Electromagnetic stir casting process of A357-Si C nanocomposite was discussed using the D-optimal design of experiment(DODOE) method. As the main objective, nine random experiments obtained by DX-7 software were perfo...Electromagnetic stir casting process of A357-Si C nanocomposite was discussed using the D-optimal design of experiment(DODOE) method. As the main objective, nine random experiments obtained by DX-7 software were performed. By this method, A357-Si C nanocomposites with 0.5, 1.0 and 1.5 wt.% Si C were fabricated at three different frequencies(10, 35 and 60 Hz) in the experimental stage. The microstructural evolution was characterized by scanning electron and optical microscopes, and the mechanical properties were investigated using hardness and roomtemperature uniaxial tensile tests. The results showed that the homogeneous distribution of Si C nanoparticles leads to the microstructure evolution from dendritic to non-dendritic form and a reduction of size by 73.9%. Additionally, based on DODOE, F-values of 44.80 and 179.64 were achieved for yield stress(YS) and ultimate tensile strength(UTS), respectively, implying that the model is significant and the variables(Si C fraction and stirring frequency) were appropriately selected. The optimum values of the Si C fraction and stirring frequency were found to be 1.5 wt.% and 60 Hz, respectively. In this case, YS and UTS for A357-Si C nanocomposites were obtained to be 120 and 188 MPa(57.7% and 57.9 % increase compared with those of the as-cast sample), respectively.展开更多
To solve the problem of time difference of arrival(TDOA)positioning and tracking of targets by the unmanned aerial vehicles(UAV)swarm in future air combat,this paper adopts the TDOA positioning method and uses time di...To solve the problem of time difference of arrival(TDOA)positioning and tracking of targets by the unmanned aerial vehicles(UAV)swarm in future air combat,this paper adopts the TDOA positioning method and uses time difference sensors of the UAV swarm to locate target radiation sources.Firstly,a TDOA model for the target is set up for the UAV swarm under the condition that the error variance varies with the received signal-to-noise ratio.The accuracy of the positioning error is analyzed by geometric dilution of precision(GDOP).The D-optimality criterion of the positioning model is theoretically derived.The target is positioned and settled,and the maximum value of the Fisher information matrix determinant is used as the optimization objective function to optimize the track of the UAV in real time.Simulation results show that the track optimization improves the positioning accuracy and stability of the UAV swarm to the target.展开更多
[Objectives] To study the optimal proportion and formulation process of Jinweng granule,the physicochemical properties of the optimal preparing process was observed. [Methods] Adopting the D-optimal mixture design met...[Objectives] To study the optimal proportion and formulation process of Jinweng granule,the physicochemical properties of the optimal preparing process was observed. [Methods] Adopting the D-optimal mixture design method,selecting the mixing ratio of starch,dextrin,fumei powder and lactose as tested factors,and selecting the most significant factor between hygroscopicity,formability,solubility as the evaluation index,the optimal proportion of filler was examined by system experiments. Granularity,solubility,the angle of repose,and critical relative humidity( CRH) were used to evaluate the optimal proportion and formulation process of Jinweng granule. [Results]The optimal prescription of Jinweng granule is extract∶ starch∶ dextrin∶ lactose∶ fumei powder( 1∶ 0. 5∶ 0. 05∶ 0. 3∶ 0. 15),and the binder was consisted of 1% sodium carboxymethylcellulose( CMC) slurry and 3% starch syrup. The CRH of the optimum formulation process of granule is 72%,and the fluidity,solubility and granularity were qualified. [Conclusions] The process model established by D-optimum mixture design has good predictability,and the granule prepared by the optimal proportion has good repeatability,and the granule proportion and formulation process is stable and reliable.展开更多
