Stream of Variation Modeling And Analysis for Multistage Manufacturing Processes

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ISBN: 9780849321511 | 0849321514
Cover: Hardcover
Copyright: 12/4/2006

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Variability arises in multistage manufacturing processes (MMPs) from a variety of sources. Variation reduction demands data fusion from product/process design, manufacturing process data, and quality measurement. Statistical process control (SPC), with a focus on quality data alone, only tells half of the story and is a passive method, taking corrective action only after variations occur. Learn how the Stream of Variation (SoV) methodology helps reduce or even eliminate variations throughout the entire MMP in Jianjun Shi's Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes.The unified methodology outlined in this book addresses all aspects of variation reduction in a MMP, which consists of state space modeling, design analysis and synthesis, engineering-driven statistical methods for process monitoring and root-cause diagnosis, and quick failure recovery and defect prevention. Coverage falls into five sections, beginning with a review of matrix theory and multivariate statistics followed by variation propagation modeling with applications in assembly and machining processes. The third section focuses on diagnosing the sources of variation while the fourth section explains design methods to reduce variability. The final section assembles advanced SoV-related topics and the integration of quality and reliability.Introducing a powerful and industry-proven method, this book fuses statistical knowledge with the engineering knowledge of product quality and unifies the design of processes and products to achieve more predictable and reliable manufacturing processes.

Chapter 1 What Is Stream of Variation for Multistage Manufacturing Processes?

(14)

1.1 History and Current Status of SoV

(4)

1.1.1 SoV Initiation and Impact in Industry

(2)

1.1.2 The History of SoV Methodology Development

(2)

1.2 Overview of SoV Methodology

(4)

1.3 Relationship of SoV Methodologies with Other Existing Methods

(2)

References

(4)

PART I Basis of Matrix Theory and Multivariate Statistics

Chapter 2 Basics of Matrix Theory

(18)

2.1 Introduction

(1)

2.2 Definitions of Vector, Matrix, and Operations

(4)

2.2.1 Definitions

(3)

2.2.2 Partitioned Matrices

(1)

2.3 Quadratic Forms

(1)

2.4 Vector Space and Geometrical Interpretations

(2)

2.5 Eigenvalues and Eigenvectors of a Matrix

(2)

2.6 Vector and Matrix Differentiation, Maximization, and Operators

(6)

2.6.1 Differentiation with Vectors

(2)

2.6.2 Matrix Inequalities and Maximization

(1)

2.6.3 Vec Operator, Kronecker Product, and Hadamard Product

(6)

2.6.3.1 Vec Operator and Kronecker Product

(3)

2.6.3.2 Hadamard Product

(1)

2.7 Exercises

(2)

References

(1)

Chapter 3 Basics of Multivariate Statistical Analysis

(24)

3.1 Introduction

(1)

3.2 Multivariate Distribution and Properties

(7)

3.2.1 Random Vectors, Cumulative Distribution Functions (CDF), and Probability Density Functions (PDF)

(1)

3.2.2 Marginal and Conditional Distributions

(2)

3.2.3 Population Moments

(3)

3.2.4 Correlation Coefficients

(1)

3.3 Multivariate Normal Distribution and Quadratic Forms

(5)

3.3.1 Multivariate Normal Distribution and Its Properties

(1)

3.3.2 Quadratic Forms

(1)

3.3.3 Noncentral x² and F Distributions

(1)

3.4 Sampling Theory

(6)

3.4.1 Sample Geometry

(1)

3.4.2 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix

(1)

3.4.3 Some Important Results of Sampling from Multivariate Normal Distributions

(1)

3.5 The Wishart Distribution and Some Properties

(2)

3.6 Exercises

(2)

References

(2)

Chapter 4 Statistical Inferences on Mean Vectors and Linear Models

(34)

4.1 Statistical Inferences on Mean Vectors

(11)

4.1.1 Hotelling's T² Test

(2)

4.1.2 Confidence Regions and Simultaneous Confidence Intervals

(4)

4.1.2.1 Confidence Regions

(2)

4.1.2.2 Simultaneous Confidence Intervals

(2)

4.1.3 Inference on a Population Mean Vector with Large Sample Size

(1)

4.1.4 Multivariate Quality Control Charts

(4)

4.1.4.1 Control Charts for One Multivariate Sample

(2)

4.1.4.2 Control Charts Based on Subgroup Means

(2)

4.2 Multiple Linear Regression

(18)

