A COMPILATION OF THE D-OPTIMAL DESIGNS IN CHEMICAL KINETICS

This paper links the chemical kinetic models that obey the framework of nonlinear statistical models with optimal design theory. We provide the appropriate optimal designs for them, so that the involved parameters can be estimated as well as possible. Therefore, the D-optimality criterion is adopted, under the optimal design approach, for a number of models used in chemical kinetic applications. In the tables, the collected results are presented for 15 models.

[1]  George E. P. Box,et al.  Correcting Inhomogeneity of Variance with Power Transformation Weighting , 1974 .

[2]  Krizia M. Karry,et al.  Design and In-line Raman Spectroscopic Monitoring of a Protein Batch Crystallization Process , 2008, Journal of Pharmaceutical Innovation.

[3]  Amaro G. Barreto,et al.  A new approach for sequential experimental design for model discrimination , 2006 .

[4]  W K Wong,et al.  Optimal Designs When the Variance Is A Function of the Mean , 1999, Biometrics.

[5]  R. Fisher,et al.  On the Mathematical Foundations of Theoretical Statistics , 1922 .

[6]  Eric Walter,et al.  Qualitative and quantitative experiment design for phenomenological models - A survey , 1990, Autom..

[7]  T. Öberg.  Importance of the first design matrix in experimental simplex optimization , 1998 .

[8]  Holger Dette,et al.  Bayesian D-optimal designs for exponential regression models , 1997 .

[9]  R. Steiner,et al.  D-optimal design of DSC experiments for nth order kinetics , 2009 .

[10]  Gilbert F. Froment,et al.  Isomerization on n-Pentane , 1971 .

[11]  J. Downie,et al.  The vapor-phase oxidation of benzene over a vanadium oxide catalyst , 1969 .

[12]  L. Rodríguez-Aragón,et al.  Optimal designs for the Arrhenius equation , 2005 .

[13]  David W. Bacon,et al.  Prospects for reducing correlations among parameter estimates in kinetic models , 1978 .

[14]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[15]  Yonathan Bard,et al.  Nonlinear parameter estimation , 1974 .

[16]  Ignacio Martínez-López,et al.  Optimal designs for weighted rational models , 2009, Appl. Math. Lett..

[17]  K. Harmsen.  A modified mitscherlich equation for rainfed crop production in semi-arid areas: 1. Theory , 2000 .

[18]  D. Himmelblau,et al.  Optimization of Chemical Processes , 1987 .

[19]  Holger Dette,et al.  Optimal designs for the emax, log-linear and exponential models , 2010 .

[20]  U. Kockelkorn.  Lineare statistische Methoden , 2000 .

[21]  J. Downie,et al.  Kinetics of the vapor‐phase oxidation of napthalene over a vanadium catalyst , 1960 .

[22]  Anthony C. Atkinson,et al.  The Design of Experiments for Parameter Estimation , 1968 .

[23]  Holger Dette,et al.  Locally E-optimal designs for expo-nential regression models , 2003 .

[24]  Mark E. Davis,et al.  Fundamentals of Chemical Reaction Engineering , 2002 .

[25]  A. Atkinson.  Developments in the Design of Experiments, Correspondent Paper , 1982 .

[26]  Lorens A. Imhof,et al.  Maximin designs for exponential growth models and heteroscedastic polynomial models , 2001 .

[27]  Venkat Venkatasubramanian,et al.  High fidelity mathematical model building with experimental data: A Bayesian approach , 2008, Comput. Chem. Eng..

[28]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[29]  George E. P. Box,et al.  SEQUENTIAL DESIGN OF EXPERIMENTS FOR NONLINEAR MODELS. , 1963 .

[30]  Jules Thibault,et al.  Process modeling with neural networks using small experimental datasets , 1999 .

[31]  Dennis K. J. Lin,et al.  Ch. 4. Uniform experimental designs and their applications in industry , 2003 .

[32]  W. Näther.  Optimum experimental designs , 1994 .

[33]  K. Chaloner,et al.  Optimum experimental designs for properties of a compartmental model. , 1993, Biometrics.

[34]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[35]  A. Desideri,et al.  Superefficient enzymes , 2001, Cellular and Molecular Life Sciences CMLS.

[36]  A. C. Atkinson,et al.  Developments in the Design of Experiments , 1982 .

[37]  K. Kobe,et al.  Chemical engineering kinetics , 1956 .

[38]  P. Mars,et al.  Oxidations carried out by means of vanadium oxide catalysts , 1954 .

[39]  Aravind Mannarswamy,et al.  D-optimal designs for sorption kinetic experiments: Slabs , 2011 .

[40]  Linda M. Haines,et al.  Bayesian D-optimal designs for the exponential growth model , 1995 .

[41]  Kathryn Chaloner,et al.  D- and c-optimal designs for exponential regression models used in viral dynamics and other applications , 2003 .

[42]  G. Milliken.  Nonlinear Regression Analysis and Its Applications , 1990 .

[43]  D. M. Titterington,et al.  Recent advances in nonlinear experiment design , 1989 .

[44]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[45]  D. Majumdar,et al.  Some results on D-optimal designs for nonlinear models with applications , 2009 .

[46]  Andrew C. Hooker,et al.  An Evaluation of Population D-Optimal Designs Via Pharmacokinetic Simulations , 2004, Annals of Biomedical Engineering.