An optimized formulation of a sustained release tablet of Gliclazide was developed. The use of Doptimal design with a polynomial statistical model to analyze dissolution data reduced the number of laboratory tests req...An optimized formulation of a sustained release tablet of Gliclazide was developed. The use of Doptimal design with a polynomial statistical model to analyze dissolution data reduced the number of laboratory tests required to obtain an optimal dosage form. The final formulation contained 22 mg of Methocel®E15LV, 16.5 mg Methocel®E15 and 10.0 mg of Dibasic Calcium Phosphate per 30 mg Gliclazide sustained release tablet. Dissolution studies performed on tablets from 5000 tablet test batches released greater than 90 percent of loaded drug in eight hours. Drug release from the optimized tablets followed a pattern more closely similar to zero-order than other mechanisms of drug release tested. Storage of tablets in accelerated and ambient conditions for 6 and 12 months respectively did not alter any of the physico-chemical properties, drug release or the drug release rate compared to initial observations and dissolution data of the prepared tablets. The addition of potassium phosphate and monosodium phosphate to the tablet reduced the effect pH has on Gliclazide dissolution compared to the commercially available product.展开更多
In this paper, the limitations of the single cube D-optimal design scheme is studied, and a double cube D-optimal design scheme is suggested in order to overcome the limitations. For a sort of incomplete cubic polynom...In this paper, the limitations of the single cube D-optimal design scheme is studied, and a double cube D-optimal design scheme is suggested in order to overcome the limitations. For a sort of incomplete cubic polynomials, the test design of the identification is developed with this new scheme, and the comparation with the single cube scheme is also given. This scheme is shown to be perfectly suitable for the optimal identification of the complete cubic polynomials.展开更多
Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments;therefore, optimum designs are a valuable tool for experimenters, leading...Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments;therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model where q is an indicator variable. We have considered an experiment based on the dose-response to a fly insecticide in which males and females respond in different ways, proposed in Atkinson et al. (1995) [1]. To find the D-optimal designs, this problem has been reduced to a canonical form.展开更多
An optimized formulation of capsules containing Lansoprazole enteric-coated pellets using D-Optimal design with a polynomial statistical model were prepared by using Eudragit?L100 as an enteric coated polymer to provi...An optimized formulation of capsules containing Lansoprazole enteric-coated pellets using D-Optimal design with a polynomial statistical model were prepared by using Eudragit?L100 as an enteric coated polymer to provide resistance to simulated gastric acid dissolution in buffer media. D-Optimal experimental design was used to determine the optimal level for three coating layers that were applied to formulate the enteric-coated pellets including a drug loading layer, a sub-coating, and an outer enteric coating. Dissolution studies were performed on the prepared Lansoprazole capsules. Less than 5 percent of Lansoprazole was released in 60 minutes in an acidic dissolution medium (pH 1.2) and greater than 90 percent of active ingredient was released in the next 60 minutes in a buffer dissolution medium (pH 6.8). The Lansoprazole capsules were stable with no observable change in physico-chemical properties in accelerated and normal storage conditions for 6 and 18 months, respectively. The pharmacokinetic parameters Cmax, Tmax, AUC0-t, and AUC0-∞ were determined after administration of the D-Optimal design optimized capsules of LPZ to healthy beagle dogs and were statistically compared to Gastevin? capsules as a reference (KRKA, Slovenia) using the non-compartmental method with the aid of WinNonlin 5.2 software. The analysis of variance showed that the two formulations did not demonstrate bioequivalence using a 90% confidence interval range (80% - 120%) of Cmax, AUC0-t, and AUC0-∞. No significant difference in Tmax was found at the 0.95 significance level using the Wilcoxon signed-rank test. D-Optimal Experimental Design provided definitive direction for an optimal formulation of capsules containing enteric-coated pellets of lansoprazole loaded within the coating of pellets that provided similar bioequivalence to Gastevin.展开更多
In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the u...In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the unbiased estimation of the non-negligible parameters of interest.We propose a method for the construction of D-optimal saturated designs for the mean,the main effects,and the second-order interactions of one factor with the remaining factors.In the process,we show the problem is just as hard as the Hadamard determinant problem.展开更多