4.2.1 Model Description

(1)

4.2.2 Least-Squares Estimates

(3)

4.2.3 Inferences about the Regression Model

(2)

4.2.4 Model Checking: Normality Checking and Outlier Detection

(1)

4.2.5 Inferences from the Estimated Regression Model

(2)

4.2.6 Multivariate Linear Regression

(13)

4.2.6.1 Multivariate Linear Regression Model

(1)

4.2.6.2 Least-Squares Estimation (LSE) and Maximum Likelihood Estimation (MLE) of Parameters

(3)

4.2.6.3 Inferences for Multivariate Regression Model under Normality Assumption

(1)

4.2.6.4 Predictions from Multivariate Regression

(2)

4.2.6.5 Selection Method of Independent Variables

(1)

4.3 Exercises

(3)

References

(2)

Chapter 5 Principal Component Analysis and Factory Analysis

(26)

5.1 Principal Component Analysis

(8)

5.1.1 Mathematical Model of PCA

(4)

5.1.2 Geometrical Interpretation

(1)

5.1.3 Inferences on PCs

(1)

5.1.4 Applying PCs to Process Control

(2)

5.2 Factor Analysis

(12)

5.2.1 Introduction

(1)

5.2.2 Comparison of Factor Analysis and PCA

(1)

5.2.3 Orthogonal Factor Model

100

(2)

5.2.4 Statistical Interpretations of Factor Loadings and Communality

102

(1)

5.2.4.1 Interpretation of Factor Loadings

102

(1)

5.2.4.2 Interpretation of Communality

102

(1)

5.2.5 Estimation of Loading Matrix

103

(2)

5.2.6 Factor Rotation

105

(4)

5.2.7 Factor Score

109

(2)

5.2.8 General Procedures for Factor Analysis

111

(1)

5.3 Exercises

111

(2)

References

113

(4)

PART II Variation Propagation Modeling in MMP

Chapter 6 State Space Modeling for Assembly Processes

117

(26)

6.1 Introduction of Multistage Assembly Processes

117

(2)

6.2 Variation Factors and Assumptions

119

(3)

6.2.1 Station-Level Variation Factors

119

(1)

6.2.2 Across-Station Variation Factors

120

(1)

6.2.3 Summary and Assumptions for Modeling

121

(1)

6.3 State Space Modeling

122

(9)

6.3.1 Representation of Part Position and Its Deviation State

122

(1)

6.3.2 Some Preliminary Results

123

(2)

6.3.3 State Space Representation

125

(6)

6.4 Model Validation

131

(2)

6.5 Exercises

133

(4)

Appendix 6.1: Determination of the Deviations of a Part (Lemma 6.1)

137

(1)

Appendix 6.2: Effect of Fixture Deviation on Part Deviation (Lemma 6.2)

138

(2)

References

140

(3)

Chapter 7 State Space Modeling for Machining Processes

143

(32)

7.1 Introduction

143

(5)

7.1.1 Introduction to Machining Processes and Dimensional Variation Sources

143

(2)

7.1.2 Modeling of Variation Propagation in Multistage Machining Processes

145

(2)

7.1.3 Model Formulation

147

(1)

7.2 Derivation of Variation Propagation Model

148

(14)

7.2.1 Basics of Kinematic Analysis of Machining Operations

148

(4)

7.2.2 Representation of Workpiece Geometric Deviation

152

(1)

7.2.3 Single-Stage Modeling of Dimensional Variation

153

(9)

7.2.3.1 Analysis of Datum-Induced Error

154

(4)

7.2.3.2 Analysis of Fixture Errors

158

(1)

7.2.3.3 Identify the Overall Dimensional Error by Combining Error Sources Together

159

(2)

7.2.3.4 Modeling Variation Propagation in Multistage Machining Processes

161

(1)

7.3 Model Validation

162

(4)

7.3.1 Introduction to the Experimental Machining Process

162

(2)

7.3.2 Comparison between the Real Measurement and the Model Prediction

164

(2)

7.4 Summary

166

(1)

7.5 Exercises

166

(3)

7.6 Appendix: The System Matrices Used in Equation 7.27

169

(4)

References

173

(2)

Chapter 8 A Factor Analysis Method for Variability Modeling

175

(26)

8.1 Introduction

175

(1)

8.2 A Factor Analysis Model for Process Variability

176

(4)

8.2.1 Model Structure

176

(1)

