dual Response Surface Optimization With Hard-To-Control Variables For Sustainable Gasifier Performance. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS. 2008, 57: 567~587.
4 L. Michielan, M. Bacilieri, C. Kaseda and S. Moro. Prediction Of The Aqueous Solvation Free Energy Of Organic Compounds By Using Autocorrelation Of Molecular Electrostatic Potential Surface Properties Combined With Response Surface Analysis. BIOORGANIC & MEDICINAL CHEMISTRY. 2008, 16(10): 5733~5742
5 J. H. Noguera and E. F. Watson. Response Surface Analysis Of A Multi-Product Batch Processing Facility Using A Simulation Metamodel. INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS. 2006, 102(2): 333~343.
6 T. C. Bailey and P. J. Hewson. Simultaneous Modelling Of Multiple Traffic Safety Performance Indicators By Using A Multivariate Generalized Linear Mixed Model. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY. 2004, 167(Part 3): 501~517.
7 H. H. Lai, Y. M. Chang and H. C. Chang. A Robust Design Approach For Enhancing The Feeling Quality Of A Product: A Car Profile Case Study. INTERNATIONAL JOURNAL OF INDUSTRIAL ERGONOMICS. 2005, 35(5): 445~460.
8何桢,张生虎,刘子先,齐二石.双响应曲面方法在改进产品设计中的应用研究.系统工程理论与实践,2001,(9).
9付梦印,邓志红,张继伟. Kalman滤波理论及其在导航系统中的应用.北京:科学出版社,2003: 12~20.
10 Zhang Fan,Liu Yu. Study on quality control method of using the Kalman filtering. International Conference on E-Business and Information System Security (EBISS), 2009, Wuhan: 572~576.
11杨康,蒋明青.基于卡尔曼滤波的需求预.科学技术与工程,2009,(15):4576~4578
12潘志刚,韩颖.组合预测法在我国汽车市场需求预测中的应用.商业研究,2006,(20):126~129
13胡伟.我国汽车销售量预测研究.河海大学硕士学位论文.2007,9~20
14付保宗,.我国乘用车市场特点及影响因素分析.中国经贸导刊,2009,(24): 15~16 .
15卢幸.未来几年国内乘用车市场的主要特征.上海汽车,2009,(3): 39~42.
16朱翠珊.基于价值体系模型的乘用车消费者需求研究.东华大学,2005: 59~60.
17 V. N. Nair, B. Abraham, J. Mackay, G. Box, R. N. Kacker, T. J. Lorenzen, J. M. Lucas, R. H. Myers, G. G. Vining, J. A. Nelder, M. S. Phadke, J. Sacks, W. J. Welch, A. C. Shoemaker, K. L. Tsui, S. Taguchi and C. Wu. Taguchi Parameter Design - A Panel Discussion. TECHNOMETRICS. 1992, 34(2): 127~161.
18 Lin DKJ, Tu W. Dual response surface optimization. Journal of Quality Technology 1995; 27:34–39.
19 Copeland KAF, Nelson PR. Dual response optimization via direct function minimization. Journal of Quality Technology 1996; 28:331–336.
20 Kim K, Lin DKJ. Dual response surface optimization: A fuzzy modeling approach. Journal of Quality Technology 1998; 30:1–10.
21 Del Castillo E, Fan SK, Semple J. Computation of global optima in dual response systems. Journal of Quality Technology 1997; 29:347–353.
22 Fan SKS. A generalized global optimization algorithm for dual response systems. Journal of Quality Technology 2000;32:444–456.
23 Tang LC, Xu K. A unified approach for dual response optimization. Journal of Quality Technology 2002; 34:437–447.
24 K¨oksoy O, Doganaksoy N. Joint optimization of mean and standard deviation using response surface methods. Journal of Quality Technology 2003; 35:239–252.
25 O. Koksoy and T. Yalcinoz. A Hopfield Neural Network Approach To The Dual Response Problem. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2005, 21(6): 595~603.
