Tolerance Design: A Handbook for Developing Optimal Specifications [Hardback]

Preface		xv	(4)
Acknowledgments		xix
Section I: Setting the Stage for Understanding the Science of Tolerancing		1	(84)
1 Introduction to Tolerancing and Tolerance Design		3	(22)
The Historical Roots of Tolerancing		3	(3)
The State of the Art in Tolerancing Techniques		6	(3)
What Should a Modern Tolerance Development Process Look Like?		6	(1)
The Relationship between Traditional Tolerancing Methods and the Taguchi Approach		6	(3)
Developing Tolerances: The Role of Engineers and Designers		9	(1)
Concepts, Definitions, and Relationships		10	(2)
Matching Design Tolerances with Appropriate Manufacturing Processes		12	(1)
Introduction to the Taguchi Approach to Tolerance Analysis		12	(11)
Review of the Three Phases of a Quality Engineering--Based Product--Development Process		13	(7)
Taguchi's Approach to Tolerancing		20	(3)
Summary		23	(1)
References		24	(1)
2 The Relationship of Quality Engineering and Tolerancing to Reliability Growth		25	(26)
The Three Initial Phases of Product Development		26	(22)
Phase 1: Subsystem Concept Selection and Robustness Optimization		28	(11)
Gate 1		39	(1)
Phase 2: System Robustness Optimization		39	(3)
Gate 2		42	(1)
Phase 3: Product Design		42	(5)
Gate 3		47	(1)
The Reliability Bathtub Curve and Tolerancing		48	(1)
Summary		49	(1)
References		50	(1)
3 Introductory Statistics and Data Analysis for Tolerancing and Tolerance Design		51	(34)
The Role of Data in Tolerance Analysis		51	(1)
Graphical Methods of Data Analysis		52	(3)
The Histogram		54	(1)
Quantitative Methods of Data Analysis		54	(1)
Introduction to the Fundamentals of Descriptive Statistics		55	(7)
The First Moment of the Data about the Mean -- The Arithmetic Average		55	(1)
The Second Moment about the Mean: The Variance		56	(1)
The Standard Deviation		57	(1)
The Third Moment about the Mean: The Skew		58	(1)
The Fourth Moment about the Mean: The Kurtosis		59	(2)
The Coefficient of Variation		61	(1)
The Use of Distributions		62	(1)
The Use of Distributions in Taguchi's Parameter and Tolerance Design		62	(1)
The Use of Distributions in Traditional Tolerance Analysis		63	(1)
Introduction to the Fundamentals of Inferential Statistics		63	(9)
The Z Transformation Process		63	(3)
The Student--t Transformation Process		66	(1)
The Adjusted Z Transformation Process for Working with Nonnormal Distributions		67	(5)
Manufacturing Process Capability Metrics		72	(4)
Six Sigma Process Metrics		76	(3)
The Relationship between the Quality--Loss Function, Cp, and Cpk		79	(2)
Summary		81	(2)
References		83	(2)
Section II: Traditional Tolerance Analysis		85	(114)
4 Using Standard Tolerance Publications and Manufacturer's Process Capability Recommendations		87	(14)
Starting the Tolerance Design Process		87	(1)
The Three Sigma Paradigm		88	(2)
Processes for Establishing Initial Tolerances		90	(6)
Establishing Process Capability and Process Control for Identifying Initial Tolerances		96	(3)
Creating a Library for Process Capabilities as a Data Base		98	(1)
Summary		99	(1)
References		99	(2)
5 Linear and Nonlinear Worst--Case Tolerance Analysis		101	(23)
Standard Worst--Case Methods		101	(21)
Six Sigma Worst--Case Tolerance Analysis		102	(2)
Analysis for Nonlinear Tolerance Stacks Using the Worst--Case Method		104	(1)
Process Diagrams for Worst--Case Analysis for the Stackup of Tolerances in Assemblies		105	(4)
A Case Study for a Linear Worst--Case Tolerance Stackup Analysis		109	(2)
A Process for Modeling Worst--Case Nonlinear Tolerance Stackup Problems		111	(11)
Summary		122	(1)
References		123	(1)
6 Linear and Nonlinear Statistical Tolerance Analysis		124	(25)
The Root Sum of Squares (RSS) Approach		126	(6)
The Z Transformation Process		127	(1)
One--Dimensional Tolerance Stacks		127	(3)
Motorola's Dynamic Root Sum of Squares Approach		130	(1)
Motorola's Static Root Sum of Squares Approach		131	(1)
The Nonlinear RSS Case Method		132	(1)
Process Diagrams for the StatisticalMethods of Tolerance Stackup Analysis		133	(12)
The Linear RSS Method		133	(5)
The Dynamic RSS Method		138	(1)
The Static RSS Method		139	(6)
The Nonlinear RSS Example		145	(2)
Summary		147	(1)
References		148	(1)
7 Sensitivity Analysis and Related Topics		149	(11)
The Various Approaches to Performing Sensitivity Analysis		149	(5)
Mathematical Sensitivity Analysis		149	(1)
Tolerance--Range Sensitivity Analysis		150	(1)
Component Manufacturing Process Output Distribution Sensitivity Analysis		151	(1)
Nonlinear Tolerance Sensitivity Analysis		151	(1)
The Steps for Basic Nonlinear Sensitivity Analysis		152	(1)
Empirical Sensitivity Analysis		153	(1)
ANOVA Sensitivity Analysis		153	(1)
One--Factor--at--a--Time Sensitivity Analysis		153	(1)
Using Sensitivity Analysis in Concept Design		154	(2)
An Example of the Use of Sensitivity Analysis in Concept Development		156	(2)
