Dr. Gary BlauNov, 2007 Overview of Modules on Statistical and Mathematical Modeling in the Pharmaceutical Sciences by Gary Blau, Research Professor E-enterprise Center Discovery Park Purdue University

Nov, 2007 Dr. Gary Blau COURSE BACKGROUND Initial ideas developed for Pharmaceutical Scientists at the Dow Chemical Plant in Brindisi, Italy (1975) Subsequently evolved into a global course on Process Optimization presented to Dow Scientists and engineers in Europe and North America.

Nov, 2007 Dr. Gary Blau COURSE BACKGROUND Morphed into two courses in the chemical engineering department (Module 1: Statistical Model Building and Design of Experiments for undergraduates) and (Module 2: Mathematical Model Building for Process Optimization for Graduate students) Reformulated into a Short Course for Practicing Professionals in the Pharmaceutical Sciences

Nov, 2007 Dr. Gary Blau WHAT IS A MODEL? Model (Noun) A miniature representation of something A person who serves as a pattern for an artist. A type of design of a product (car, airplane) A description or analogy used to visualize something that cannot be observed directly (atom) A system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs (a system)

Nov, 2007 Dr. Gary Blau WHAT DOES IT MEAN TO “MODEL” SOMETHING? Model (Verb) To produce a mathematical relationship representation or simulation of a problem

Nov, 2007 Dr. Gary Blau WHY BUILD A MATHEMATICAL MODEL? To Answer Questions: More specifically, to predict the behavior of the system under various conditions without running a test or experiment e.g. Process Operations Process Design and Scale-Up Process Optimization Process Control One-to-One Relationship Math Model  Question Math Models are “built” to answer specific question Therefore, never use a math model to try to answer questions not addressed in its construction. “Remember”: ALL MODELS ARE WRONG BUT SOME ARE USEFUL (George Box)

Nov, 2007 Dr. Gary Blau TYPE OF MATHEMATICAL MODELS Empirical Response= Linear Function of Operating Conditions yield = bo + b1*Temp + b2*Pressure + b3*Agitation+….. Semi-Empirical/Mechanistic lnp = A + B/(C+T) (Vapour Pressure) Q=UA(LMΔT) (Heat Transfer) k=k o exp(-E/RT) (Arrhenius Temp) Mechanistic/Fundamental/First Principles PV=nRT (Gas Laws) Navier Stokes Ficks Law

Nov, 2007 Dr. Gary Blau TYPE OF MATHEMATICAL MODELS Mass/Energy Balances across “units” Input –Output + Generation=Accumulation Generation: Many models can frequently be postulated for this term so that “model building” is associated with the identification of the proper form of the model to ANSWER questions

Nov, 2007 Dr. Gary Blau TAXONOMY OF MATHEMATICAL MODELS Black versus White Empirical(Statistical) versus Mechanistic Linear(Statistical) versus Nonlinear Small versus Large Complex versus Simple Integer/Discrete versus Continuous Algebraic versus Differential Equations

Nov, 2007 Dr. Gary Blau MATHEMATICAL MODELS Reverse Engineering Process Optimization Plant Design Process Debottlenecking “What” Variables and “How” the work together. Questions “Why” do processes work the way they do. Questions

Nov, 2007 Dr. Gary Blau STEPS IN MODEL BUILDING 1)Define the problem (the question to be answered by the model) 2)Postulate one or model models that could be used to solve the problem. 3)Design/Analyse a set of experimental data to choose between these models and generate statistically meaningful model parameter estimates. 4)If the resultant model selected is inadequate return to step 2. 5) Use the model to solve the problem.

Nov, 2007 Dr. Gary Blau WHAT IS EXPERIMENTAL DESIGN A methodological approach to planning and conducting experiments which ensures: –Experiments will contain the necessary information content to choose between models, estimate model parameters and test model adequacy

Nov, 2007 Dr. Gary Blau WHEN TO APPLY EXPERIMENTAL DESIGN When you know something about the process. When you can afford to make at least several runs

Nov, 2007 Dr. Gary Blau PHASE OF AN EXPERIMENTAL PROGRAM A)EXPERIMENT: 1) Statement of the Problem 2) Choice of Response or Dependent Variable 3) Selection of Factors (independent variables) that can be controlled or varied. 4) Determine feasible ranges and choice of levels of these factors.

Nov, 2007 Dr. Gary Blau PHASE OF AN EXPERIMENTAL PROGRAM B: DESIGN 1) Number of Experiments 2) Sequential Experimentation 3) Randomization/Blocking/Replication 4) Postulated Mathematical Model PROPER DESIGN AVOIDS Excessive data collection Futile data analysis High GI/GO Ratio

Nov, 2007 Dr. Gary Blau PHASE OF AN EXPERIMENTAL PROGRAM ANALYSIS 1) Data Collection and processing 2) Computation of Test Statistics to Validate Model and Estimate Model Parameters 3) Interpretation of Results

Nov, 2007 Dr. Gary Blau TOPICS TO BE COVERED IN THESE MODULES Module 1: 1) Quantification of Uncertainty in Experimental data and impact on model analysis using Probability Theory 2) Review of Statistics for building Statistical Models (Multilinear Regression analysis) 3) Design of Experiments for Building Statistical models Single factor Experiments Multifactor Experiments Factorial Experimentation Fractional Factorial Experimentation Response Surface Modeling Process Optimization

Nov, 2007 Dr. Gary Blau TOPICS TO BE COVERED IN THESE MODULES Module 2 1) When is it necessary to use nonlinear models. 2) Design and Analysis of Experiments with Nonlinear Models (1) Liklihood Estimation -Nonlinear Regression Methods (2) Bayesian Estimation -Markov Chain/Monte Carlo Methods (3) Discrimination of Rival Nonlinear Models (4) Statistical Properties of Estimators (5) Properties of Predicted Values

Nov, 2007 Dr. Gary Blau HOW WILL THE MATERIAL BE COVERED Three Scenarios Lecture Examples –Software tutorials End of Section Problems

Nov, 2007 Dr. Gary Blau HELPFUL HINTS Review Probability and Statistics or have a text available during Module 1 (e.g. Runger and Montgomery, Applied Statistics and Probability for Engineers) Work all lecture examples using your own version of the software. Work all problems at the end of the lectures. Complete Module 1 before starting Module 2. GOOD LUCK

Nov, 2007 Dr. Gary Blau WHEN SHOULD YOU NOT APPLY EXPERIMENTAL DESIGN When you are not trying to predict behavior –Just making a product –Just a demonstration When only a “couple” of runs are to be made –We will get answer with “just one more” run. –Can’t afford any more When you are not even close to the right operating region –Most runs are infeasible –Your product is just junk When you don’t know much about process –Brand new process BUT DON”T USE THESE EXCUSES TOO LONG!!!