26 W. R. Myers, W. A. Brenneman and R. H. Myers. A Dual-Response Approach To Robust Parameter Design For A Generalized Linear Model. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(2): 130~138.
27 A. Giovagnoli and D. Romano. Robust Design Via Simulation Experiments: A Modified Dual Response Surface Approach. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2008, 24(4): 401~416.
28 Welch WJ, Yu TK, Kang SM, Sacks J. Computer experiments for quality control by parameter design. Journal of Quality Technology 1990; 22:15~22.
29 Myers RH, Khuri AI, Vining GG. Response surface alternatives to the Taguchi robust parameter design approach. The American Statistician 1992; 46:131~139.
30 Myers RH, Montgomery DC. Response Surface Methodology: Process and Product Optimization Using Designed Experiments (2nd). Wiley: New York, 2002.
31 Myers RH, Kim Y, Griffiths KL. Response surface methods and the use of noise variables. Journal of Quality Technology 1997; 29:429–440.
32 Khuri AI. Response surface models with mixed effects. Journal of Quality Technology 1996; 28:177–186.
33 Jeong, I. J. and K. J. Kim, et al.. Optimal weighting of bias and variance in dual response surface optimization. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(3): 236~247.
34 Borkowski, J. J.. A comparison of prediction variance criteria for response surface designs. JOURNAL OF QUALITY TECHNOLOGY. 2003, 35(1): 70~77.
35 Wesley, W. R. and J. R. Simpson, et al.. Exact Calculation of Integrated Prediction Variance for Response Surface Designs on Cuboidal and Spherical Regions. JOURNAL OF QUALITY TECHNOLOGY. 2009, 41(2): 165~180.
36 Mee, R. W.. Optimal three-level designs for response surfaces in spherical experimental regions. JOURNAL OF QUALITY TECHNOLOGY. 2007, 39(4): 340~354.
37 Sahni, N. S. and G. F. Piepel, et al.. Product and Process Improvement Using Mixture-Process Variable Methods and Robust Optimization Techniques. JOURNAL OF QUALITY TECHNOLOGY. 2009, 41(2): 181~197.
38 Ringrose, T. J. and S. A. Forth. Simplifying multivariate second-order response surfaces by fitting constrained models using automatic differentiation. TECHNOMETRICS. 2005, 47(3): 249~259.
39 Govaerts, B. and J. Noel. Analysing the results of a designed experiment when the response is a curve: Methodology and application in metal injection moulding. QUALITY ANDRELIABILITY ENGINEERING INTERNATIONAL. 2005, 21(5): 509-520.
40 Giovagnoli, A. and D. Romano. Robust design via simulation experiments: A modified dual response surface approach. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2008, 24(4): 401~416.
41 Vining, G. G. and S. M. Kowalski, et al.. Response surface designs within a split-plot structure. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(2): 115~129.
42 Parker, P. A. and S. A. Kowalski, et al.. Classes of split-plot response surface designs for equivalent estimation. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2006, 22(3): 291~305.
43 Naes, T. and A. H. Aastveit, et al.. Analysis of split-plot designs: An overview and comparison of methods. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2007, 23(7): 801-820.
44 Vining, G. G. and S. M. Kowalski. "Exact inference for response surface designs within a split-plot structure." JOURNAL OF QUALITY TECHNOLOGY. 2008, 40(4): 394~406.
45 Wang, L.,Kowalski, S. and Vining, G. G.. Orthogonal blocking of response surface split-plot designs. Journal of Applied Statistics. 2009, 36(3): 303~321.
46胡雅琴.响应曲面二阶设计方法比较研究.天津大学硕士学位论文,2005:2~3
47蒙哥马利(Montgomery, Douglas C.).实验设计与分析.人民邮电出版社, 2009:347~392
48梁保松.模糊数学及其应用.科学出版社,2007:131~142 .
