Proceedings for
Symposium on Theory of Uniform Design and Its Application
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Design of Experiment: A Historical Perspective
Dennis K.J. Lin
(Management Science and Information Systems,The Pennsylvania State University)

Statistical design of experiments, while popular in many disciplines, originated with agricultural applications in the 1920's.  This paper discusses the fundamental ideas behind various branches of design of experiments.  This includes treatment allocation, multiple comparisons, blocking, combinatorics, response surface methodology, and the following types of designs: fractional factorials, ANOVA-type, optimal, bayesian, Taguchi, mixture, uniform, supersaturated, and other related designs.  Relationships among them will be described.  Through these relationships, it is hoped that we can generated future research ideas on design of experiments.  This seems to be particularly important for the information technology era we are currently in and that can be expected to continue for decades.
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Connections and Comparisons between Uniform Design and Orthogonal Design
Kai-Tai Fang
(Hong Kong Baptist University & Chinese Academy of Sciences)
Changxing, Ma
(Nankai University)
In this paper we review recent development of theory of the uniform design and its applications, in particular, review connections and comparisons between the uniform design and the orthogonal design from various aspects.
This acticle consists of eight sections: model, construction of orthogonal designs and uniform designs, measures of uniformity, searching orthogonal and nearly orthogonal designs by optimization, uniformly orthogonal designs, applications of the uniformity in isomorphism and projection properties of the orthogonal design, some problems in application of the uniform design and lattice design, some problems in application of the uniform design and lattice design in Fourier regression models.  Several orthogonal design tables are recommended.
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Optimal Designs for Experiments with Mixtures: A Survey
Ling-Yau Chan
(Dept. Of Industrial and manufacturing Systems Engineering, The University of Hong Kong)

This is a survey article on known results about analytic solutions and some numerical solutions of optimal designs for various regression models for experiments with mixtures.  The regression models include polynomial models, models containing homogeneous functions, models containing inverse terms and ratios, log contrast models, models with process variables, and models containing the amount of mixture.  Optimality criteria considered include D-, A-, e- Fp- and Il - optimalities.  Uniform design and uniform optimal design for mixture components, and efficiencies of the {q,2} simplex-centroid design are briefly discussed.
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Uniform Design and Its Applications in Chemistry and Chemical Engineering
Yizeng Liang
(College of Chemistry and Chemical Engineering, Institute of Chemonetrics and Chemical Sensoring Technology, Changsha, PRC. 410082)
Kai-Tai Fang
(Dept. of Mathematics, Hong Kong Baptist University)
Three major methods of experimental design, such as factorial design including fractional factorial design and orthogonal design, D-optimal design and uniform design, and their applications in chemistry and chemical engineering are reviewed and compared.  The features of uniform design are specially addressed.  Several different cases applying uniform design to chemical research showed that the uniform design is a very promising and powerful experimental design method.  Uniformity of space filling is the most important and essential feature of the uniform design.  Based on this feature, its cost-efficiency, robustness and flexibility make it very useful in chemistry and chemical engineering.
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Uniform Designs with Categorical Factors
Zhu Wang
(Computer Centre, China National Star Petroleum Corporation)
Kai-Tai Fang
(Dept. of Mathematics, Hong Kong Baptist University)
Categorical factors are often involved in design of experiments.  There are not many papers dealing with uniform designs with categorical factors.  In this article, we give a brief discussion of the use of the uniform design that involves categorical factors and related data analysis.  Some illustration examples are given.
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Promoting Further Spread and Application of the Uniform Designed Method
Yin He-ling     Wang Fen
(Dept. of Electronics, Information and Basis Headquarters of the General Equipment)
Summing up experience and constantly bring forth new ideas, raising the research and spread of the uniform designed method to a high level.
To establish a good operative mechanism is the key to promoting the development of science and technology achievement spread.  This paper expounds the important role played in developing institute organization and promoting technology spread by combing administration with institute.  Meanwhile, to the needs of economic and national defense building and the developing strategy of achieving China's rejuvenation by science and education, the spread of the uniform designed method is significant potential and broad prospects in application.  This paper is emphatically geared to national defense science and technology and weaponry development, puts forward a few suggestions of further spread and application of the uniform designed method.
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Improved Uniform Sequential Algorithm for Optimization by Genetic Algorithm and its Application
Hongqian Liu      Zixin Li      Dexian Ma     Jiagang Ren

While dealing with the problem of synthesis on process system engineering(PSE), we often meet multi-peak and singularity, even fail to get optimum. In this paper, we introduce sequential algorithm for optimization into the synthesis of PSE, and we do some improvement to this algorithm by the technique of genetic algorithm(GA).  Finally, we test the enhanced sequential algorithm for optimization by some test functions form GA and from standard synthesis problem in PSE .
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Statistical Analysis with Repeated Trials in Uniform Design
Sun, Shang-gong
(Beijing Medical University)

