Table Of ContentThe correct bibliographic citation for this manual is as follows: Snee, Ronald, and Roger Hoerl. 2016. Strategies
for Formulations Development: A Step-by-Step Guide Using JMP. Cary, NC: SAS Institute Inc.
Strategies for Formulations Development: A Step-by-Step Guide Using JMP
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Contents
Preface ................................................................................................ vii
About This Book ................................................................................... xv
About These Authors ......................................................................... xxiii
Part 1: Fundamentals .................................................... 1
Chapter 1 Introduction to Formulations Development ........................... 3
Overview .................................................................................................................................. 3
1.1 Examples of Formulations ............................................................................................... 4
1.2 How Formulation Experiments are Different ................................................................. 6
Displaying Formulation Compositions Using Trilinear Coordinates ........................... 8
1.3 Formulation Case Studies .............................................................................................. 10
Food Product .................................................................................................................. 11
Pharmaceutical Tablet Formulation ............................................................................. 13
Lubricant Formulation .................................................................................................... 15
Pharmaceutical Tablet Compactability ........................................................................ 17
1.4 Summary and Looking Forward .................................................................................... 19
1.5 References ....................................................................................................................... 19
Chapter 2 Basics of Experimentation and Response Surface
Methodology ....................................................................................... 21
Overview ................................................................................................................................ 21
2.1 Fundamentals of Good Experimentation ...................................................................... 22
Well-Defined Objectives ................................................................................................ 23
High Quality Data ............................................................................................................ 23
How Many Formulations or Blends Do I Need to Test? ............................................. 32
2.2 Diagnosis of the Experimental Environment ................................................................ 33
2.3 Experimentation Strategy and the Evolution of the Experimental Environment ...... 34
Screening Phase ............................................................................................................. 36
Optimization Phase ........................................................................................................ 37
2.4 Roadmap for Experimenting with Formulations .......................................................... 37
iv
Part 2: Design and Analysis of Formulation
Experiments ............................................................... 41
Chapter 3 Experimental Designs for Formulations .............................. 43
Overview ................................................................................................................................ 43
3.1 Geometry of the Experimental Region .......................................................................... 44
3.2 Basic Simplex Designs ................................................................................................... 45
3.3 Screening Designs .......................................................................................................... 48
3.4 Response Surface Designs ............................................................................................ 51
3.5 Summary and Looking Forward .................................................................................... 53
3.6 References ....................................................................................................................... 54
Chapter 4 Modeling Formulation Data ................................................. 55
Overview ................................................................................................................................ 55
4.1 The Model Building Process .......................................................................................... 56
4.2 Summary Statistics and Basic Plots ............................................................................. 59
4.3 Basic Formulation Models and Interpretation of Coefficients ................................... 60
4.4 Model Evaluation and Criticism ..................................................................................... 65
4.5 Residual Analysis ............................................................................................................ 69
4.6 Transformation of Variables .......................................................................................... 82
4.7 Models with More Than Three Components ................................................................ 86
4.8 Summary and Looking Forward .................................................................................... 90
4.9 References ....................................................................................................................... 90
Chapter 5 Screening Formulation Components ................................... 93
Overview ................................................................................................................................ 93
5.1 Purpose of Screening Experiments .............................................................................. 94
5.2 Screening Concepts for Formulations .......................................................................... 95
5.3 Simplex Screening Designs ........................................................................................... 99
5.4 Graphical Analysis of Simplex-Screening Designs ................................................... 107
5.5 After the Screening Design .......................................................................................... 113
5.6 Estimation of the Experimental Variation ................................................................... 114
5.7 Summary and Looking Forward .................................................................................. 115
5.8 References ..................................................................................................................... 115
Part 3: Experimenting With Constrained Systems ..... 117
Chapter 6 Experiments with Single and Multiple Component
Constraints ........................................................................................ 119
Overview .............................................................................................................................. 119
6.1 Component Constraints ............................................................................................... 120
v
6.2 Components with Lower Bounds ................................................................................ 121
6.3 Three-Component Example ......................................................................................... 123
6.4 Computation of the Extreme Vertices ........................................................................ 124
6.5 Midpoints of Long Edges ............................................................................................. 127
6.6 Sustained Release Tablet Development - Three Components ................................ 129
6.7 Four-Component Flare Experiment ............................................................................ 135