2肖粤翔.非参数响应曲面方法研究及应用.天津大学硕士学位论文,2004:4-5
3 R. Coetzer, R. F. Rossouw and D. Lin. Dual Response Surface Optimization With Hard-To-Control Variables For Sustainable Gasifier Performance. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS. 2008, 57: 567~587.
4 L. Michielan, M. Bacilieri, C. Kaseda and S. Moro. Prediction Of The Aqueous Solvation Free Energy Of Organic Compounds By Using Autocorrelation Of Molecular Electrostatic Potential Surface Properties Combined With Response Surface Analysis. BIOORGANIC & MEDICINAL CHEMISTRY. 2008, 16(10): 5733~5742
5 J. H. Noguera and E. F. Watson. Response Surface Analysis Of A Multi-Product Batch Processing Facility Using A Simulation Metamodel. INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS. 2006, 102(2): 333~343.
6 T. C. Bailey and P. J. Hewson. Simultaneous Modelling Of Multiple Traffic Safety Performance Indicators By Using A Multivariate Generalized Linear Mixed Model. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY. 2004, 167(Part 3): 501~517.
7 H. H. Lai, Y. M. Chang and H. C. Chang. A Robust Design Approach For Enhancing The Feeling Quality Of A Product: A Car Profile Case Study. INTERNATIONAL JOURNAL OF INDUSTRIAL ERGONOMICS. 2005, 35(5): 445~460.
8何桢,张生虎,刘子先,齐二石.双响应曲面方法在改进产品设计中的应用研究.系统工程理论与实践,2001,(9).
9付梦印,邓志红,张继伟. Kalman滤波理论及其在导航系统中的应用.北京:科学出版社,2003: 12~20.
10 Zhang Fan,Liu Yu. Study on quality control method of using the Kalman filtering. International Conference on E-Business and Information System Security (EBISS), 2009, Wuhan: 572~576.
11杨康,蒋明青.基于卡尔曼滤波的需求预.科学技术与工程,2009,(15):4576~4578
12潘志刚,韩颖.组合预测法在我国汽车市场需求预测中的应用.商业研究,2006,(20):126~129
13胡伟.我国汽车销售量预测研究.河海大学硕士学位论文.2007,9~20
14付保宗,.我国乘用车市场特点及影响因素分析.中国经贸导刊,2009,(24): 15~16 .
15卢幸.未来几年国内乘用车市场的主要特征.上海汽车,2009,(3): 39~42.
16朱翠珊.基于价值体系模型的乘用车消费者需求研究.东华大学,2005: 59~60.
17 V. N. Nair, B. Abraham, J. Mackay, G. Box, R. N. Kacker, T. J. Lorenzen, J. M. Lucas, R. H. Myers, G. G. Vining, J. A. Nelder, M. S. Phadke, J. Sacks, W. J. Welch, A. C. Shoemaker, K. L. Tsui, S. Taguchi and C. Wu. Taguchi Parameter Design - A Panel Discussion. TECHNOMETRICS. 1992, 34(2): 127~161.
18 Lin DKJ, Tu W. Dual response surface optimization. Journal of Quality Technology 1995; 27:34–39.
19 Copeland KAF, Nelson PR. Dual response optimization via direct function minimization. Journal of Quality Technology 1996; 28:331–336.
20 Kim K, Lin DKJ. Dual response surface optimization: A fuzzy modeling approach. Journal of Quality Technology 1998; 30:1–10.
21 Del Castillo E, Fan SK, Semple J. Computation of global optima in dual response systems. Journal of Quality Technology 1997; 29:347–353.
22 Fan SKS. A generalized global optimization algorithm for dual response systems. Journal of Quality Technology 2000;32:444–456.
23 Tang LC, Xu K. A unified approach for dual response optimization. Journal of Quality Technology 2002; 34:437–447.
24 K¨oksoy O, Doganaksoy N. Joint optimization of mean and standard deviation using response surface methods. Journal of Quality Technology 2003; 35:239–252.
25 O. Koksoy and T. Yalcinoz. A Hopfield Neural Network Approach To The Dual Response Problem. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2005, 21(6): 595~603.