Summary		158	(1)
References		159	(1)
8 Computer Aided Tolerancing Techniques		160	(27)
Various Software and Platform Options to Support CAT Analysis		161	(2)
Commercially Available Pro/ENGINEER--Based Tolerance Analysis Software		162	(1)
Monte Carlo Simulations in Tolerance Analysis		163	(4)
Characterizing Probability Distributions for Tolerance Analysis Applications		167	(5)
The Common Probability Distributions Available in Crystal Ball		167	(1)
The Less Common Probability Distributions Available in Crystal Ball		168	(2)
Step--by--Step Process Diagrams for a Crystal Ball Monte Carlo Analysis		170	(2)
Sensitivity Analysis Using Crystal Ball		172	(3)
How to Use Crystal Ball		175	(6)
Running the Monte Carlo Simulation		181	(3)
Preparing Engineering Analysis Reports		184	(1)
Another Computer--Aided Tolerance Approach		185	(1)
Summary		185	(1)
References		186	(1)
9 Introduction to Cost--Based Optimal Tolerancing Analysis		187	(4)
Skills Required for Cost--Based Optimal Tolerance Analysis		188	(1)
The Various Approaches to Cost--Based Optimal Tolerance Analysis		188	(2)
Cost versus Tolerance Plots		190	(1)
Summary		190	(1)
References		190	(1)
10 Strengths and Weaknesses of the Traditional Tolerance Approaches		191	(8)
Using Standard Tolerance Publications and Manufacturer's Process Capability Recommendations		192	(1)
Worst--Case Tolerance Analysis		193	(1)
The Statistical Methods of Tolerance Analysis		193	(1)
The Root Sum Square Approach		193	(1)
The Dynamic Root Sum of Squares Approach		193	(1)
The Static Root Sum of Squares Approach		194	(1)
The Nonlinear Tolerance Approaches		194	(1)
Sensitivity Analysis		194	(1)
Computer--Aided Tolerancing		194	(1)
Cost--Based Optimal Tolerance Analysis		195	(1)
How the Six Processes Relate to the Overall Product Tolerancing Process		195	(1)
Summary		196	(1)
References		197	(2)
Section III: Taguchi's Approach to Tolerancing and Tolerance Design		199	(162)
11 The Quality--Loss Function in Tolerancing and Tolerance Design		201	(23)
Linking Cost and Functional Performance		201	(1)
An Example of the Cost of Quality		202	(4)
The Step Function: An Inadequate Description of Quality		206	(1)
The Customer Tolerance		207	(1)
The Quality--Loss Function: A Better Description of Quality		208	(1)
The Quality--Loss Coefficient		209	(1)
An Example of the Quality--Loss Functions		210	(9)
The Types of Quality--Loss Functions		210	(9)
Developing Quality--Loss Functions in a Customer's Environment		219	(1)
Constructing the Quality--Loss Economic Coefficient		220	(2)
Summary		222	(1)
References		223	(1)
12 The Application of the Quadratic Loss Function to Tolerancing		224	(22)
The Difference between Customer, Design, and Manufacturing Tolerances		224	(1)
Customer Tolerances		224	(1)
Design and Manufacturing Tolerances		225	(1)
The Taguchi Tolerancing Equations		225	(4)
Taguchi's Economical Safety Factor		225	(1)
The Derivation of Taguchi's Tolerance Equation and the Factor of Safety		226	(3)
Relating Customer Tolerances to Engineering Tolerances		229	(1)
An Example of Tolerancing Using the Loss Function (Nominal--the--Best Case)		229	(1)
Relating Customer Tolerances to Subsystem and Component Tolerances		230	(1)
The Linear Sensitivity Factor		231	(1)
Using the Loss Function for Multiple--Component Tolerance Analysis		232	(1)
An Example of Applying the Quality--Loss Function to a Multicomponent Problem		233	(1)
Setting Up the Problem		234	(1)
Identifying Critical Parameters		234	(3)
Mapping the Critical Parameters and Their Sensitivities		235	(2)
Converting the Traditional Tolerance Problem into a Quality--Loss		237	(1)
How to Evaluate Aggregated Low Level Tolerances		238	(2)
Case 1: Ratio of Losses are Much Less than Unity		239	(1)
Case 2: Ratio of Losses are Much Greater than Unity		239	(1)
Case 3: Ratio of Loss Approximately Equal Unity		239	(1)
Using the Loss Function Nonlinear Relationships		240	(1)
Developing Tolerances for Deterioration Characteristics in the Design		241	(1)
Tolerancing the Deterioration Rate of a Higher Level Product Characteristic		242	(1)
Determining Initial and Deterioration Tolerances for a Product Characteristic		243	(1)
Summary		244	(1)
References		245	(1)
13 General Review of Orthogonal Array Experimentation for Tolerance Design Applications		246	(16)
Developing Tolerances Using a Designed Experiment		246	(1)
Use of Orthogonal Arrays in Tolerance Design		247	(1)
The Build--Test--Fix Approach		248	(1)
Introduction to Full Factorial Experiments		248	(7)
Designed Experiments Based on Fractional Factorial Orthogonal Arrays		249	(2)
Degrees of Freedom: The Capacity to do Experimental Analysis		251	(1)
Degrees of Freedom for the Full Factorial		251	(1)
The DOF for the Fractional Factorial Orthogonal Array		251	(1)
DOF for Two--Level Full Factorial Arrays		252	(3)
