AXIOMATIC DESIGN wm%mm;mmM*m«imim™*mwm™m mmm^m^mmmm^mw^ ^mmmm-

ADVANCES A N D APPLICATIONS

Nam Pyo Suh Massachusetts Institute of Technology

New York • Oxford OXFORD UNIVERSITY PRESS 2001

Contents

PREFACE XV

ACKNOWLEDGMENTS xix

O N THE CIRP DESIGN BOOK SERIES xxiii

1 Introduction to Axiomatic Design 1

1.1 Introduction 1

1.2 Current State of Design Practice 1 1.3 Who Are the Designers? How Do We Design? What Is Design? 2 1.4 What Is the Ultimate Goal of Axiomatic Design? 5 1.5 Role of Axioms in Development of Science and Technology:

A Historical Perspective 6 1.6 Axiomatic Approach versus Algorithmic Approach 9 1.7 Axiomatic Design Framework 10

1.7.1 The Concept of Domains 10

1.7.2 Definitions 12 1.7.3 Mapping from Customer Needs to Functional Requirements 14

1.7.4 The First Axiom: The Independence Axiom 1 6 1.7.5 Ideal Design, Redundant Design, and Coupled Design: A Matter of Relative Numbers

ofDPsandFRs 22 1.7.6 Examples Involving Decoupling of Coupled Designs 24 1.7.7 Decomposition, Zigzagging, and Hierarchy 29 1.7.8 Requirements for Concurrent Engineering 37 1.7.9 The Second Axiom: The Information Axiom 39 1.7.10 Reduction of the Information Content: Robust Design 45 1.7.11 Reduction of the Information Content through Integration of DPs 50 1.7.12 Designing with Incomplete Information 51

1.8 Common Mistakes Made by Designers 53 1.9 Comparison of Axiomatic Design with Other Methodologies 5 7 1.10 Summary 58

viii CONTENTS

References 59 Appendix 1A Corollaries and Theorems 60 Homework 65

2 One-FR Design, the Information Axiom, and Robust Design 67

2.1 Introduction 67 2.2 Introduction to One-FR Design 68

2.2.1 One-FR Design versus Multi-FR Design 69 2.2.2 Minimization of the Information Content 70

2.3 Design Issues for the One-FR Design 73 2.4 One-FR Design and Information Content 74

2.4.1 One-FR Design with No Constraints 74 2.4.2 One-FR Design with Constraints 86 2.4.3 Nonlinear One-FR Design with Constraints 88

2.5 Elimination of Bias and Reduction of Variance 95 2.6 Robust Design 95

2.6.1 Determination of Tolerances for Robust Design 95 2.6.2 Effect of Noise on FRs in Design and Manufacturing 96 2.6.3 Robustness and the Rate of Response in Nonlinear Design 99

2.7 Design Process 100 2.8 Summary 102 References 102

Appendix 2A Stress in a Thick Wall Tube 102 Appendix 2B Discrete Random Variables: Expected Value, Variance,

and Standard Deviation 105

Appendix 2C Continuous Random Variables: Expected Value, Variance,

Standard Deviation, and Multivariate Random Variables 106

Homework 108

3 Multi-FR Design 109

3.1 Introduction 109 3.2 Brief Review of Axiomatic Theory for Multi-FR Designs 112

3.3 The Independence Axiom and the Information Axiom: Their Implications for a Multi-FR Design Task 114

3.4 On Ideal Multi-FR Design 116 3.5 Uncoupled and Decoupled Multi-FR Designs 124

3.5.1 Propagation of Tolerances in Uncoupled, Decoupled, and Coupled Designs and Its Implication for Design Robustness 124

3.5.2 Examples of Multi-FR Design 126

3.6 Information Content, Complexity, and Noise of Multi-FR Design 142

Contents ix

3.6.1 The Relationship between Complexity and Information Content 142 3.6.2 Determination of Information Content of Uncoupled, Decoupled, and

