What Is Stream of Variation for Multistage Manufacturing Processes? | p. 1 |
History and Current Status of SoV | p. 1 |
SoV Initiation and Impact in Industry | p. 1 |
The History of SoV Methodology Development | p. 3 |
Overview of SoV Methodology | p. 5 |
Relationship of SoV Methodologies with Other Existing Methods | p. 9 |
References | p. 11 |
Basis of Matrix Theory and Multivariate Statistics | |
Basics of Matrix Theory | p. 15 |
Introduction | p. 15 |
Definitions of Vector, Matrix, and Operations | p. 15 |
Definitions | p. 15 |
Partitioned Matrices | p. 18 |
Quadratic Forms | p. 19 |
Vector Space and Geometrical Interpretations | p. 20 |
Eigenvalues and Eigenvectors of a Matrix | p. 22 |
Vector and Matrix Differentiation, Maximization, and Operators | p. 24 |
Differentiation with Vectors | p. 24 |
Matrix Inequalities and Maximization | p. 26 |
Vec Operator, Kronecker Product, and Hadamard Product | p. 27 |
Vec Operator and Kronecker Product | p. 27 |
Hadamard Product | p. 30 |
Exercises | p. 30 |
References | p. 32 |
Basics of Multivariate Statistical Analysis | p. 33 |
Introduction | p. 33 |
Multivariate Distribution and Properties | p. 33 |
Random Vectors, Cumulative Distribution Functions (CDF), and Probability Density Functions (PDF) | p. 34 |
Marginal and Conditional Distributions | p. 35 |
Population Moments | p. 37 |
Correlation Coefficients | p. 40 |
Multivariate Normal Distribution and Quadratic Forms | p. 40 |
Multivariate Normal Distribution and Its Properties | p. 43 |
Quadratic Forms | p. 44 |
Noncentral X[superscript 2] and F Distributions | p. 45 |
Sampling Theory | p. 45 |
Sample Geometry | p. 49 |
Random Samples and the Expected Values of the Sample Mean and Covariance Matrix | p. 50 |
Some Important Results of Sampling from Multivariate Normal Distributions | p. 50 |
The Wishart Distribution and Some Properties | p. 51 |
Exercises | p. 53 |
References | p. 55 |
Statistical Inferences on Mean Vectors and Linear Models | p. 57 |
Statistical Inferences on Mean Vectors | p. 57 |
Hotelling's T[superscript 2] Test | p. 57 |
Confidence Regions and Simultaneous Confidence Intervals | p. 59 |
Confidence Regions | p. 59 |
Simultaneous Confidence Intervals | p. 61 |
Inference on a Population Mean Vector with Large Sample Size | p. 63 |
Multivariate Quality Control Charts | p. 64 |
Control Charts for One Multivariate Sample | p. 64 |
Control Charts Based on Subgroup Means | p. 66 |
Multiple Linear Regression | p. 68 |
Model Description | p. 69 |
Least-Squares Estimates | p. 70 |
Inferences about the Regression Model | p. 73 |
Model Checking: Normality Checking and Outlier Detection | p. 75 |
Inferences from the Estimated Regression Model | p. 76 |
Multivariate Linear Regression | p. 78 |
Multivariate Linear Regression Model | p. 78 |
Least-Squares Estimation (LSE) and Maximum Likelihood Estimation (MLE) of Parameters | p. 79 |
Inferences for Multivariate Regression Model under Normality Assumption | p. 82 |
Predictions from Multivariate Regression | p. 83 |
Selection Method of Independent Variables | p. 85 |
Exercises | p. 86 |
References | p. 89 |
Principal Component Analysis and Factory Analysis | p. 91 |
Principal Component Analysis | p. 91 |
Mathematical Model of PCA | p. 91 |
Geometrical Interpretation | p. 95 |
Inferences on PCs | p. 96 |
Applying PCs to Process Control | p. 97 |
Factor Analysis | p. 99 |
Introduction | p. 99 |
Comparison of Factor Analysis and PCA | p. 99 |
Orthogonal Factor Model | p. 100 |
Statistical Interpretations of Factor Loadings and Communality | p. 102 |
Interpretation of Factor Loadings | p. 102 |
Interpretation of Communality | p. 102 |
Estimation of Loading Matrix | p. 103 |
Factor Rotation | p. 105 |
Factor Score | p. 109 |
General Procedures for Factor Analysis | p. 111 |
Exercises | p. 111 |
References | p. 113 |