Methods to Account for Interactions within Tolerance Design Experiments		255	(5)
Interactions Defined		255	(2)
Quantifying the Effect of an Interaction		257	(2)
Defining the Degrees of Freedom Required for Evaluating Interactions		259	(1)
Summary		260	(1)
References		261	(1)
14 Introducing Noise into a Tolerance Experiment		262	(16)
Defining Noises and Creating Noise Diagrams and Maps		262	(15)
Selecting Noise Factors for Inclusion in a Tolerance Experiment		264	(1)
Noise Diagrams and System Noise Maps		265	(2)
Experimental Error and Induced Noise		267	(4)
The Noise Factor Experiment		271	(1)
Creating Compound Noise Factors		272	(1)
Setting Up and Running the Noise Experiment		273	(1)
Analysis of Means for the Noise Experiment		274	(2)
Verification of the Predicted Response		276	(1)
Summary		277	(1)
References		277	(1)
15 Setting Up a Designed Experiment for Variance and Tolerance Analysis		278	(28)
Preparing to Run a Statistical Variance Experiment		279	(13)
Selecting the Right Orthogonal Array for the Experiment		279	(2)
Special Instructions for Running Three--Level Statistical Variance Experiments		281	(11)
Using the V.3 Transformation		292	(4)
A Comparison of Output Statistics		296	(4)
Conducting a Tolerance Experiment for Worst--Case Conditions		300	(1)
An L9 Experiment and Monte Carlo Simulation Using Levels Assuming Uniform Distributions		301	(3)
Metrology and Experimental Technique		304	(1)
Summary		304	(1)
References		305	(1)
16 The ANOVA Method		306	(19)
Accounting for Variation Using Experimental Data		307	(1)
A Note on Computer--Aided ANOVA		308	(1)
An Example of the ANOVA Process		308	(3)
Degrees of Freedom in ANOVA		311	(1)
Error Variance and Pooling		312	(1)
Error Variance and Replication		312	(1)
Error Variance and Utilizing Empty Columns		313	(1)
The F--Test		313	(1)
A WinRobust ANOVA Example		314	(4)
An ANOVA--TM Example		318	(5)
Summary		323	(1)
References		324	(1)
17 The Tolerance Design Process: A Detailed Case Study		325	(36)
The Steps for Performing the Tolerance Design Process		325	(2)
Option 1: A Company Cost--Driven Process		327	(1)
Option 2: A Manufacturing Capability and Cost--Driven Process		328	(2)
The ASI Circuit Case Study		330	(4)
Identifying the Parameters for Tolerancing		330	(1)
Improving Quality in Cases where Parameter Design was Not Done		331	(1)
Constructing the Loss Function		332	(2)
Setting Up and Running the Experiment		334	(3)
Two--versus Three--Level Experiments		337	(1)
Techniques for Putting Noise into the Tolerance Experiment		338	(1)
Running the Experiment		338	(2)
Data Entry		340	(3)
Measuring the Proper Response Characteristic		343	(1)
Interactions in Tolerance Experiments		343	(1)
Analyzing the Data		344	(1)
Applying ANOVA		344	(5)
Relating the ANOVA Data to the Loss Function and Process Capability (Cp)		349	(1)
Defining the Critical to Function (CTF) Factors		350	(1)
Defining the Cost Improvement Parameters (CIP)		351	(1)
Identifying and Quantifying the Costs Associated with Improving Quality		352	(1)
Working with Suppliers to Lower Customer Losses through Reducing the Component Parameter Standard Deviations		352	(1)
Calculating New Variances and MSD Values Using the Variance Equation		353	(1)
Quantifying the Cost of Reducing the Parameter Standard Deviations		354	(2)
Identifying and Quantifying the Opportunities for Lowering Costs		356	(1)
Relaxing Tolerances and Material Specifications of CIPs to Balance Cost and Quality		356	(1)
New Loss and Cp after Upgrading the Critical To Function Factors and Downgrading the Cost Improvement Parameters		357	(1)
Using Tolerance Design to Help Attain Six Sigma Quality Goals		357	(1)
Using Tolerance Design to Improve System Reliability		357	(1)
Summary		358	(1)
References		359	(2)
Section IV: Industrial Case Studies		361	(28)
18 Drive System Case Studies		363	(26)
The Drive System		364	(1)
The Drive Module		365	(2)
Case 1: Defining Tolerances for Standard Drive Module Components		367	(2)
Tolerancing Custom Parts to Assemble with Standard Parts		368	(1)
Case 2: Drive Module for Worst--Case Assembly Analysis		369	(2)
Worst--Case Linear Stack Analysis		369	(2)
Case 3: Drive Module for Computer--Aided Assembly Analysis		371	(2)
RSS Case Linear Stack Analysis		371	(2)
Case 4: Drive Module for Computer--Aided Assembly Analysis		373	(7)
Case 5: Drive System Aided by the Use of a Designed Experiment		380	(8)
Preparing for the Drive System Tolerance Developmental Experiment		381	(1)
Setting Up the Experiment		382	(3)
Data Acquisition		385	(1)
Results from the L9 Experiment		386	(2)
Summary		388	(1)
Appendix A: The Z Transformation Tables and the t Transformation Table		389	(4)
Appendix B: The Adjusted Z Transformation Tables		393	(10)
Appendix C: The F Tables		403	(6)
Appendix D: Additional References for Tolerance Design		409	(2)
Appendix E: Suppliers for Tolerance Design		411	(2)
Index		413