[47]  J France,et al.  A generalized Michaelis-Menten equation for the analysis of growth. , 2000, Journal of animal science.

[48]  C. Georgakis,et al.  Steady state optimal test signal design for multivariable model based control , 2006 .

[49]  Jonas Sjöblom,et al.  Latent variable projections of sensitivity data for experimental screening and kinetic modeling , 2008, Comput. Chem. Eng..

[50]  K. Smith.  ON THE STANDARD DEVIATIONS OF ADJUSTED AND INTERPOLATED VALUES OF AN OBSERVED POLYNOMIAL FUNCTION AND ITS CONSTANTS AND THE GUIDANCE THEY GIVE TOWARDS A PROPER CHOICE OF THE DISTRIBUTION OF OBSERVATIONS , 1918 .

[51]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[52]  D. W. Bacon,et al.  Further Consideration of Heteroscedasticity in Fitting Kinetic Models , 1977 .

[53]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[54]  Maciej Patan,et al.  Optimum Design of Experiments for Enzyme Inhibition Kinetic Models , 2011, Journal of biopharmaceutical statistics.

[55]  S. Silvey.  Optimal Design: An Introduction to the Theory for Parameter Estimation , 1980 .

[56]  William G. Hunter,et al.  An experimental design strategy for distinguishing among rival mechanistic models an application to the catalytic hydrogenation of propylene , 1967 .

[57]  Christos P. Kitsos.  Nonlinear-Optimal-Sequential Experiment Designs and Applications , 1997 .

[58]  N. L. Carr.  Kinetics of Catalytic Isomerization of n-Pentane , 1960 .

[59]  G. Box,et al.  A Basis for the Selection of a Response Surface Design , 1959 .

[60]  Χρήστος Π. Κίτσος.  Fully-sequential procedures in nonlinear design problems , 2015 .

[61]  Kai-Tai Fang,et al.  An example of a sequential uniform design: Application in capillary electrophoresis , 1997 .

[62]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[63]  W. G. Cochran.  Experiments for Nonlinear Functions (R.A. Fisher Memorial Lecture) , 1973 .

[64]  Holger Dette,et al.  A note on Bayesian D-optimal designs for a generalization of the exponential growth model , 1994 .

[65]  Eberhard P. Hofer,et al.  Nonlinear D-optimal design of experiments for polymer–electrolyte–membrane fuel cells , 2009 .

[66]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[67]  Sandro Macchietto,et al.  Model-based design of experiments for parameter precision: State of the art , 2008 .

[68]  Holger Dette,et al.  Optimal Design for Goodness-of-Fit of the Michaelis–Menten Enzyme Kinetic Function , 2005 .

[69]  Michael L. Brisk,et al.  Sequential experimental design for precise parameter estimation. 1. Use of reparameterization , 1985 .

[70]  Yizeng Liang,et al.  Uniform design and its applications in chemistry and chemical engineering , 2001 .

[71]  Vinay Prasad,et al.  Multiscale Model and Informatics-Based Optimal Design of Experiments : Application to the Catalytic Decomposition of Ammonia on Ruthenium , 2008 .

[72]  G. Seber,et al.  Nonlinear Regression: Seber/Nonlinear Regression , 2005 .

[73]  Vasilios Zarikas,et al.  Evaluation of the optimal design “cosinor model” for enhancing the potential of robotic theodolite kinematic observations , 2010 .

[74]  Michael L. Brisk,et al.  Sequential experimental design for precise parameter estimation. 2. Design criteria , 1985 .

[75]  Licesio J. Rodríguez-Aragón,et al.  T-, D- and c-optimum designs for BET and GAB adsorption isotherms , 2007 .

[76]  Aravind Mannarswamy,et al.  D-optimal designs for sorption kinetic experiments: Cylinders , 2011 .

[77]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[78]  Nils-Olof Lindberg,et al.  Multivariate methods in pharmaceutical applications , 2002 .

[79]  Holger Dette,et al.  Locally D-optimal Designs for Exponential Regression , 2004 .

[80]  Holger Dette,et al.  Maximin efficient design of experiment for exponential regression models , 2006 .

[81]  A. S. Hedayat,et al.  LOCALLY D-OPTIMAL DESIGNS BASED ON A CLASS OF COMPOSED MODELS RESULTED FROM BLENDING EMAX AND ONE-COMPARTMENT MODELS ⁄ , 2008, 0803.2108.

[82]  C. T. de Wit,et al.  Resource use efficiency in agriculture , 1992 .

[83]  Peter D. H. Hill.  D-Optimal Designs for Partially Nonlinear Regression Models , 1980 .

[84]  Michael L. Brisk,et al.  "Sequential experimental design for precise parameter estimation. 1. Use of reparameterization". Reply to comments , 1986 .

[85]  W. G. Cochran.  Experiments for Nonlinear Functions , 1973 .

[86]  Christos P. Kitsos,et al.  AN OPTIMAL CALIBRATION DESIGN FOR pH METERS , 2010 .

[87]  Holger Dette,et al.  A Web-Based Tool for Finding Optimal Designs for the Michaelis–Menten Model and an Overview , 2010 .

[88]  Andrej Pázman,et al.  Nonlinear Regression , 2019, Handbook of Regression Analysis With Applications in R.

[89]  H. L. Lucas,et al.  DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS , 1959 .

[90]  Douglas M. Bates,et al.  Nonlinear Regression Analysis and Its Applications , 1988 .