The weighted regression analysis is listed in paper, and the reciprocal of trial variance is taken as the weight.  The theoretical optimal coefficient of determination of data and the degree of lack of fit on the regression function could be estimated.  An example is detailed and its problems in SAS software are pointed out.  Author does not think it is good that using average value of the repeated trial results analyze data and the stepwise procedure of regression analysis select variables if size of variables is more than sample size.
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The Usefulness of Repeated Experiments in Experimental Designs
Chang-xing Ma
(Nankai University)
Kai-tai Fang
(Hong Kong Baptist University)

Most classical experimental designs request duplicates of experiment points.  Obviously, repeated experiments increase the budget and time of the experiments, but give in general better estimation of parameters in the underlying model.  Is it necessary to have duplicates in experimental design?  In this note we give several examples to show the usefulness of repeated experiments and to discuss when one can do experiment without duplicated.
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The Practice and Research for the Application of the Uniform Design Method
Lin shou-yi            Yang hong-yuan
(China Defense Science and Technology information Center)

The spread of the uniform design method is an important task after the invention of uniform designed method.  Through studying and summarizing the spread practice since 1994, this paper describes how construct framework for the spread of the uniform design method and amplify service function of the spread system. Organized and planned to proceed technology transfer and diffusion. Call up science and technology researcher and community to apply this method in our country all trades and demesnes for quick Formation scale and benefit. Acceleration the uniform design method to conversion reality productive forces.
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Uniform Design Table for Parameter Estimates of Wave Growth Curve Model
Wu Lijun      Hu Xijian
(Mathematics Department, Xinjiang University)
Paper [1] estimates the parameters of logical curves by orthogonal table. Paper [2] fits the parameter of wave growth curve model by principal component analysis. They apply mainly to the social economic phenomena growing but less undulating. In this paper, we put forward a extended growth curve model attempt to forecasting and analyzing the social economic phenomena more undulating.   Where c(x),w(x) both are variables, and control the range and period of undulate.  Generally, by the case of wave, they may be line, parabola, index curve and logarithm curve etc. The parameters a and b are obtained by principal component analysis and c(x), w(x) and f are estimated by uniform design table motivated by the idea of the work in [1].
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On Uniform Design and Knowledge Discovery in Database and Data Mining
Qian jin
(Zhongnan University of Finance and Economics, Wuhan, P.R.C)

When uniform design (UD) is used to solve an optimization problem, a set of uniform distributed points in the test area is produced based on the Number Theorem ( NTM). Usually the number of points is very large, for example, to do an experiment for a problem with S factors and Q levels, S! possible selections are produced and QS records are written into the database. Knowledge discovery in database (KDD) and data mining (DM) is another technique for optimization, it discovers the rich knowledge from the experiment data, so it is better to combine these two methods in solving optimization problems. In this paper a case study is presented by using the joined method. In this study, the joined method is applied to the problem of material mix in designing the deep-water leakage-proof cofferdam in the Three Gorge Project. The UD method is used to do 10 experiments and the data from the experiments are used to train a neural network, then two mix results are obtained. It has been verified that the result is satisfactory. This shows the ability of NTM-based UD method to simplify optimization problems and extract useful information. At the same time, if the UD is not combined with Artificial Neural Network (ANN), then the solution can only be selected among the data groups 6, 7 and 8, which is worse than the obtained one and cannot meet the requirement in respect to1995's standard. In this case study, by using ANN, 900 data groups are "mined out" from the 10 data "mineral deposit", so two satisfactory solutions are "discovered". These solutions produce the mix for the flexible material that meets the mechanics requirement under the water of 100 meters. This shows important role played by the technique of KDD & DM in UD applications.
In Fang, Wang 1996, [3] it is pointed out that in optimization NTM makes great challenge to other methods including simulated annealing method (SAM). Thus, it gives rise to a question that can we use UD to conduct the ANN to make knowledge discovery?
In the past 20 years, regression model is widely used to analyze the data produced by UD experiments. In this way, less than one tenth of KDD & DM is used. We use UD to conduct DELPHI polling, with four factors considered and six exports selected , 24 tables of U6 (64) can be produced. By using the method proposed by the author of this paper in [9], a database be called UD database with 64 = 1296 records is produced. By using the criteria of extenics and based on the practical applications, we can select a set of solutions for consideration.
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Application of Uniform Design of Experiments with Mixtures in Refractories Technology
Li Haiyan
(Dept.of Math. and Phy., Anshan Iron and Steel Inst., Anshan China)
Li Jiukun
(Dept.of Management, Shenyang Arch. and Civ. Eng. Inst., Shenyang China)
Sun Hongbo
(Dept.of Basic course, Shenyang Arch. and Civ. Eng. Inst., Shenyang China)