26 W. R. Myers, W. A. Brenneman and R. H. Myers. A Dual-Response Approach To Robust Parameter Design For A Generalized Linear Model. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(2): 130~138.
27 A. Giovagnoli and D. Romano. Robust Design Via Simulation Experiments: A Modified Dual Response Surface Approach. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2008, 24(4): 401~416.
28 Welch WJ, Yu TK, Kang SM, Sacks J. Computer experiments for quality control by parameter design. Journal of Quality Technology 1990; 22:15~22.
29 Myers RH, Khuri AI, Vining GG. Response surface alternatives to the Taguchi robust parameter design approach. The American Statistician 1992; 46:131~139.
30 Myers RH, Montgomery DC. Response Surface Methodology: Process and Product Optimization Using Designed Experiments (2nd). Wiley: New York, 2002.
31 Myers RH, Kim Y, Griffiths KL. Response surface methods and the use of noise variables. Journal of Quality Technology 1997; 29:429–440.
32 Khuri AI. Response surface models with mixed effects. Journal of Quality Technology 1996; 28:177–186.
33 Jeong, I. J. and K. J. Kim, et al.. Optimal weighting of bias and variance in dual response surface optimization. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(3): 236~247.
34 Borkowski, J. J.. A comparison of prediction variance criteria for response surface designs. JOURNAL OF QUALITY TECHNOLOGY. 2003, 35(1): 70~77.
35 Wesley, W. R. and J. R. Simpson, et al.. Exact Calculation of Integrated Prediction Variance for Response Surface Designs on Cuboidal and Spherical Regions. JOURNAL OF QUALITY TECHNOLOGY. 2009, 41(2): 165~180.
36 Mee, R. W.. Optimal three-level designs for response surfaces in spherical experimental regions. JOURNAL OF QUALITY TECHNOLOGY. 2007, 39(4): 340~354.
37 Sahni, N. S. and G. F. Piepel, et al.. Product and Process Improvement Using Mixture-Process Variable Methods and Robust Optimization Techniques. JOURNAL OF QUALITY TECHNOLOGY. 2009, 41(2): 181~197.
38 Ringrose, T. J. and S. A. Forth. Simplifying multivariate second-order response surfaces by fitting constrained models using automatic differentiation. TECHNOMETRICS. 2005, 47(3): 249~259.
39 Govaerts, B. and J. Noel. Analysing the results of a designed experiment when the response is a curve: Methodology and application in metal injection moulding. QUALITY ANDRELIABILITY ENGINEERING INTERNATIONAL. 2005, 21(5): 509-520.
40 Giovagnoli, A. and D. Romano. Robust design via simulation experiments: A modified dual response surface approach. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2008, 24(4): 401~416.
41 Vining, G. G. and S. M. Kowalski, et al.. Response surface designs within a split-plot structure. JOURNAL OF QUALITY TECHNOLOGY. 2005, 37(2): 115~129.
42 Parker, P. A. and S. A. Kowalski, et al.. Classes of split-plot response surface designs for equivalent estimation. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2006, 22(3): 291~305.
43 Naes, T. and A. H. Aastveit, et al.. Analysis of split-plot designs: An overview and comparison of methods. QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL. 2007, 23(7): 801-820.
44 Vining, G. G. and S. M. Kowalski. "Exact inference for response surface designs within a split-plot structure." JOURNAL OF QUALITY TECHNOLOGY. 2008, 40(4): 394~406.
45 Wang, L.,Kowalski, S. and Vining, G. G.. Orthogonal blocking of response surface split-plot designs. Journal of Applied Statistics. 2009, 36(3): 303~321.
46胡雅琴.响应曲面二阶设计方法比较研究.天津大学硕士学位论文,2005:2~3
47蒙哥马利(Montgomery, Douglas C.).实验设计与分析.人民邮电出版社, 2009:347~392
48梁保松.模糊数学及其应用.科学出版社,2007:131~142 .