This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-opti...This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.展开更多
This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the ...This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.展开更多
Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies th...Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.展开更多
The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data.Observations of each response variable within subjects are assumed to have a fi...The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data.Observations of each response variable within subjects are assumed to have a first-order autoregressive structure,possibly with observation error.The equivalence theorems are provided to characterise theD-optimal population designs for the estimation of fixed effects in the model.The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered.Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design,while the experimental costs are important factors in the optimal designs.展开更多
The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust fo...The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.展开更多
The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information ...The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information at their disposal to reduce the amount of resources needed for an experiment without trading the accuracy of the experiment.Suppose we have k+1 factors and the investigator knows one of the factors(we call this factor an extra factor throughout the paper)does not interact with any of the remaining k factors.Furthermore,the investigator believes among the remaining k factors,one factor potentially interacts with the rest of the k−1 factors.In this paper,we show how a D-optimal saturated design can be constructed for this problem with the minimum number of runs.In the process,we show the investigator can even forgo the presence of the extra factor in certain runs without compromising the D-optimality of the saturated design.展开更多
文摘Electromagnetic stir casting process of A357-Si C nanocomposite was discussed using the D-optimal design of experiment(DODOE) method. As the main objective, nine random experiments obtained by DX-7 software were performed. By this method, A357-Si C nanocomposites with 0.5, 1.0 and 1.5 wt.% Si C were fabricated at three different frequencies(10, 35 and 60 Hz) in the experimental stage. The microstructural evolution was characterized by scanning electron and optical microscopes, and the mechanical properties were investigated using hardness and roomtemperature uniaxial tensile tests. The results showed that the homogeneous distribution of Si C nanoparticles leads to the microstructure evolution from dendritic to non-dendritic form and a reduction of size by 73.9%. Additionally, based on DODOE, F-values of 44.80 and 179.64 were achieved for yield stress(YS) and ultimate tensile strength(UTS), respectively, implying that the model is significant and the variables(Si C fraction and stirring frequency) were appropriately selected. The optimum values of the Si C fraction and stirring frequency were found to be 1.5 wt.% and 60 Hz, respectively. In this case, YS and UTS for A357-Si C nanocomposites were obtained to be 120 and 188 MPa(57.7% and 57.9 % increase compared with those of the as-cast sample), respectively.
基金This work was supported by the National Natural Science Foundation of China(61502522)the Equipment Pre-Research Field Fund(JZX7Y20190253036101)+1 种基金the Equipment Pre-Research Ministry of Education Joint Fund(6141A02033703)the Hubei Provincial Natural Science Foundation(2019CFC897).
文摘To solve the problem of time difference of arrival(TDOA)positioning and tracking of targets by the unmanned aerial vehicles(UAV)swarm in future air combat,this paper adopts the TDOA positioning method and uses time difference sensors of the UAV swarm to locate target radiation sources.Firstly,a TDOA model for the target is set up for the UAV swarm under the condition that the error variance varies with the received signal-to-noise ratio.The accuracy of the positioning error is analyzed by geometric dilution of precision(GDOP).The D-optimality criterion of the positioning model is theoretically derived.The target is positioned and settled,and the maximum value of the Fisher information matrix determinant is used as the optimization objective function to optimize the track of the UAV in real time.Simulation results show that the track optimization improves the positioning accuracy and stability of the UAV swarm to the target.
