Contents

Preface

About This Book

About These Authors

Part 1: Fundamentals

Chapter 1 Introduction to Formulations Development

Overview

1.1 Examples of Formulations

1.2 How Formulation Experiments are Different

Displaying Formulation Compositions Using Trilinear Coordinates

1.3 Formulation Case Studies

Food Product

Pharmaceutical Tablet Formulation

Lubricant Formulation

Pharmaceutical Tablet Compactability

1.4 Summary and Looking Forward

1.5 References

Chapter 2 Basics of Experimentation and Response Surface Methodology

Overview

2.1 Fundamentals of Good Experimentation

Well-Defined Objectives

High Quality Data

How Many Formulations or Blends Do I Need to Test?

2.2 Diagnosis of the Experimental Environment

2.3 Experimentation Strategy and the Evolution of the Experimental Environment

Screening Phase

Optimization Phase

2.4 Roadmap for Experimenting with Formulations

Part 2: Design and Analysis of Formulation Experiments

Chapter 3 – Experimental Designs for Formulations

Overview

3.1 Geometry of the Experimental Region

3.2 Basic Simplex Designs

3.3 Screening Designs

3.4 Response Surface Designs

3.5 Summary and Looking Forward

3.6 References

Chapter 4 – Modeling Formulation Data

Overview

4.1 The Model Building Process

4.2 Summary Statistics and Basic Plots

4.3 Basic Formulation Models and Interpretation of Coefficients

4.4 Model Evaluation and Criticism

4.5 Residual Analysis

4.6 Transformation of Variables

4.7 Models with More Than Three Components

4.8 Summary and Looking Forward

4.9 References

Chapter 5 – Screening Formulation Components

Overview

5.1 Purpose of Screening Experiments

5.2 Screening Concepts for Formulations

5.3 Simplex Screening Designs

5.4 Graphical Analysis of Simplex-Screening Designs

5.5 After the Screening Design

5.6 Estimation of the Experimental Variation

5.7 Summary and Looking Forward

5.8 References

Part 3: Experimenting With Constrained Systems

Chapter 6 – Experiments with Single and Multiple Component Constraints

Overview

6.1 Component Constraints

6.2 Components with Lower Bounds

6.3 Three-Component Example

6.4 Computation of the Extreme Vertices

6.5 Midpoints of Long Edges

6.6 Sustained Release Tablet Development - Three Components

6.7 Four-Component Flare Experiment

Computation of the Vertices

Number of Blends Required

Addition of the Constraint Plane Centroids

Regions with Long Edges

Evaluation of the Results

6.8 Graphical Display of a Four-Component Formulation Space

6.9 Identification of Clusters of Vertices

6.10 Construction of Extreme Vertices Designs for Quadratic Formulation Models

Replication and Assessing Model Lack of Fit

6.11 Designs for Formulation Systems with Multicomponent Constraints

6.12 Sustained Release Tablet Formulation Study

6.13 Summary and Looking Forward

6.14 References

Chapter 7 – Screening Constrained Formulation Systems

Overview

7.1 Strategy for Screening Formulations

7.2 A Formulation Screening Case Study

7.3 Blending Model and Design Considerations

7.4 Analysis: Estimation of Component Effects

Calculating Component Effects: Examples

7.5 Formulation Robustness

7.6 XVERT Algorithm for Computing Subsets of Extreme Vertices

Eight-Component XVERT Design and Analysis

7.7 Summary and Looking Forward

7.8 References

Plackett-Burman Designs for 12, 16, and 20 Runs

Chapter 8 – Response Surface Modeling With Constrained Systems

Overview

8.1 Design and Analysis Strategy for Response Surface Methodology

8.2 Plastic Part Optimization Study

8.3 Quadratic Blending Model Design Considerations

8.4 Example – Plastic Part Formulation

8.5 Example – Glass Formulation Optimization

8.6 Using the XVERT Algorithm to Create Designs for Quadratic Models

8.7 How to Use Computer-Aided Design of Experiments

8.8 Using JMP Custom Design

8.9 Blocking Formulation Experiments

8.10 Summary and Looking Forward

8.11 References

Part 4: Further Extensions

Chapter 9 - Experiments Involving Formulation and Process Variables

Overview

9.1 Introduction

9.2 Additive and Interactive Models

9.3 Designs for Formulations with Process Variables

9.4 The Option of Non-Linear Models

9.5 A Recommended Strategy

9.6 An Illustration Using the Fish Patty Data

9.7 Summary and Looking Forward

9.8 References

Chapter 10 – Additional and Advanced Topics

Overview

10.1 Model Simplification

10.2 More Advanced Model Forms

Common Alternative Model Forms

Application of Alternative Models to the Flare Data

10.3 Response Optimization

10.4 Handling Multiple Responses

The Derringer and Suich Approach

10.5 Multicollinearity in Formulation Models

What Is Multicollinearity?

Quantifying Multicollinearity

The Impact of Multicollinearity

Addressing Multicollinearity

10.6 Summary

10.7 References

Index

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