The paper analyses the factors effecting compressive strength.  According to the experiment extent decided by the factors the research is carried out by improving uniform design of experiments with mixtures and a perfect technique for increasing compressive strength of magnesia brick is found.
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Application of Uniform Design to Evolutionary Operation
Liao Sen
(School of Chemistry and Chemical Engineering, Zhongshan University, Guangzhou, 510275)
In this paper, we propose the idea and method that employ the uniform design instead of two-level orthogonal design ot the evolutionary operation.  As illustration example is given.
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Evaluation of Terrain Suitability for Navigation Based on the Uniform Design Principle
Su Kang     Guan Shiyi     Yan Hongyi      Song Wei     Zhang Jianzhou
(The Third Design Dept. Of  The Third Research Academy, China Aerospace Corporation, Beijing, China, 100074)

Evaluation of terrain suitability for navigation is a difficult problem encountered in the development of a terrain-aided navigation system. An evaluation method based on the uniform design principle is proposed. It provides a total solution for the problem.
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Nonparametric Experimental Design and Data Analysis
Tian Guoliang
(Dept. of Probability and Statistics, Peking University, Beijing,  100871, PRC)
Xie and Fang (1999) considered the problem of nonparametric experimental design and pointed out that the uniform design measure is an admissible minimax design under a certain sense.  For the case of one variable (or factor), in this paper the uniform design is employed to the arrangement for the nonparametric experiment, and three fitted models (polynomial, Fourier and wavelet) are borrowed to the analysis of experimental data.  Simulation shows that wavelet model possesses a better performance under the criterion of mean square error and with a robust fit.
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Inquiry Into Abustion Oil No.1 Preparation Condition With Uniform Design Method
Zhen Shaoli       Wang Weiping
(Guangzhou First manicipal People Hospital)
The three factors that may affect quality of Abustion Oil No.1 were experimentally observer in nine levels by using Uniform Design and Drafting level.  The test result was analyzed  with Partial Least Square and Residual Analyze. The result of regression analysis shows that the best  preparation  Condition are : Kind of Radix Amebize seu Lithospermi is Lithospermum Erythrorhizon Zucc.; the temperature of oil is 175oC and the soaking time is 19 hours.  The experiment of the optimum seeking preparation condition was applied shows the preparation condition is believable.
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Experiment Research of Purging Down about Prescription Da Chengqi Tang By Uniform Design
Yu Riyue     Zhu Jiagu     Xie Wengung      Chen Sihong     Wu Pei
(Faculty Parmacolloge, Jiangxi College of TCM, Nanchang,China, 330006)

Da Chengqi Tang, composed of Rhubarb (X1), Mirabilite (X2), Immature bitter orange (X3) and Magnolia bark (X4), is one of purgative prescriptions.  The compatible properties of this recipe was explored by experimental researches with uniform design.  The results show that X1, X2 and X4 act as principal drug to expel large intestine of rat  ( Y = 11.1537 + 2.7750X1 + 1.7493X22 + 1.4814X4 - 0.3036X1X2 - 0.0814X3 ),  that X1, X4 and X3 possess the effect of purging stool but X2 inversely (Y =  4.5291 + 0.3763X1 - 0.5357X2 + 0.1986X3 + 0.2458X4 ), that X2 is used to increase the water inside intestine softening hard mass ( Y = 0.8723 + 0.3510X2 - 0.0394X22 + 0.0115X4 + 0.0046X3 ) and to increase the mice numbers of diarrhea (Y= - 0.270 + 3.8985X2 + 0.0234X3 - 0.3558X22 - 0.1531X1).  These results match with those of orthogonal design.  A new result was found that X2 has a optimal dose which was not found by orthogonal design. This experiment shows that uniform design is availability in analyzing the compatible properties of TCM prescription.
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Method of NN Structure Optimization Design Based on Uniform Design
Wang Jianhua    Liu Weiting    Zhu Zhiyu    Chen Yue
(East China Shipbuilding Institute)

The researches of Artificial Neural Networks (ANN) have achieved remarkably wide application and development since its revival in the 1980's. But the characteristic feature -- the abilities of strong learning, strong adaptation, large scale parallel processing, have not been shown obviously. The learning capacity and generalization capacity of ANN are not satisfactory. Yet, its adaptive abilities is weak and it is difficulty to construct networks. As a result, the two major problem in ANN engineering application are researching the optimization design of the topology structure of networks and efficient learning algorithm.
The structure design of ANN mainly depended on experience and repeated experiments, there was not a systematically method to determine the satisfactory networks structure all along. A kind of heuristic construction algorithm or prune algorithm to design networks automatically has been proposed during recent years, but this algorithm is too complicated to be applied. In this paper, uniform design is used to optimize NN structure design, achieving a good effect.
The method of ANN structure optimization design based on uniform design is introduced in this paper, making use of NN detecting pulse compressed signal as example. Three layers structure of ANN is adopted, which consists of input layer, hidden layer, one node in output layer. The 13 digits Barker code signal is taken for input signal, and input layer is acted as classifier. The output value will approach to 1 on condition that receiving code sequential signals is pulse compressed signals. As optimizing design, Backpropagation NN (BP) and Radius Base Function (RBF) NN are adopted respectively, and the number of units in hidden layer, the learning step and the learning rate are chose as three factors for design, and learning error as the performance index.
The conclusion is derived through the experiment in 7 levels of 3 factors: both BP NN and RBF NN should employ 52 hidden units and take 20 as learning rate, 28 as learning step in order to achieve the best effect, that is to say, the time is the shortest and the error is the smallest .
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The Position the Regression Analysis has Occupied in the Data Analysis of the Uniform Design
Yao Zhong Yao
(Dept. of Polymer Material Science and Engineering, South China University of  Technology, Guangzhou, 510641)