基金Supported by Public Welfare and Industry Special Fund Project of the Ministry of Agriculture(201303040-05)Natural Science Foundation Project of CQCSTC(2013FYF110600)
文摘[Objectives] To study the optimal proportion and formulation process of Jinweng granule,the physicochemical properties of the optimal preparing process was observed. [Methods] Adopting the D-optimal mixture design method,selecting the mixing ratio of starch,dextrin,fumei powder and lactose as tested factors,and selecting the most significant factor between hygroscopicity,formability,solubility as the evaluation index,the optimal proportion of filler was examined by system experiments. Granularity,solubility,the angle of repose,and critical relative humidity( CRH) were used to evaluate the optimal proportion and formulation process of Jinweng granule. [Results]The optimal prescription of Jinweng granule is extract∶ starch∶ dextrin∶ lactose∶ fumei powder( 1∶ 0. 5∶ 0. 05∶ 0. 3∶ 0. 15),and the binder was consisted of 1% sodium carboxymethylcellulose( CMC) slurry and 3% starch syrup. The CRH of the optimum formulation process of granule is 72%,and the fluidity,solubility and granularity were qualified. [Conclusions] The process model established by D-optimum mixture design has good predictability,and the granule prepared by the optimal proportion has good repeatability,and the granule proportion and formulation process is stable and reliable.
文摘An optimized formulation of a sustained release tablet of Gliclazide was developed. The use of Doptimal design with a polynomial statistical model to analyze dissolution data reduced the number of laboratory tests required to obtain an optimal dosage form. The final formulation contained 22 mg of Methocel®E15LV, 16.5 mg Methocel®E15 and 10.0 mg of Dibasic Calcium Phosphate per 30 mg Gliclazide sustained release tablet. Dissolution studies performed on tablets from 5000 tablet test batches released greater than 90 percent of loaded drug in eight hours. Drug release from the optimized tablets followed a pattern more closely similar to zero-order than other mechanisms of drug release tested. Storage of tablets in accelerated and ambient conditions for 6 and 12 months respectively did not alter any of the physico-chemical properties, drug release or the drug release rate compared to initial observations and dissolution data of the prepared tablets. The addition of potassium phosphate and monosodium phosphate to the tablet reduced the effect pH has on Gliclazide dissolution compared to the commercially available product.
文摘In this paper, the limitations of the single cube D-optimal design scheme is studied, and a double cube D-optimal design scheme is suggested in order to overcome the limitations. For a sort of incomplete cubic polynomials, the test design of the identification is developed with this new scheme, and the comparation with the single cube scheme is also given. This scheme is shown to be perfectly suitable for the optimal identification of the complete cubic polynomials.
文摘Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments;therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model where q is an indicator variable. We have considered an experiment based on the dose-response to a fly insecticide in which males and females respond in different ways, proposed in Atkinson et al. (1995) [1]. To find the D-optimal designs, this problem has been reduced to a canonical form.
文摘An optimized formulation of capsules containing Lansoprazole enteric-coated pellets using D-Optimal design with a polynomial statistical model were prepared by using Eudragit?L100 as an enteric coated polymer to provide resistance to simulated gastric acid dissolution in buffer media. D-Optimal experimental design was used to determine the optimal level for three coating layers that were applied to formulate the enteric-coated pellets including a drug loading layer, a sub-coating, and an outer enteric coating. Dissolution studies were performed on the prepared Lansoprazole capsules. Less than 5 percent of Lansoprazole was released in 60 minutes in an acidic dissolution medium (pH 1.2) and greater than 90 percent of active ingredient was released in the next 60 minutes in a buffer dissolution medium (pH 6.8). The Lansoprazole capsules were stable with no observable change in physico-chemical properties in accelerated and normal storage conditions for 6 and 18 months, respectively. The pharmacokinetic parameters Cmax, Tmax, AUC0-t, and AUC0-∞ were determined after administration of the D-Optimal design optimized capsules of LPZ to healthy beagle dogs and were statistically compared to Gastevin? capsules as a reference (KRKA, Slovenia) using the non-compartmental method with the aid of WinNonlin 5.2 software. The analysis of variance showed that the two formulations did not demonstrate bioequivalence using a 90% confidence interval range (80% - 120%) of Cmax, AUC0-t, and AUC0-∞. No significant difference in Tmax was found at the 0.95 significance level using the Wilcoxon signed-rank test. D-Optimal Experimental Design provided definitive direction for an optimal formulation of capsules containing enteric-coated pellets of lansoprazole loaded within the coating of pellets that provided similar bioequivalence to Gastevin.