8.2.2 Interpretation of Variation Patterns

177

(3)

8.3 Limitations of PCA and Factor Rotation

180

(1)

8.4 Estimating the Number of Faults

181

(6)

8.4.1 Likelihood Ratio Test

181

(1)

8.4.2 AIC and MDL Information Criteria

182

(1)

8.4.3 An Illustrative Example

183

(4)

8.5 Unique Identification of Multiple Faults

187

(6)

8.5.1 Estimating the Fault Geometry Vectors

187

(2)

8.5.2 Identifying Subgroups

189

(1)

8.5.3 Fault Interpretation and Illustrative Example

190

(3)

8.6 Statistical Properties

193

(2)

8.7 Summary

195

(1)

8.8 Exercises

196

(1)

8.9 Appendix 8.1: Discussion of the Distributions of Test Statistics

196

(1)

References

197

(4)

PART III Variation Source Diagnosis

Chapter 9 Diagnosability Analysis for Variation Source Identification

201

(28)

9.1 Motivation and Formulation of Diagnosability Study

201

(2)

9.2 Definitions of Diagnosability

203

(2)

9.3 Criterion of Fault Diagnosability

205

(2)

9.4 Minimal Diagnosable Class

207

(3)

9.5 Gauging System Evaluation Based on Minimal Diagnosable Class

210

(2)

9.5.1 Information Quantity

210

(1)

9.5.2 Information Quality

211

(1)

9.5.3 System Flexibility

211

(1)

9.6 Case Study

212

(9)

9.6.1 Case Study of A Multistage Assembly Process

212

(7)

9.6.2 Case Study of A Multistage Machining Process

219

(2)

9.7 Summary

221

(3)

9.8 Exercises

224

(2)

Reference

226

(3)

Chapter 10 Diagnosis through Variation Pattern Matching

229

(20)

10.1 Introduction to Variation Patterns

229

(2)

10.2 Links between the Fault-Quality Model and Variation Patterns

231

(2)

10.3 Procedure of Pattern Matching for Variation Source Identification

233

(7)

10.3.1 Disturbance due to Unstructured Noises

235

(1)

10.3.2 Disturbance due to Sampling Uncertainty

236

(1)

10.3.3 A Robust Pattern Matching Procedure

237

(3)

10.4 Case Study

240

(4)

10.4.1 A Machining Process and Its Variation Propagation Model

240

(1)

10.4.2 Pattern Matching for Root Cause Identification in the Machining Process

241

(3)

10.5 Summary

244

(1)

10.6 Exercises

244

(4)

References

248

(1)

Chapter 11 Estimation-Based Diagnosis

249

(26)

11.1 LS Estimators for Variance Components

249

(5)

11.1.1 Deviation LS Estimator

250

(1)

11.1.2 Variation LS Estimator

251

(1)

11.1.3 Other Variation LS Estimators

252

(2)

11.2 Relationship among Variance Estimators

254

(8)

11.3 Comparison of Variance Estimators

262

(8)

11.3.1 Unbiasedness of Variance Estimators

262

(1)

11.3.2 Dispersion of Variance Estimators

263

(1)

11.3.3 Comparison of Variance Estimators

264

(6)

11.4 Chapter Summary

270

(1)

11.5 Exercises

270

(2)

References

272

(3)

PART IV Design for Variation Reduction

Chapter 12 Optimal Sensor Placement and Distribution

275

(30)

12.1 Introduction

275

(3)

12.2 Design Criteria for Sensor Placement

278

(4)

12.2.1 Diagnosability Index as Design Criterion

278

(1)

12.2.2 Sensitivity Index As Design Criterion

279

(3)

12.3 Single-Station Sensor Placement

282

(8)

12.3.1 Optimization Formulation

282

(1)

12.3.2 Exchange Algorithms from Optimal Experimental Design

283

(1)

12.3.3 Fast Exchange Algorithm with Sort-and-Cut

284

(2)

12.3.4 Comparison among Alternative Algorithms

286

(2)

12.3.5 Results of Optimal Sensor Layout on a Single Station

288

(2)

12.4 Multiple-Station Sensor Distribution

290

(11)

12.4.1 Optimization Formulation

290

(1)

12.4.2 Variation Transmissibility Ratio

291

(2)

12.4.3 Detection Power on An Individual Station

293

(3)

12.4.4 Optimal Strategy of Sensor Distribution

296

(2)