The regression analysis should be used in the data analysis of the uniform design, however, the multi-attribution determination method (MADM) only was used in the data analysis of the uniform design for rubber formula experiment. In view of this situation, the author had analysis the same data with regression analysis method of the computer aided research (CAR) system programmed by the author. The procedure and MADM was pointed, it is impossible for other method to replace the regression analysis in the data analysis of uniform design.
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Liu Yongcai        Wang Jianmin
Cruising missile weapon is very complicated system, in which there are lots of designing calculations and testing projects involved.  This article introduces adopting a uniform designing model to solve these problems by illustrations of several application examples.  Compared with comprehensive test and orthogonal designing, this method will bring more significant economical and social benefit, which is worth extending to be applied in the field of cruising missile designing.
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Application of Orthogonal Design and Uniform Design in Chemical Research
Sui Baoyou  Shao Changdong  Xu Xiaodong  Zhao Shuyan
(Research Institute of Qilu Petrochemical co., Zhibo 255400)
Experiment schedules of 6 chemical research subjects were designed with Orthogonal Design and Uniform Design.  The experiment data were treated by Regression Analysis and Variance Analysis and the mathematics models based on them were set up accordingly.  By the bound solution of object function, process conditions and formulas  were optimized.  This paper describes the experiment schedule design and optimization course of 3 of the 6 research subjects, presents the practical effect of the others, and discusses the advantages and disadvantages as well as the questions that should be paid attention to in the application of Orthogonal Design and Uniform Design in chemical scientific research.
The major contributions of this paper are stated as follows: Back to Titles

Optimizing on Processing of Addition Glucose in Glutamic Acid Fermentationby Using Uniform Design Method
Zeng Zhaojun
(Shenyang Pharmaceutical University,110015)
Li Jiukun
(Department of Management Engineering, Shenyang Architectural and Civil Engineering Institute, 110015)

The processing of addition glucose in Glutamic acid fermentation were optimized by using uniform design method.  The yield of Glutamic acid increased by 0.79 g/dl, the transformation rate from glucose into Glutamic acid increased by 2.0%.
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The Distinct Structures of Uniform Designs with 8 Rows
Pang Shanqi
(Dept. of Mathematics, Henan Normal University, Xinxiang, 453002)
In this paper we distinguish the different structures of uniform arrays with 8 rows and 2-5 columns and compute the supremum-minimum distance of each structure.  Then we find the used arrays of uniform arrays which are less in discrepancy are also less in supremum-minimum distance.
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Using Uniform Design in Additive Component Optimization
Li Yuansheng
(Fushun Research Institute of Petroleum & Petrochemicals, Fushun, Liaoning, 113001)

"Uniform design" and optimizing technology are used in the research of additive component optimization and hence desire results are got quickly.
When use the technology in emulsifying component optimization, 5 different compounds are pre-selected as base elements of the promoter for enhancing the emulsifier and U10*(108) form (applying form when S=5) is used designing experiment. Adding amount of every element is used as Xi and dewatering experiment results as Y.  The data are treated with optimization software and the experiential model is built. According to the direction of the model, new promoter components are selected and used in the emulsifying experiments. New results are added to the data and new experiential model is built. After several cycles, desire promoter is made up and the desire delusion results are got.
The promoter is blended with two samples of polyethoxy polypropoxy emulsifier (product name SP169) taking from different producers and the mixtures are added to the crude oil emulsion. Compare with the demulsifier without promoter, the dewatering ability increases obviously in the experiments for two different Liaohe crude. When using promoter 15% in the demulsifying components (15% promoter and 85% demulsifier), the water contain in the demulsified crude can be reduced from 6.30% to 2.41% and 2.38% to 2.04% for two SP169 samples. The promoter cost is much lower than the demulsifier used in the experiments.
When use the technology in toluene emulsion project, 4 factors are examined and the U7 form is used for designing experiment. In the same way as in the crude demulsion project, after several cycles, stable toluene-water emulsion is got quickly. Because many different toluene-water emulsion components can meet the demand, the stable area chart is made out and the effect of different emulsifying agent on emulsion stability is clear.
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Experiment Study of Concrete Filled Steel Square Tubular Columns under Bias Compression on The Basis of Uniform Design
Li Guochang  Feng Guohui
(Shenyang University)