Coupled Designs 146

3.6.3 Accommodating Noise in the Design Process 152

3.7 Integration of DPs to Minimize the Information Content 1 53

3.8 Nonlinear Multi-FR Design 154

3.9 Design of Dispatching Rules and Schedules: Avoiding Traffic Congestion 156

3.9.1 Dispatching Rules and the Independence Axiom 1 58

3.9.2 Scheduling 158

3.10 Axiomatic Design Basis for Robust Design 162

3.10.1 One-FR Design 162

3.10.2 Multi-FR Design 165

3.10.3 Information Content of Multi-FR Design 167

3.11 Summary 174

References 174

Appendix 3 A Independence of the Two Design Axioms 1 74

Appendix 3B Corollaries and Theorems Related to Information and Complexity 1 77 Appendix 3C Probability of Success of Decoupled and Uncoupled Designs When There Is

No Bias 1 79

Appendix 3D Why Coupling in Design Should Be Avoided 185 Homework 187

4 Design of Systems 192

4.1 Introduction 192

4.2 Issues Related to System Design 195

4.3 Classification of Systems 195

4.4 Axiomatic Design Theory for Fixed Systems 1 96

4.5 Design and Operation of Large Systems 201

4.5.1 Introduction to Large-System Issues 201

4.5.2 What Is a Large System? 201

4.5.3 Definition of a Large Flexible System 202

4.5.4 Axiomatic Design of a Large Flexible System 203

4.5.5 System Synthesis through Physical Integration of DPs 205

4.5.6 On Designing the Best Large Flexible System 205

4.5.7 Theorems Related to the Design of Large Systems 206

4.6 Representation of the System Architecture of Fixed Systems 207 4.6.1 Hierarchies in Design Domains through Decomposition of FRs, DPs, and PVs: A

Representation of the System Architecture 208 4.6.2 Design Matrix and Module-Junction Diagrams: Another Means of System

Representation 209

x CONTENTS

4.6.3 Flow Diagram: A Representation of System Architecture 211

4.6.4 System Control Command (SCC) 213

4.7 Mathematical Modeling, Simulation, and Optimization of Systems 234

4.8 Application of the Flow Diagram of the System Architecture 235

4.9 On Human-Machine Interface 235

4.10 Summary 236

References 237

Homework 237

5 Axiomatic Design of Software 239

5.1 Introduction 239

5.2 Axiomatic Design Theory for Software Design 244

5.2.1 Review of the Axiomatic Design Process for Software 245

5.2.2 Application of the Flow Diagram 249

5.3v Software Design Process 249

5.4 Axiomatic Design of Object-Oriented Software Systems 266

5.4.1 Object-Oriented Techniques 266

5.4.2 Modified OOT for Compatibility wifh Axiomatic Design 270

5.4.3 Basics of Axiomatic Design of Object-Oriented Software Systems 271

5.5 Axiomatic Design of Object-Oriented Software System for Designers: Acclaro Software 279

5.5.1 Introduction 279

5.5.2 Axiomatic Design of Acclaro Software 280

5.5.3 Axiomatic Design on the FR114i Branch 281

5.5.4 Object-Oriented Model: Bottom-Up Approach 281

5.5.5 Coding with the System Architecture 284

5.6 Design of Rapid-Prototyping Software for Real-Time Control of Hardware/Software System 286

5.7 An Ideal Software System 291

5.8 Other Issues Related to Software Design 292

5.8.1 Reusability 292

5.8.2 Extensionality 292

5.8.3 Knowledge and Information Requirements in Software Design 293

5.9 Implications of the Information Axiom in Software Design 295

5.9.1 Qualitative Implementation of the Information Axiom 295

5.9.2 Quantitative Measure of the Information Content 295

5.10 Summary 296

References 297

Homework 298

Contents xi

6 Axiomatic Design of Manufacturing Systems 301

6.1 Introduction 301 6.2 Basic Requirements of a Manufacturing System 306 6.3 Elements of Manufacturing Systems 307 6.4 Axiomatic Design of Fixed Manufacturing Systems for Identical Parts 309