Clyde "Skip" Creveling is the president and founder of Product Development Systems & Solutions Inc. (PDSS) (http://www.pdssinc.com). Since PDSS' founding in 2002, Mr. Creveling has led Design for Six Sigma (DFSS) initiatives at Motorola, Carrier Corporation, StorageTek, Cummins Engine, BD, Mine Safety Appliances, Callaway Golf, and a major pharmaceutical company. Prior to founding PDSS, Mr. Creveling was an independent consultant, DFSS Product Manager, and DFSS Project Manager with Sigma Breakthrough Technologies Inc. (SBTI). During his tenure at SBTI he served as the DFSS Project Manager for 3M, Samsung SDI, Sequa Corp., and Universal Instruments.

Mr. Creveling was employed by Eastman Kodak for 17 years as a product development engineer within the Office Imaging Division. He also spent 18 months as a systems engineer for Heidelberg Digital as a member of the System Engineering Group. During his career at Kodak and Heidelberg he worked in R&D, Product Development/Design/System Engineering, and Manufacturing. Mr. Creveling has five U.S. patents.

He was an assistant professor at Rochester Institute of Technology for four years, developing and teaching undergraduate and graduate courses in mechanical engineering design, product and production system development, concept design, robust design, and tolerance design. Mr. Creveling is also a certified expert in Taguchi Methods.

He has lectured, conducted training, and consulted on product development process improvement, design for Six Sigma methods, technology development for Six Sigma, critical parameter management, robust design, and tolerance design theory and applications in numerous U.S, European, and Asian locations. He has been a guest lecturer at MIT, where he assisted in the development of a graduate course in robust design for the System Design and Management program.

Mr. Creveling is the author or coauthor of several books, including Six Sigma for Technical Processes, Six Sigma for Marketing Processes, Design for Six Sigma in Technology and Product Development, Tolerance Design, and Engineering Methods for Robust Product Design. He is the editorial advisor for Prentice Hall's Six Sigma for Innovation and Growth Series.

Mr. Creveling holds a B.S. in mechanical engineering technology and an M.S. from Rochester Institute of Technology.