12.4.4.1 Strategy of Sensor Distribution

297

(1)

12.4.5 Example

298

(3)

12.5 Summary

301

(1)

12.6 Exercises

301

(1)

References

302

(3)

Chapter 13 Design Evaluation and Process Capability Analysis

305

(28)

13.1 Introduction

305

(2)

13.2 Sensitivity-Based Design Evaluation

307

(6)

13.3 Multivariate Process Capability Analysis

313

(2)

13.4 Examples

315

(6)

13.4.1 Sensitivity-Based Design Evaluation

315

(4)

13.4.2 Multivariate Process Capability Analysis

319

(2)

13.5 Exercises

321

(1)

13.6 Appendix 13.1: System Matrices of Configuration C1

322

(4)

13.7 Appendix 13.2: System Matrices of Configuration C2

326

(1)

13.8 Appendix 13.3: System Matrices of Configuration C3

327

(3)

13.9 Appendix 13.4: System Matrices of Configuration C4

330

(1)

References

331

(2)

Chapter 14 Optimal Fixture Layout Design

333

(28)

14.1 Introduction

333

(2)

14.2 Design Criteria for Variation Reduction

335

(3)

14.3 Data-Mining-Aided Design Algorithm

338

(15)

14.3.1 Overview of the Data-Mining-Aided Design

339

(2)

14.3.2 Candidate Design Space

341

(1)

14.3.3 Uniform Coverage Selection

342

(2)

14.3.4 Feature and Feature Function

344

(2)

14.3.5 Clustering Method

346

(1)

14.3.6 Classification Method

347

(2)

14.3.7 Selection of K and J

349

(3)

14.3.8 An Overall Description of the Data-Mining-Aided Design

352

(1)

14.4 Example and Performance Comparison

353

(3)

14.5 Summary

356

(1)

14.6 Exercises

356

(2)

References

358

(3)

Chapter 15 Process-Oriented Tolerance Synthesis

361

(28)

15.1 Concept of Process-Oriented Tolerancing

361

(1)

15.2 Framework of Process-Oriented Tolerancing

362

(6)

15.2.1 Overview

362

(1)

15.2.2 Variation Propagation Model

363

(1)

15.2.3 Relationship between Tolerance and Variation

364

(2)

15.2.4 Process Degradation Model

366

(2)

15.2.5 Cost Function

368

(1)

15.2.6 Optimization Formulation and Optimality

368

(1)

15.3 Case Study for Process-Oriented Tolerancing

368

(4)

15.3.1 Tolerance Allocation when Tooling Degradation Is Not Considered

368

(2)

15.3.2 Tolerance Allocation Considering Tooling Degradation

370

(2)

15.4 Integration of Process-Oriented Tolerance Synthesis and Maintenance Planning

372

(3)

15.4.1 Decision Variables of Tolerance and Maintenance Design

372

(1)

15.4.2 Cost Components

373

(1)

15.4.2.1 Tolerance Cost

373

(1)

15.4.2.2 Maintenance Cost

373

(1)

15.4.2.3 Quality Loss Function

374

(1)

15.4.3 Formulation of Optimization Problems

374

(3)

15.4.3.1 Optimization Formulation Using a Quality Loss Function (F1)

374

(1)

15.4.3.2 Optimization Formulation with a Quality Constraint

375

(1)

15.5 Integrated Tolerance and Maintenance Design in BIW Assembly Processes

375

(2)

15.6 Optimizations and Optimality for Integrated Tolerance and Maintenance Design

377

(3)

15.6.1 Optimality Analysis of Optimization Formulation Fl

377

(2)

15.6.2 Optimality Analysis of Optimization Formulation F2

379

(1)

15.7 Case Study for Integrated Tolerance and Maintenance Design

380

(4)

15.7.1 Optimal Tolerance and Maintenance Design for Optimization Formulation F1

380

(1)

15.7.2 Optimal Tolerance and Maintenance Design for Optimization Formulation F2

381

(1)

15.7.3 Cost Comparison under Different Design Schemes

382

(2)

15.8 Exercises

384

(1)

References

385

(4)

PART V Quality and Reliability Integration and Advanced Topics

Chapter 16 Quality and Reliability Chain Modeling and Analysis

389

(30)

16.1 Introduction

389

(4)

16.1.1 Example 1: Machining Processes

391

(1)

16.1.2 Example 2: Transfer or Progressive Die-Stamping Processes

392

(1)