6.4.1 Highest Level Design of a Fixed Manufacturing System 309

6.4.2 Analytical Solutions for Queues in Decouplers 312 6.5 Axiomatic Design of a Flexible Manufacturing System for Different Types of Parts 31 7 6.6 Mathematical Modeling and Optimization of Design 331 6.7 Representation of Manufacturing System Architecture 331 6.8 Summary 336 References 337 Homework 338

7 Axiomatic Design of Materials and Materials-Processing Techniques 341

7.1 Introduction 341 7.2 Mixalloys 343

7.2.1 Historyof Mixalloys 343 7.2.2 Design of Dispersion-Strengthened Metals: Mapping from the Functional Domain to the

Physical Domain 344 7.2.3 Design of the Process: Mapping from the Physical Domain to

the Process Domain 346 7.2.4 Further Development of the Process 347

7.2.5 Mixalloy Equipment 350 7.2.6 Properties of Mixalloys: Dispersion-Strengthened Copper 350

7.3 Microcellular Plastics 352 7.3.1 Introduction to Microcellular Plastics 352 7.3.2 Design ofaBatch Process 354 7.3.3 Design of Continuous Process 355 7.3.4 Performance of Microcellular Plastics 368 7.3.5 Other Advantages of the MuCell Process 369

7.4 Layered Manufacturing Processes for Rapid Prototyping 370 7.4.1 Design of Layered Manufacturing Processes 371 7.4.2 Information Content of Layered Manufacturing Processes 372

7.5 Summary 372 References 372 Homework 374

8 Product Design 376

8.1 Introduction 376

xii CONTENTS

8.1.1 Important Questions to Ask before Developing a New Product 378 8.1.2 Basic Requirements of Product Manufacture 380

8.1.3 How Should Companies Avoid Making Mistakes during Product Development? 380

8.1.4 What Have Universities Done in This Area? 382

8.1.5 Customization of Products to Satisfy Individual Customers 383

8.1.6 Total Quality Management (TQM) 384

8.2 Mapping from the Customer Domain to the Functional Domain 384

8.2.1 For Existing Products 385

8.2.2 For New Innovative Products 388

8.3 Mapping from FRs to DPs 390

8.3.1 DecompositionofFR2andDP2 393

8.4 Application of the Information Axiom 395

8.4.1 General Criteria 395

8.4.2 Error Budgeting 396

8.5 Case Study—Depth Charge 399

8.5.1 Case Study Background 399

8.5.2 Effectively Searching for Potential Design Solutions 400

8.5.3 Design of the Depth Charge Initiator 400

8.6 Chemical-Mechanical Planarization (CMP) Machine 406

8.6.1 Design of the Mechanical System 407

8.6.2 Axiomatic Development of CMP a Machine Control System 441

8.7 Concurrent Engineering: Mapping from FR to DP to PV 461

8.8 Product Service 462

8.9 System Architecture 464

8.10 Summary 464

References 465

Homework 465

9 A Theory of Complexity: The Design Axioms, Information, Complexity, and Periodicity 470

9.1 Introduction 470

9.2 Complexity, Uncertainty, Information, and Periodicity 473

9.2.1 Preliminary Remarks 473

9.2.2 Definition of Complexity 474

9.2.3 Time-Independent Complexities: Real Complexity, Imaginary Complexity, and Absolute Complexity 475

9.2.4 Time-Dependent Complexity: Combinatorial Complexity and Periodic Complexity 483

Contents xiii

9.3 Reduction of Uncertainty: Conversion of a Design with Time-Dependent Combinatonal Complexity to a Design with Time-Dependent Periodic Complexity 484

9.4 Distinction between Time-Independent and Time-Dependent Complexities 494

9.5 Other Implications of the Design Axioms and Periodic Complexity: A Speculation 495

9.5.1 Nature 495

9.5.2 Biological Systems and Living Beings 495

9.5.3 Artificial Systems 496 9.6 Complexity of Natural Phenomena 497 9.7 Summary 498 References 499 Homework 499

INDEX 501