基金partially supported by the US National Science Foundation(NSF)[grant number 1809681].
文摘In a 2^(k)-factorial experiment with limited resources,when practitioners can identify the nonnegligible effects and interactions beforehand,it is common to run an experiment with a saturated design that ensures the unbiased estimation of the non-negligible parameters of interest.We propose a method for the construction of D-optimal saturated designs for the mean,the main effects,and the second-order interactions of one factor with the remaining factors.In the process,we show the problem is just as hard as the Hadamard determinant problem.
基金supported by NSFC Grant(11871143,11971318)the Fundamental Research Funds for the Central UniversitiesShanghai Rising-Star Program(No.20QA1407500).
文摘This paper investigates the optimal design problem for the prediction of the individual parameters in hierarchical linear models with heteroscedastic errors.An equivalence theorem is established to characterize D-optimality of designs for the prediction based on the mean squared error matrix.The admissibility of designs is also considered and a sufficient condition to simplify the design problem is obtained.The results obtained are illustrated in terms of a simple linear model with random slope and heteroscedastic errors.
基金supported by the National Natural Science Foundation of China (Nos.11971318, 11871143)the Fundamental Research Funds for the Central Universities (No.2232020D-38)。
文摘This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.
基金Project supported by the Science Foundation of China for Postdoctors (No.5(2001)).
文摘Let A be a j x d (0,1) matrix. It is known that if j = 2k - 1 is odd, then det(AAT) ≤ (j+1)((j+1)d/4j)j; if j is even, then det(AAT) ≤ (j+1)((j+2)d/4(j+1))j. A is called a regular D-optimal matrix if it satisfies the equality of the above bounds. In this note, it is proved that if j = 2k - 1 is odd, then A is a regular D-optimal matrix if and only if A is the adjacent matrix of a (2k - 1, k, (j + l)d/4j)-BIBD; if j = 2k is even, then A is a regular D-optimal matrix if and only if A can be obtained from the adjacent matrix B of a (2k + 1,k + 1,(j + 2)d/4(j +1))-BIBD by deleting any one row from B. Three 21 x 42 regular D-optimal matrices, which were unknown in [11], are also provided.
基金partly supported by the National Natural Science Foundation of China(Nos.11971318,11871143)Shanghai Rising-Star Program(No.20QA1407500).
文摘The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data.Observations of each response variable within subjects are assumed to have a first-order autoregressive structure,possibly with observation error.The equivalence theorems are provided to characterise theD-optimal population designs for the estimation of fixed effects in the model.The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered.Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design,while the experimental costs are important factors in the optimal designs.
基金Supported by Science and Technology Fund for Basic Research of Guizhou Province([2020]1Y010)National Nature Sciences Foundation of China(11901260,12071096,12501342)Specialized Fund for the Doctoral Development of Kaili University(BS202502028)。
文摘The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.
基金supported by the US National Science Foundation[grant number 1809681].
文摘The allocation of resources in a 2𝑘-factorial experiment is crucial when the experimental resources are limited.In practice,when resources are limited,it is common for investigators to use all the information at their disposal to reduce the amount of resources needed for an experiment without trading the accuracy of the experiment.Suppose we have k+1 factors and the investigator knows one of the factors(we call this factor an extra factor throughout the paper)does not interact with any of the remaining k factors.Furthermore,the investigator believes among the remaining k factors,one factor potentially interacts with the rest of the k−1 factors.In this paper,we show how a D-optimal saturated design can be constructed for this problem with the minimum number of runs.In the process,we show the investigator can even forgo the presence of the extra factor in certain runs without compromising the D-optimality of the saturated design.