The test is an important link for scientific research. It can offer a large number of evidence and examine if the result of theory analysis is right. The method of test affects seriously its results. A simple and definite method is adopted usually.
The concrete filled steel square tube is a composite material that the concrete is placed into empty steel tube. It has high compressive strength. It is suitable to be used as the columns of buildings. This kind of structure has many advantages. For instance, the weight of a building is only about 50 percent of reinforced concrete structure. The size of a column is merely 30 percent of a reinforced concrete column suffering the same number of outer load. The construction time is shortened considerably. The amount of steel required to build equals to that of reinforced concrete structure; it is about 50 percent of that of steel structure. Thus, the building costs are reduced on the same condition. The new type of structure has a very good future of development. So, the performance of every kind of some structural pieces is needed to investigate next.
The experiment plan is made using the Uniform Design on concrete filled steel square tubular columns under bias compressive loading. The number of specimens is minimized compared to the Orthogonal Design. The data are more reasonable. A large amount of labor, materials and money is saved. The equation to calculate the bearing capacity of the columns is deduced. It compensates the disadvantages of the equation of the ordinary concrete filled steel tubular columns under bias compressive loading. The discount coefficient on the basis of short axial columns is given by regression analysis. It is the function of the ratio between length and radius and eccentricity. According to the equation of the ordinary concrete filled steel tubular columns, if the columns have different ratios between length and radius and the same eccentricity, they have the same bearing capacity. There is something wrong in theory with this result. It is proved in this paper. The columns with different ratios between length and radius and the same eccentricity have different bearing capacity. The calculation results with this equation are very accurate compared with the experiment results.
Through the analysis as above, the Uniform Design method can be used in structural experiments and it is very convenient.
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Uniform Design Application in Technology Exploitation
Yang Yanling      Lan Cheng
The text first introduces the main conception of quality engineering and technology exploitation.  Then it details how to apply uniform design to the technology exploitation question for discussion of the filling plastic modding technology, and decrease examination times, depresses the examination expenditure and achieves the purpose of technology exploitation.
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Application of Number-Theoretic Methods to Welding Parameter Establishment
Chen Lilong        Li Zhihuan           Du Mingliang
(Hebei University of Technology)

This article provides a new high efficiency, time-saving access to the process parameter establishment for the welding of new materials and new constructions. It applies Number Theoretic Methods to the design of Slit Type cracking test of welded joint between two different base metals, and Linear Regression Analysis to the processing of test result. A Mathematics Model is established based on the test to describe the relationship between the cracking rate of welded joint and its several effective factors. Process parameters of welding of different base metals are also given out from the test. By using this testing method, the amount and cost of test are reduced dramatically.
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Comparisons between Orthogonal and Uniform Designs
Cheung Sau Hung
(Hong Kong Baptist University)

Concerns with comparisons between Orthogonal Designs (LDs) and Uniform Designs (UDs) from many angles, such that Star  L2-discrepancy, Symmetric L2-discrepancy, Centered L2-discrepancy, Unanchored L2-discrepancy, D-optimality and A-optimality. The results show that UD has lower discrepancy especially when the number of experiments (n) equal to 8, 12, 16 (level, q = 2 in LD) and 27, and UD needs less experiments in the case that LD and UD have a close discrepancy. On the other hand, under the seven models in this article, LD gives better A-optimality and D-optimality in linear models or when n is equal to 16 (q = 4 in LD) and 25.
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Application of UST Software System in Development of Asphalt Products
Feng Minke    Chen Baolian
(Fushun Research Institute of Petroleum and Petrochemicals, 113001)

A mathematical model is proposed and applied to develop the polymer-modified asphalt products with UST software. A suitable factor-level form is selected to arrange experiments and the model is set up by regression method using experimental data. The results of verification tests indicate that all the expected results can be achieved by this model.
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The Application of Uniform Design Method in the Research of Oxidation Reaction of the Wax of by-product PE
Wei Tongcheng
(Research institute of Liao Yang petrochemical Fiber Company)

This report had represented adaptation of uniform design method for arranging design plan in the research of oxidation reaction of the wax of by-product PE (polyethylene). To achieve the optimum of process by the way of statistical optimization, and attain the goal of optimization of developing experiment and results of forecast optimum.  Moreover, the author put forward application for fuzzy conception, and method of uniform design to realize fuzzy simulate optimization of process, and thus attain the goal of analyze and transcend of patent.
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Uniform Design Method Promote Research Level
----uniform design method's application in 3rd RESEARCH ACADEMY of CASC
Wang Jianmin         Zhang Jianzhou     Wang Lianjun

UNIFORM DESIGN METHOD illustrated in this article is the result of special need of China at the time, China's emphasis on basic theory research, Professor Wang Yuan and Fang Kai-Tai have high research level in this field, and cooperation of the scientists and engineer of CASC. Adopting uniform design method has such advantages: promote tactical and technical level; achieve best technological process and prescription; improve products performance; achieve better products quality and reliability; high value/cost ratio and make excellent economical and social benefit.
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A Tentative Study on Mathematical Model of Economic Benefit Evaluation for Uniform Design
 Tao Lixin    Du Jiangping
(School of International Economics & Trade, Jiangxi University of Finance & Economics,
Nanchang, Jiangxi  330013, PRChina)