Computation of the Vertices ....................................................................................... 135
Number of Blends Required ........................................................................................ 137
Addition of the Constraint Plane Centroids ............................................................... 137
Regions with Long Edges ............................................................................................ 138
Evaluation of the Results ............................................................................................. 139
6.8 Graphical Display of a Four-Component Formulation Space .................................. 140
6.9 Identification of Clusters of Vertices .......................................................................... 143
6.10 Construction of Extreme Vertices Designs for Quadratic Formulation Models ... 144
Replication and Assessing Model Lack of Fit ........................................................... 145
6.11 Designs for Formulation Systems with Multicomponent Constraints .................. 147
6.12 Sustained Release Tablet Formulation Study .......................................................... 150
6.13 Summary and Looking Forward ................................................................................ 155
6.14 References ................................................................................................................... 156
Chapter 7 Screening Constrained Formulation Systems ................... 157
Overview .............................................................................................................................. 157
7.1 Strategy for Screening Formulations .......................................................................... 158
7.2 A Formulation Screening Case Study ......................................................................... 159
7.3 Blending Model and Design Considerations .............................................................. 161
7.4 Analysis: Estimation of Component Effects ............................................................... 163
Calculating Component Effects: Examples ............................................................... 165
7.5 Formulation Robustness .............................................................................................. 168
7.6 XVERT Algorithm for Computing Subsets of Extreme Vertices ............................... 171
Eight-Component XVERT Design and Analysis......................................................... 175
7.7 Summary and Looking Forward .................................................................................. 179
7.8 References ..................................................................................................................... 180
Plackett-Burman Designs for 12, 16, and 20 Runs ................................................... 181
Chapter 8 Response Surface Modeling with Constrained Systems .... 185
Overview .............................................................................................................................. 185
8.1 Design and Analysis Strategy for Response Surface Methodology ........................ 186
8.2 Plastic Part Optimization Study ................................................................................... 187
8.3 Quadratic Blending Model Design Considerations ................................................... 188
8.4 Example – Plastic Part Formulation ............................................................................ 190
vi
8.5 Example – Glass Formulation Optimization ............................................................... 195
8.6 Using the XVERT Algorithm to Create Designs for Quadratic Models .................... 201
8.7 How to Use Computer-Aided Design of Experiments ............................................... 205
8.8 Using JMP Custom Design .......................................................................................... 207
8.9 Blocking Formulation Experiments ............................................................................. 209
8.10 Summary and Looking Forward ................................................................................ 213
8.11 References ................................................................................................................... 213
Part 4: Further Extensions ........................................ 215
Chapter 9 Experiments Involving Formulation and Process Variables 217
Overview .............................................................................................................................. 217
9.1 Introduction ................................................................................................................... 218
9.2 Additive and Interactive Models .................................................................................. 219
9.3 Designs for Formulations with Process Variables .................................................... 221
9.4 The Option of Non-Linear Models ............................................................................... 225
9.5 A Recommended Strategy ........................................................................................... 229
9.6 An Illustration Using the Fish Patty Data .................................................................... 231
9.7 Summary and Looking Forward .................................................................................. 235
9.8 References ..................................................................................................................... 236
Chapter 10 Additional and Advanced Topics ..................................... 237
Overview .............................................................................................................................. 237
10.1 Model Simplification ................................................................................................... 238
10.2 More Advanced Model Forms ................................................................................... 241
Common Alternative Model Forms ............................................................................. 242
Application of Alternative Models to the Flare Data ................................................. 244
10.3 Response Optimization .............................................................................................. 247
10.4 Handling Multiple Responses .................................................................................... 250
The Derringer and Suich Approach ............................................................................ 252
10.5 Multicollinearity in Formulation Models ................................................................... 255
What Is Multicollinearity?............................................................................................. 255
Quantifying Multicollinearity ........................................................................................ 257
The Impact of Multicollinearity .................................................................................... 259
Addressing Multicollinearity ........................................................................................ 260
10.6 Summary ...................................................................................................................... 263
10.7 References ................................................................................................................... 263
Index ................................................................................................. 265
Preface
“The height of sophistication is simplicity.”
Clare Boothe Luce, 1931
Overview
In this preface, we provide an introduction to our book that includes our experiences
in formulation development. Guidance is also provided on what you will learn and
important success factors to be aware of and applied.
At all times we are focused on simplicity: simplicity in experimental design, data
analysis, interpretation and communication of results. By focusing constantly on
simplicity, we have found that formulations are developed faster and their
characteristics are easier to understand and communicate to others.