Variation Propagation Modeling in MMP | |
State Space Modeling for Assembly Processes | p. 117 |
Introduction of Multistage Assembly Processes | p. 117 |
Variation Factors and Assumptions | p. 119 |
Station-Level Variation Factors | p. 119 |
Across-Station Variation Factors | p. 120 |
Summary and Assumptions for Modeling | p. 121 |
State Space Modeling | p. 122 |
Representation of Part Position and Its Deviation State | p. 122 |
Some Preliminary Results | p. 123 |
State Space Representation | p. 125 |
Model Validation | p. 131 |
Exercises | p. 133 |
Determination of the Deviations of a Part (Lemma 6.1) | p. 137 |
Effect of Fixture Deviation on Part Deviation (Lemma 6.2) | p. 138 |
References | p. 140 |
State Space Modeling for Machining Processes | p. 143 |
Introduction | p. 143 |
Introduction to Machining Processes and Dimensional Variation Sources | p. 143 |
Modeling of Variation Propagation in Multistage Machining Processes | p. 145 |
Model Formulation | p. 147 |
Derivation of Variation Propagation Model | p. 148 |
Basics of Kinematic Analysis of Machining Operations | p. 148 |
Representation of Workpiece Geometric Deviation | p. 152 |
Single-Stage Modeling of Dimensional Variation | p. 153 |
Analysis of Datum-Induced Error | p. 154 |
Analysis of Fixture Errors | p. 158 |
Identify the Overall Dimensional Error by Combining Error Sources Together | p. 159 |
Modeling Variation Propagation in Multistage Machining Processes | p. 161 |
Model Validation | p. 162 |
Introduction to the Experimental Machining Process | p. 162 |
Comparison between the Real Measurement and the Model Prediction | p. 164 |
Summary | p. 166 |
Exercises | p. 166 |
Appendix: The System Matrices Used in Equation 7.27 | p. 169 |
References | p. 173 |
A Factor Analysis Method for Variability Modeling | p. 175 |
Introduction | p. 175 |
A Factor Analysis Model for Process Variability | p. 176 |
Model Structure | p. 176 |
Interpretation of Variation Patterns | p. 177 |
Limitations of PCA and Factor Rotation | p. 180 |
Estimating the Number of Faults | p. 181 |
Likelihood Ratio Test | p. 181 |
AIC and MDL Information Criteria | p. 182 |
An Illustrative Example | p. 183 |
Unique Identification of Multiple Faults | p. 187 |
Estimating the Fault Geometry Vectors | p. 187 |
Identifying Subgroups | p. 189 |
Fault Interpretation and Illustrative Example | p. 190 |
Statistical Properties | p. 193 |
Summary | p. 195 |
Exercises | p. 196 |
Appendix 8.1: Discussion of the Distributions of Test Statistics | p. 196 |
References | p. 197 |
Variation Source Diagnosis | |
Diagnosability Analysis for Variation Source Identification | p. 201 |
Motivation and Formulation of Diagnosability Study | p. 201 |
Definitions of Diagnosability | p. 203 |
Criterion of Fault Diagnosability | p. 205 |
Minimal Diagnosable Class | p. 207 |
Gauging System Evaluation Based on Minimal Diagnosable Class | p. 210 |
Information Quantity | p. 210 |
Information Quality | p. 211 |
System Flexibility | p. 211 |
Case Study | p. 212 |
Case Study of A Multistage Assembly Process | p. 212 |
Case Study of A Multistage Machining Process | p. 219 |
Summary | p. 221 |
Exercises | p. 224 |
Reference | p. 226 |
Diagnosis through Variation Pattern Matching | p. 229 |
Introduction to Variation Patterns | p. 229 |
Links between the Fault-Quality Model and Variation Patterns | p. 231 |
Procedure of Pattern Matching for Variation Source Identification | p. 233 |
Disturbance due to Unstructured Noises | p. 235 |
Disturbance due to Sampling Uncertainty | p. 236 |
A Robust Pattern Matching Procedure | p. 237 |
Case Study | p. 240 |
A Machining Process and Its Variation Propagation Model | p. 240 |
Pattern Matching for Root Cause Identification in the Machining Process | p. 241 |
Summary | p. 244 |
Exercises | p. 244 |
References | p. 248 |