The paper probes into the relation between test design and economic benefit, and specially gives a detailed discussion on the relations among even design, opportunity cost, product life cycle and investment risks. Based on these relations and marketing theory, the paper advances and proves a mathematical model of economic benefit evaluation for uniform design:
(1)         p(t) = R(t)-[C1(t) + C2(t)]
                     = P(t)Q(t) - [C11(Q) + C21(Q) + C31(t) + C12(Q) + C22(Q) + C32(t)]
Herein,  t in Formula (1) refers to the time for the test, and the length of t distinguishes different test design approaches: the shortest time is uniform design, next is orthogonal design, the longest is overall test; p(t) in Formula (1) indicates economic benefits (profits) with different test designs; id., R(t) and [C1(t) + C2(t)]  denotes the corresponding revenues and costs respectively (C1(t) -- accounting cost,  C2(t) -- opportunity cost); P(t), Q(t), C11(Q), C21(Q), C31(t), C12(Q), C22(Q), C32(t) are the related price, sales quantity, production accounting cost, sales accounting cost, R&D accounting cost, production opportunity cost, sales opportunity cost, and R&D opportunity cost respectively.
Besides, with five assumptions, the paper puts forward 3 models of economic benefit evaluation for uniform design.
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Application of Uniform Design in Research of Foam Lightweight Material
Zhang Xiaoping     Gu Qiangsheng
(Hohai University, Nanjing)
Bao Chenggang
(Yangtze River Scientific Research Institute, Wuhan)

The instinct features of foam lightweight material are light weight and cellular structure. The raw materials of the foam material are cement, sand, foam and others.  As the foam existing, every composition of the raw material shows complex nonlinear relationship to the mechanics index of the lightweight material.  In order to find out the optimum mix proportion, the experimental design is conducted by application of uniform design theory.  Since the experimental data are too scattered to analyze by using regression method, neural networks model is adopted for analyzing experimental result. Back propagation (BP) algorithms neural networks has very strong capacity of mapping nonlinearity, the artificial neural networks model is trained by given sample of input and output, so that it can research a simulate relationship of the input and the output.  The trained network model can forecast the mechanics index of the foam material in any mix proportion, which have not been experimented.  So, the optimum mix proportion for the engineering request can be found by means of the trained neural networks model.  In a word, this paper verifies that uniform design theory is reasonable for experimental design of foam lightweight material, and the neural networks model is practical and efficient for tackling experimental data with uniform design.
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Preliminary Studies on Cultivation Experiment with Multiple Factors in Rape seed (cv. high oil 605) using Uniform Design
Xu Guanghua
(Shangyu Municipal Seed Company, Shangyu 312300)
Zhou Wejun
(Zhejiang Agricultural University, Hangzhou 310029)
(ZhangYing Zhejiang Wolong Group Co.,Shangyu 312300)

The cultivation experiment with four factors and four levels was carried out in oilseed rape (cv. high-oil 605) using the uniform design. Results showed that the suitable sowing date was 28 September and the seedling age was 47 days. The population of 135000 plants/hm2 and the nitrogen of 37500kg standard fertilizer/hm2 were recommended in the present experiment. Similar results were obtained from the calculated values of the uniform design and the observed values of the direct measurement. Therefore, there was a practical utilization of the uniform design in the crop cultivation experiment with multiple factors and levels.
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The Analysis of Driver-Vehicle Closed-Loop System by Means of Uniform Design
Hongwei Zhu
(Changchun Automotive Research Institute)
Konghui Guo
(Jilin University of Technology)