Many products are formulations in which various ingredients or components are
blended (mixed) together and processed to produce the final product. Some
examples are shown in Table 1 (adapted from Smith 2005). In understanding
formulations and how they arise, it is helpful to see the various industries that create
and manufacture formulations. Some examples of such industries are summarized in
Table 2.
viii Strategies for Formulations Development: A Step-by-Step Guide Using JMP
Table 1 - Products Created by Blending Two or More Ingredients or Components
Adhesives Dyes Lubricants Rocket Propellants
Aluminum Fiber Finishes Metal Alloys Rubber
Animal Feed Floor Coverings Paints Sealants
Artificial Sweeteners Floor Finishes Paper Coatings Soaps
Beverages Foams Personal Care Products Steel
Biological Solutions Food Ingredients Pesticides Surfactants
Cement Froth Flotation Reagents Petroleum Products Synthetic Fibers
Ceramic Glazes Gasket Materials Pharmaceuticals Tobacco Blends
Ceramics Gasoline Photoconductors UV Curable Coatings
Water Treatment
Cleaning Agents Glasses Photoresists Chemicals
Window Glass
Cloth Fiber Blends Hair Spray Polymer Additives Coatings
Cocktails Herbicides Polymers Wine
Combination Vaccines Hydrogels Powder Coatings
Construction Materials Inks Protective Coatings
Cosmetics Insecticides Railroad Flares
Table 2 - Industries that are Major Producers of Formulations
Biotech Metals
Ceramics Paint
Chemicals Petroleum
Coatings Pharmaceuticals
Electronics Plastics
Food Textiles
The authors first met at while working at the DuPont Company’s engineering center
in Newark, DE. DuPont’s original product, gunpowder, is a mixture of three
components: potassium nitrate (saltpeter), sulfur, and charcoal.
Preface ix
Figure 1 – Ingredients of Black Powder
© Jeff J. Daly, FUNDAMENTAL PHOTOGRAPHS, NEW YORK
The quality of the powder was a function of the proportions of the components in
the mixture, NOT the total amount of the mixture (Figure 1). The typical formulation
consisted of:
75% Saltpeter, 12.5% Charcoal and 12.5% Sulfur. Other formulations used for specific
applications were:
Use Saltpeter Charcoal Sulfur
General 75 12.5 12.5
Hunting 78 12 10
Military 75 15 10
Blasting 62 18 20
We note that the blasting formulation was considerably different from the other
formulations. Wilkson (1966, page 23) noted that “Manufacturers would often
experiment, changing their formulas after tests of a finished powder proved it was
not giving the results desired.” The objective then, as it is today, was to find a
desirable balance between product properties and manufacturing costs.
The DuPont Company was founded in 1802 to produce high quality black powder,
as the quality of the black powder in the US was of very poor quality at that time
(DuPont Company 1952). Guides at the Hagley Museum in Wilmington Delaware,
the site of DuPont's original powder mill on the Brandywine River, explain that one
of DuPont’s advantages was development of a device to measure the explosive
charge of gunpowder in manufacturing, which enabled them to reduce variation
below that of their competitors (Hoerl 1990). That is, DuPont’s product was more
consistent than their competitors’ products.
x Strategies for Formulations Development: A Step-by-Step Guide Using JMP
Formulations are typically developed through experimentation. One quickly
recognizes that experimenting with formulations is different from typical
experimentation, as the response is a function of the proportions of the components
in the formulation. This results in the component levels being dependent on each
other, as the total amount of the formulation must add to 100%, or 1.0 when
expressed as fractions of the total amount.
Our Experiences with Formulations
The first author to recognize this summation constraint was Claringbold (1955). The
methodology, literature, and software has developed significantly over the years to
the point that formulation scientists have a sound methodology to use, supported by
software such as JMP (marketed by the SAS Institute in Cary, NC).
We encountered formulation experimentation early in our careers. Roger Hoerl first
worked on paint formulation studies while working as an intern at the DuPont
Company in the early 1980’s. He went on to work on other formulation studies as
part of his work at Hercules, Inc., Scott Paper Company, and at General Electric (GE)
Plastics. At Hercules, his formulation work included coatings and polymer
formulations, especially for wrapping films. It was during this work that he
developed an approach to applying ridge analysis to mixture problems (Hoerl 1987).
At Scott Paper Company, Roger worked on formulation problems such as wood
pulping chemicals and the impact of incorporating recycled fiber with various
"virgin" fibers in the pulping process. This was at the beginning of the recycling
movement in the paper industry, and a lot of engineers were concerned that recycled
paper fiber wouldn't work. We found out that it did!
Ron Snee was introduced to mixture experiments during his PhD work at Rutgers
University. Upon joining DuPont, he was thrust immediately into gasoline blending
studies for DuPont’s petroleum industry customers. Other formulations followed,
including lubricant blending, plastics, and hair sprays. Since the beginning of this
century, he has been working on formulation development for pharmaceutical and
biotech products.
Ron’s work at DuPont led to several advances in the design and analysis of
formulation studies that form the basis of a considerable portion of the DuPont
Strategy of Formulation Development approaches that are described in this book.
Some of these advances include:
• Formulation screening experiments: concepts and designs (Snee and
Marquardt 1976)
• Models for the analysis of mixture data (Snee 1973)