16.2 QR-Chain Modeling

393

(3)

16.2.1 Relationship between Component Performance and Product Quality

394

(1)

16.2.2 System Component Degradation

394

(1)

16.2.3 Product Quality Assessment and System Failure due to Nonconforming Products

395

(1)

16.2.4 Component Catastrophic Failure and Its Induced System Catastrophic Failure

396

(1)

16.3 System Reliability Evaluation

396

(5)

16.3.1 Challenges in System Reliability Evaluation

397

(1)

16.3.2 System Reliability Evaluation of MMPs

397

(3)

16.3.3 Self-Improvement of Product Quality and the Upper Bound of System Reliability

400

(1)

16.4 Implementation of QR-Chain Modeling and Analysis in Body-in-White Assembly Processes

401

(9)

16.4.1 QR-Chain in Multistation BIW Assembly Processes

402

(1)

16.4.2 QR-Chain Model of a BIW Assembly Process

402

(6)

16.4.2.1 Locating-Pin Degradation Model

403

(1)

16.4.2.2 Relationship between Process Variables and Deviations of Quality Characteristics

404

(3)

16.4.2.3 Product Quality Assessment and Pin Catastrophic Failure

407

(1)

16.4.2.4 System Reliability Evaluation

408

(1)

16.4.3 Case Study

408

(2)

16.5 Exercises

410

(1)

16.6 Appendix 16.1: Derivation of Equation 16.4

410

(2)

16.7 Appendix 16.2: Proof of Result 16.1

412

(1)

16.8 Appendix 16.3: Derivation of Equation 16.10

413

(1)

16.9 Appendix 16.4: Proof of Lemma 16.1

414

(1)

16.10 Appendix 16.5: Proof of Result 16.4

415

(1)

16.11 Appendix 16.6: Distribution of Random Variable ξ(tk)

415

(1)

References

416

(3)

Chapter 17 Quality-Oriented Maintenance for Multiple Interactive System Components

419

(20)

17.1 Quality-Oriented Maintenance Model

419

(3)

17.2 Multicomponent Maintenance Policies

422

(7)

17.2.1 Simple Block Resetting (Replacement)

422

(3)

17.2.2 Modified Block Resetting

425

(2)

17.2.3 Age Resetting

427

(2)

17.3 Further Discussion on Solutions of Optimization Problems

429

(3)

17.3.1 Optimal Solutions of SBR Policy

430

(2)

17.3.2 Optimal Solutions of Modified Block Resetting Policy

432

(1)

17.4 Case Study

432

(4)

17.5 Exercises

436

(1)

17.6 Appendix 17.1: Proof of Lemma 17.7

437

(1)

References

438

(1)

Chapter 18 Additional Topics on Stream of Variation

439

(20)

18.1 SoV Modeling for Multistation Assembly Process of Compliant Parts

439

(6)

18.1.1 Introduction

439

(1)

18.1.2 SoV Modeling of Compliant Parts in an MMP

440

(4)

18.1.2.1 Single Station Assembly Modeling

441

(1)

18.1.2.2 Multistation Assembly Modeling

442

(2)

18.1.3 Additional Comments

444

(1)

18.2 SoV Modeling for Serial-Parallel Multistage Manufacturing Systems

445

(4)

18.2.1 Introduction

445

(1)

18.2.2 SoV Modeling for Serial-Parallel MMPs

446

(3)

18.2.2.1 State Space Modeling for Multiple SoVs in an SP-MMP

446

(2)

18.2.2.2 Model Dimension Reduction

448

(1)

18.2.3 Additional Comments

449

(1)

18.3 SoV-Based Quality-Ensured Setup Planning

449

(4)

18.3.1 Introduction

449

(1)

18.3.2 Quality-Ensured Setup Planning Methodologies

450

(2)

18.3.2.1 Variation Propagation Modeling for Setup Planning

450

(1)

18.3.2.2 Optimization Formulation

451

(1)

18.3.3 Additional Comments

452

(1)

18.4 Active Control for Variation Reduction of Multistage Manufacturing Processes

453

(4)

18.4.1 Introduction

453

(1)

18.4.2 Active Control for Variation Reduction of MMP

454

(2)

18.4.3 Additional Comments

456

(1)

References

457

(2)

Index

459

(10)

Related Titles

469

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Stream of Variation Modeling And Analysis for Multistage Manufacturing Processes

Summary

Table of Contents

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