This paper reports a study of the relationship between the driver-vehicle closed-loop system characteristics and some vehicle parameters such as vehicle velocity and the cornering stiffness of the front and rear wheels. By means of the uniform design, the computer experiment for three factors, vehicle velocity and the cornering stiffness of the front and rear wheels, is arranged. The regression model of the closed-loop comprehensive index with respect to the vehicle velocity and the cornering stiffness of the front and rear wheels is established. The regression model is in the form of quartic polynomial. Stepwise regression and the L-H algorithm, by which a better regression subset can be generated, are used to choose the regression variables. The testing results show that the regression model is highly significant with the vehicle velocity and the cornering stiffness of the front and rear wheels adopting their values over a large scale. The regression model shows that there exist higher-order nonlinear relations among the closed-loop comprehensive index, the vehicle velocity, and the cornering stiffness of the front and rear wheels. The higher-order interactions among the vehicle velocity, the cornering stiffness of the front and rear wheels also contribute to the closed-loop comprehensive index.
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Application of Uniform Design Method in the Preparation of Cu13X Molecular Sieve by means of Ion-exchange using Microwave Radiation
Nie Yinglong       Meng Yangqiu
(Dept. of Applied Chemistry, Shenyang Institute of Chemical Technology)
Wang Minggang      Ma Lixia
(Class 9555, Speciality of Organic engineering, Chenyang Institute of Chemical Technology)
This paper applies uniform design method on preparing Cu13X molecular sieve by means of ion-exchange using microwave radiation hearing the metal cation aqueous solution.  Through uniform design, an investigation was conducted in the effect of Cu2+ concentration, exchanging time and microwave hearing power on the degrees of ion-exchange of a 13X zeolitic molecular sieve exchanged with Cu2+.  Taken the degrees of ion-exchange as target function, the regression equation has been acquired by the stepwise regression analysis in this test section.  It has been realized that influence of the interaction of microwave heating power and exchanging but the affect of the square of Cu2+ concentration is negative.  The optimizing condition was obtained with a search based on regression function.  They are: microwave heating power from 455 to 520 watt, exchanging time from 10 to 12 minutes, and Cu2+ concentration of 0.1606 mol/L.  with the above optimizing conditions, the degrees of ion-exchange of more than 96^% can be obtained.
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Research on the High Function PRC Materials by Uniform Design
Tang  Ming
(Shenyang Architectural and Civil Engineering Institute, Shenyang, CHINA  110015)

The method of uniform design with 3 factors and poly-levels is used in this paper. The properties of the high fuction PRC material is researched. The affecting rules of the pressure and quantity of fly ash and the fractal dimension are investigated. The relevant material-PRC in superfine fly ash is producted. The optimum solutions can be gotten so this paper is important to develop the kind of materials further, and to meet the demands of different engineering.
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Application's Primary Research of Uniform Design Method to Science Technology Results' Transfer
Wang Lishun
(China Defence Science Technology Information Center)

With the development of social economy and the progress of civilization, the important functions of S&T results transfer are being outstanding. within this complicated transfer system, there are many actors relating to science, economy, policies and rules.  They act and affect each other and restrain the transfer together.  Therefore the method which can be used to make these actors improve transfer's efficiency is very critical and can not be ignored.  After research it can be found that as a test design method, Uniform Design is of great use value.  It can be used to provide consultation services during making decisions such as transfer law's exploration, items selection, investment, technology analysis and market forecast.  Using Uniform Design to plan test can reduce test cost, improve test efficiency, guide work according to test's results and increase scientific level of decisions.  Its application can provide theoretical basis and methods of judge for decision-makers.
The research has some tries to use Uniform Design in S&T results transfer through the discussion of basic principles, concepts concerned and the analysis of transfer.  Of course, it is theoretical try only.  There are a lot of actual questions to be solved.  But all of these may show that Uniform Design method can be used in many fields, which are awaiting us to develop.
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Uniform Design for Synthetic Processes of Sodium Percarbonate at Ambient Temperature
Shi Jiangong
(Institute of Yanshan Petrochemical Corp.)
Wang Wanlin
(Dept. of Chemistry, Zhangjiakou Teachers' College)
With the development of chemical industry, environment pollution is getting heavier and heavier.  In China, the capability of synetheic detergent has risen sharply to three million tons pr year, but most of them contains phosphate and/or borate as auxiliary detergents.  Recent years, many lakes such as Taihu, Dianchi and rivers such as Huaihe have been contaminated by industrial wastes, large drained waste water containing phosphate ais one of the most sources.  Sodium percarbonate (SPC), as a kind of auxiliary detergent, performs remarkable functions of blanching, killing bacterium and cleaning.  It has been employed worldwide tyo substitute for phosphate and borate in artificial detergents.
At present, the capability of it has reached 700 thousand tons one year.  Since the begining of 1980's, it has been studied, developed and produced with an increasing year by year.
The synthetic methods of SPC are divided into dry method and wet method.  The latter is used widelyt home and abroad and the former used gradually less.  But the production of SPC by the wet was needed to control the reaction temperature below 5oC, so the processing is complex, inconvenient and the energy demand is higher.
The purpose of this investigation is throught adding inorganic and organic additiives, using Unfirom Design method to imporve the reaction condition.
SPC is made from sodium carbonate and aqueous hydrogen peroxide.  The optimum condition are as follows: the molar ratio of sodium carbonate to hydrogen peroxide is 1/1.7, the amount of organic stabilizer is 55cm3., that of inorganic stabilizer is 0.8g and reaction time is 40 minute, the most important change is that reaction temperature never need below 5oC, the product can be produced at room/ambient tempertaure.  Under all above condition, the highest content of SPC is gained by 88.74%.  The result shows that uniform design is useful for this study.
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Application of Uniform Design in the Preparation of Loading Catalyst for Esterification
Liao Anping  Lan Ping  Li Mei  Lan Lihong
(Dept.of Chemistry and Chemical Enginerring, Guangxi University for Nationalities,  Nanning 530006)