Estimation-Based Diagnosis | p. 249 |
LS Estimators for Variance Components | p. 249 |
Deviation LS Estimator | p. 250 |
Variation LS Estimator | p. 251 |
Other Variation LS Estimators | p. 252 |
Relationship among Variance Estimators | p. 254 |
Comparison of Variance Estimators | p. 262 |
Unbiasedness of Variance Estimators | p. 262 |
Dispersion of Variance Estimators | p. 263 |
Comparison of Variance Estimators | p. 264 |
Chapter Summary | p. 270 |
Exercises | p. 270 |
References | p. 272 |
Design for Variation Reduction | |
Optimal Sensor Placement and Distribution | p. 275 |
Introduction | p. 275 |
Design Criteria for Sensor Placement | p. 278 |
Diagnosability Index as Design Criterion | p. 278 |
Sensitivity Index As Design Criterion | p. 279 |
Single-Station Sensor Placement | p. 282 |
Optimization Formulation | p. 282 |
Exchange Algorithms from Optimal Experimental Design | p. 283 |
Fast Exchange Algorithm with Sort-and-Cut | p. 284 |
Comparison among Alternative Algorithms | p. 286 |
Results of Optimal Sensor Layout on a Single Station | p. 288 |
Multiple-Station Sensor Distribution | p. 290 |
Optimization Formulation | p. 290 |
Variation Transmissibility Ratio | p. 291 |
Detection Power on An Individual Station | p. 293 |
Optimal Strategy of Sensor Distribution | p. 296 |
Strategy of Sensor Distribution | p. 297 |
Example | p. 298 |
Summary | p. 301 |
Exercises | p. 301 |
References | p. 302 |
Design Evaluation and Process Capability Analysis | p. 305 |
Introduction | p. 305 |
Sensitivity-Based Design Evaluation | p. 307 |
Multivariate Process Capability Analysis | p. 313 |
Examples | p. 315 |
Sensitivity-Based Design Evaluation | p. 315 |
Multivariate Process Capability Analysis | p. 319 |
Exercises | p. 321 |
Appendix 13.1: System Matrices of Configuration C1 | p. 322 |
Appendix 13.2: System Matrices of Configuration C2 | p. 326 |
Appendix 13.3: System Matrices of Configuration C3 | p. 327 |
Appendix 13.4: System Matrices of Configuration C4 | p. 330 |
References | p. 331 |
Optimal Fixture Layout Design | p. 333 |
Introduction | p. 333 |
Design Criteria for Variation Reduction | p. 335 |
Data-Mining-Aided Design Algorithm | p. 338 |
Overview of the Data-Mining-Aided Design | p. 339 |
Candidate Design Space | p. 341 |
Uniform Coverage Selection | p. 342 |
Feature and Feature Function | p. 344 |
Clustering Method | p. 346 |
Classification Method | p. 347 |
Selection of K and J | p. 349 |
An Overall Description of the Data-Mining-Aided Design | p. 352 |
Example and Performance Comparison | p. 353 |
Summary | p. 356 |
Exercises | p. 356 |
References | p. 358 |
Process-Oriented Tolerance Synthesis | p. 361 |
Concept of Process-Oriented Tolerancing | p. 361 |
Framework of Process-Oriented Tolerancing | p. 362 |
Overview | p. 362 |
Variation Propagation Model | p. 363 |
Relationship between Tolerance and Variation | p. 364 |
Process Degradation Model | p. 366 |
Cost Function | p. 368 |
Optimization Formulation and Optimality | p. 368 |
Case Study for Process-Oriented Tolerancing | p. 368 |
Tolerance Allocation when Tooling Degradation Is Not Considered | p. 368 |
Tolerance Allocation Considering Tooling Degradation | p. 370 |
Integration of Process-Oriented Tolerance Synthesis and Maintenance Planning | p. 372 |
Decision Variables of Tolerance and Maintenance Design | p. 372 |
Cost Components | p. 373 |
Tolerance Cost | p. 373 |
Maintenance Cost | p. 373 |
Quality Loss Function | p. 374 |
Formulation of Optimization Problems | p. 374 |
Optimization Formulation Using a Quality Loss Function (F1) | p. 374 |
Optimization Formulation with a Quality Constraint | p. 375 |
Integrated Tolerance and Maintenance Design in BIW Assembly Processes | p. 375 |
Optimizations and Optimality for Integrated Tolerance and Maintenance Design | p. 377 |