The preparation conditions of the loading catalyst (cation exchange resin as carrier) for esterification are studied by using Uniform Design. The obtained regression equation shows well the metal salt quantity, loading temperature, loading time and particle size of catalyst carrier effects on the activity of catalyst for esterification. The loading catalyst prepared by optimization experiment conditions has high activity. Using as the catalyst of esterification reaction of ethyl alcohol and acetic acid, the percent conversion of acetic ether is about 36.56% in one hour as the loading catalyst quantity is 5% of acetic acid quantity in the reaction system. Compared with non-loading cation exchange risen as catalyst, the conversion of acetic ether rose 17.32 percent points in the same reaction conditions.
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An Application of Uniform Design Device in Optimizing the Processing Conditions of Peanut Protein Foamer
Li Yanqun   Jiang Xuewen   She Shiwang
(Jiangxi-OAI Joing Institute, Nanchang, 330047)
The uniform device was used to optimize the processing conditions of peamnut protein former.  A model, which describes the relations between foaming properties and reaction time of enzymatic hydrolysis, amount of used protease, reaction time of alkaline hydrolysis and amount of used alkali, was obtained through progressive regression on a quadratic multinomial model.
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Introduction to Logistic Regression and Its Application to Data Analysis in Uniform design
Guo Xiuhua, Zhang Xuezhong, Xu Guiyong, She Guiqing, Liu Yunrong.
(Beijing Medical College of PLA, 100071)

Uniform design is superior to orthogonal design and optimality design in their table's usage.  Uniform tables are flexible and need not specific assumptions.  The outcomes of uniform design experiments are analyzed on various assumptions and modern statistical methods.  If the response variables of the outcomes are dichotomous, for example, "yes" or "no", "qualified" or "disqualified", et la..  There are two stable states and a transition between them, which is not stable and strongly dependent on factor-level combinations.  Such problems may be analyzed with aid of logistic model:

log(p/(1-p)) = b0 + b1x1 + b2x2 + ... + bnxn
where p is the estimate of the probability responding "yes", 1-p "no" and b0  is intercept, bi ( i = 1, 2, ..., n) is regression coefficient.
x1 - xn like design matrix can be given through uniform tables.  Each run of the experiment produces a value p, which is a proportion of the positive responses in subjects of the run.  In our context x1 - xn are random samples.  Every run usually has 100-200 subjects.
A multi-center randomized clinical trial was adopted in the study.  1705 eligible women accepted the procedure of female tube sterilization by chemical instillation. The 1705 examination papers are inputted with the database of Visual Foxpro 5.0 in 586 computer and analyzed with SAS 6.04 to the 1667 examination papers that accorded with the requirements.  The article is carried on the Logistic regression of a single factor and multi factors to analyze the given 12 factors that are related to succeed of female tube sterilization by chemical instillation.  The key factors influencing contraceptive effect of the tube sterilization by chemical instillation are in proper order: the film length of the occlusion by the chemical reagents instilled into Fallopian tubes on a pelvic X-ray, the type of chemical reagent, and the eligible woman's age.
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Technology of Uniform Design and Parametric Optimization in the Application of Petrochemical
Zhang Chengen

The uniform design is first proposed by the Chinese mathematicians, and is highly valued and promoted internationally.  The Northeast Pharmaceutics Co. and the China Petrochemicals Corp. together have popularized the technology of Uniform design and parametric optimization.  Some improvements have been obtained after using this technology by different units, such as the Fushun Research Institute of Petroleum and Petrochemicals, Yanshan Petrochemical Corp., Qilu Petrochemical Co., and Shanghai Research Institute of Petroleum and Petrochemicals.  After the related conference organized by the China Petrochemicals Corp. is held in Beijing, the usage of uniform design increases immediately and becomes more popular.  It also helps for the development in the field of Petrochemicals.
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Applications of Uniform Design to Antibiotic Research
Su Weifang and Li Yan
(North China Pharmaceutical Group Corporation, China)
With the development of market economy and the deepening of quality control, more and more people have attached importance to the quality improvement in the designing stage and the applications of the statistical design.
In early 1990s, we achieved remarkable success in introducing and spreading the combined applications of homogeneous design and orthogonal design. In the six scientific research items (in the laboratory) on antibiotics introduced in this article, the increasing margin of unit reached over 20 percent. For example, in the experiment of optimizing the selecting medium of penicillium-producing strain A#, the unit per milliliter was raised by 29.27 percent, while the frequency of experiments was cut down by 237 times. So the economic benefits and potential benefits are considerable.
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Weighted Adaptive Importance Sampliing and Asymptotic Uniform Algorithm
Wei Gang        Lam Kim-Fung
(Hong Kong Baptist University)
The importance sampling is useful in higher dimensional integration.  Through the years, many of the adaptive importance sampling schemes are proposed.  In this paper, we generalized the idea of Oh's adaptive scheme (1991) by introducing the weight function in each stages to get similar results.  The rate of convergence can be improved by adjust the weight in each steps instead of using large sample size in the first few stage.
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Last Update: April 3, 2000.
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