Optimality Analysis of Optimization Formulation F1 | p. 377 |
Optimality Analysis of Optimization Formulation F2 | p. 379 |
Case Study for Integrated Tolerance and Maintenance Design | p. 380 |
Optimal Tolerance and Maintenance Design for Optimization Formulation F1 | p. 380 |
Optimal Tolerance and Maintenance Design for Optimization Formulation F2 | p. 381 |
Cost Comparison under Different Design Schemes | p. 382 |
Exercises | p. 384 |
References | p. 385 |
Quality and Reliability Integration and Advanced Topics | |
Quality and Reliability Chain Modeling and Analysis | p. 389 |
Introduction | p. 389 |
Example 1: Machining Processes | p. 391 |
Example 2: Transfer or Progressive Die-Stamping Processes | p. 392 |
QR-Chain Modeling | p. 393 |
Relationship between Component Performance and Product Quality | p. 394 |
System Component Degradation | p. 394 |
Product Quality Assessment and System Failure due to Nonconforming Products | p. 395 |
Component Catastrophic Failure and Its Induced System Catastrophic Failure | p. 396 |
System Reliability Evaluation | p. 396 |
Challenges in System Reliability Evaluation | p. 397 |
System Reliability Evaluation of MMPs | p. 397 |
Self-Improvement of Product Quality and the Upper Bound of System Reliability | p. 400 |
Implementation of QR-Chain Modeling and Analysis in Body-in-White Assembly Processes | p. 401 |
QR-Chain in Multistation BIW Assembly Processes | p. 402 |
QR-Chain Model of a BIW Assembly Process | p. 402 |
Locating-Pin Degradation Model | p. 403 |
Relationship between Process Variables and Deviations of Quality Characteristics | p. 404 |
Product Quality Assessment and Pin Catastrophic Failure | p. 407 |
System Reliability Evaluation | p. 408 |
Case Study | p. 408 |
Exercises | p. 410 |
Appendix 16.1: Derivation of Equation 16.4 | p. 410 |
Appendix 16.2: Proof of Result 16.1 | p. 412 |
Appendix 16.3: Derivation of Equation 16.10 | p. 413 |
Appendix 16.4: Proof of Lemma 16.1 | p. 414 |
Appendix 16.5: Proof of Result 16.4 | p. 415 |
Appendix 16.6: Distribution of Random Variable [xi](tk) | p. 415 |
References | p. 416 |
Quality-Oriented Maintenance for Multiple Interactive System Components | p. 419 |
Quality-Oriented Maintenance Model | p. 419 |
Multicomponent Maintenance Policies | p. 422 |
Simple Block Resetting (Replacement) | p. 422 |
Modified Block Resetting | p. 425 |
Age Resetting | p. 427 |
Further Discussion on Solutions of Optimization Problems | p. 429 |
Optimal Solutions of SBR Policy | p. 430 |
Optimal Solutions of Modified Block Resetting Policy | p. 432 |
Case Study | p. 432 |
Exercises | p. 436 |
Appendix 17.1: Proof of Lemma 17.7 | p. 437 |
References | p. 438 |
Additional Topics on Stream of Variation | p. 439 |
SoV Modeling for Multistation Assembly Process of Compliant Parts | p. 439 |
Introduction | p. 439 |
SoV Modeling of Compliant Parts in an MMP | p. 440 |
Single Station Assembly Modeling | p. 441 |
Multistation Assembly Modeling | p. 442 |
Additional Comments | p. 444 |
SoV Modeling for Serial-Parallel Multistage Manufacturing Systems | p. 445 |
Introduction | p. 445 |
SoV Modeling for Serial-Parallel MMPs | p. 446 |
State Space Modeling for Multiple SoVs in an SP-MMP | p. 446 |
Model Dimension Reduction | p. 448 |
Additional Comments | p. 449 |
SoV-Based Quality-Ensured Setup Planning | p. 449 |
Introduction | p. 449 |
Quality-Ensured Setup Planning Methodologies | p. 450 |
Variation Propagation Modeling for Setup Planning | p. 450 |
Optimization Formulation | p. 451 |
Additional Comments | p. 452 |
Active Control for Variation Reduction of Multistage Manufacturing Processes | p. 453 |
Introduction | p. 453 |
Active Control for Variation Reduction of MMP | p. 454 |
Additional Comments | p. 456 |
References | p. 457 |
Index | p. 459 |
Related Titles | p. 469 |
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