Quality improvement with design of experiments: a response surface approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2001
|
| Series: | Topics in safety, reliability and quality
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 505 S. graph. Darst. |
| ISBN: | 0792368274 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quality improvement with design of experiments |b a response surface approach |c by Ivan N. Vuchkov and Lidia N. Boyadjieva |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 2001 | |
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Record in the Search Index
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| adam_text | CONTENTS
1. INTRODUCTION TO QUALITY IMPROVEMENT 1
1.1. Why do deviations occur? 1
1.2. Random variations 2
1.3. On line and off line quality control 4
1.4. Performance characteristics, product parameters and noises 7
1.5. Design of experiments and data analysis 8
1.6. Model based robust engineering design 12
2. STATISTICAL METHODS FOR DATA ANALYSIS 14
2.1. Analysis of variance 15
2.1.1. ONE WAY CLASSIFICATION 15
Main results 15
Simplified formulae 18
Computational procedure 19
2.1.2. ANOVA: MULTIPLE CLASSIFICATION 22
2.2. Introduction to design of experiments 31
2.2.1. PROBLEM FORMULATION 31
2 2.2. COMPLETELY RANDOMIZED DESIGNS 31
2.2.3 RANDOMIZED BLOCK DESIGNS 32
2.2.4. LATIN SQUARES 34
2 2.5 GRAEKO LATIN AND HYPER GRAEKO LATIN SQUARES 36
2 2 6. OTHER DESIGNS 38
2.3. Regression analysis 39
2.3.1. DEFINING THE PROBLEM 39
2.3 2 FACTORS AND REGIONS OF INTEREST 40
2 3.3 REGRESSION MODELS 42
2.3 4 ASSUMPTIONS OF LINEAR REGRESSION ANALYSIS 44
23 5 LEAST SQUARES METHOD 45
2 3 6 CONFIDENCE INTERVALS AND SIGNIFICANCE OF
REGRESSION COEFFICIENTS 53
2.3.7. LACK OF FIT TESTS 56
Defining the problem 56
Analysis of variance for testing model adequacy 57
Lack of fit tests based on repeated observations 59
Multiple correlation coefficient 61
2.3.8. STEPWISE REGRESSION AND ALL POSSIBLE REGRESSIONS 66
2.3.9. GRAPHICAL TOOLS FOR RESIDUAL ANALYSIS 73
viii
Introduction 73
Residual plots 74
Normal and half normal plots 77
2.3.10. TRANSFORMATIONS OF VARIABLES 80
2.3.11 WEIGHTED LEAST SQUARES 82
2.4. Bibliography 84
Appendix A.2.1. Basic equation of the analysis of variance 84
Appendix A.2.2. Derivation of the simplified formulae (2.10) and (2.11) 85
Appendix A.2.3. Basic properties of least squares estimates 86
Appendix A.2.4. Sums of squares for tests for lack of fit 88
Appendix A. 2.5. Properties of the residuals 90
3. DESIGN OF REGRESSION EXPERIMENTS 96
3.1. Introduction 96
3.2. Variance optimality of response surface designs 98
3.3. Two level full factorial designs 106
3.3.1. DEFINITIONS AND CONSTRUCTION 106
3 3 2. PROPERTIES OF TWO LEVEL FULL FACTORIAL DESIGNS 109
3 3 3 REGRESSION ANALYSIS OF DATA OBTAINED THROUGH
TWO LEVEL FULL FACTORIAL DESIGNS 113
Parameter estimation 113
Effects of factors and interactions 116
Statistical analysis of individual effects and test for lack of fit 118
3.4. Two level fractional factorial designs 123
3.4.1. CONSTRUCTION OF FRACTIONAL FACTORIAL DESIGNS 123
3 4 2. FITTING EQUATIONS TO DATA OBTAINED BY FRACTIONAL
FACTORIAL DESIGNS 130
3.5. Blocking 133
3.6. Steepest ascent 135
3.7. Second order designs 142
3.7.1. INTRODUCTION 142
3 72 COMPOSITE DESIGNS 144
Rotatable central composite designs 145
D optimal composite designs 146
Hartley s designs 146
3 73 OTHER THREE LEVEL SECOND ORDER DESIGNS 147
3 7 4 STATISTICAL ANALYSIS OF DATA OBTAINED THROUGH
SYMMETRIC SECOND ORDER DESIGNS 148
3.8. Sequential generation of D optimal designs 153
3 8 1 PROCEDURES FOR SEQUENTIAL GENERATION OF
D OPTIMAL DESIGNS 153
3 82 ASYMMETRICAL SECOND ORDER D OPTIMAL DESIGNS 156
3 83 SYMMETRICAL SECOND ORDER D OPTIMAL DESIGNS 158
3.9. Dependence of the variance optimal designs on the assumptions
ix
about the model and the region of interest 159
3.9.1. MODEL DEPENDENCE 159
3.9.2 DEPENDENCE ON THE SIZE AND SHAPE OF THE REGION
OF INTEREST 162
3.10. Interpreting models 168
3.10.1. OPTIMIZATION PROCEDURES AND GRAPHICAL TOOLS FOR
MODEL INTERPRETATION 168
3.10.2 CANONICAL REPRESENTATION OF SECOND ORDER MODELS 175
3 10 3 CONFIDENCE REGION ON THE LOCATION OF THE
STATIONARY POINT 182
3.11. Bibliography 184
Appendix A3.1. Proof of formula (3.24) 184
Appendix A3.2. Sequential generation ofD optimal designs 185
Appendix A3.3. Derivation of canonical form B 186
Appendix A3.4. Covariance matrix of S = b + 2Bx 188
4. TAGUCHPS APPROACH TO QUALITY IMPROVEMENT 190
4.1. Introduction 190
4.2. Loss function 190
4.3. Stages of product design 193
4.4. Parameter design 194
4.5. Orthogonal arrays 196
4.6. Split plot designs 200
4.7. Linear graphs 201
4.8. Signal to noise ratio 202
4.9. Data analysis and decision making 204
4.10. Some practical problems 210
4 10 1 CHOICE OF EXPERIMENTAL CONDITION AND FACTOR
LEVELS 210
4.10.2. REPEATED OBSERVATIONS 21 1
4 10 3 CONFIRMATORY EXPERIMENTS 212
4.10.4. COMPUTER SIMULATIONS 212
4.11. Tolerance design 212
4.12. Taguchi method: summary 213
4.13. Advantages and disadvantages of the Taguchi method 213
4.14. Examples 216
4.15. Bibliography 233
Appendix A 4 1. Loss function 235
Appendix A 4.2. Expected loss 235
5. QUALITY IMPROVEMENT THROUGH REDUCTION OF THE
ERRORS TRANSMITTED FROM THE FACTORS TO
THE RESPONSE 237
X
5.1. Transmission of errors from product parameters to the response 237
5.2. Models of the mean value and the variance in mass production 238
5.2.1. DEFINING THE PROBLEM 238
5.2.2. MODELS OF MEAN VALUE AND VARIANCE FOR A PRODUCT
WITH TWO PARAMETERS 239
5.2.3. GENERALIZATIONS 243
Models of mean value and variance in mass production based on second and
third order polynomials 243
Models of the mean value and the variance in matrix notations 247
5.3. Estimation of noise distribution parameters 251
5.3.1. ESTIMATION OF ERROR DISTRIBUTION MOMENTS THROUGH
OBSERVATIONS 250
5.3.2. VARIANCE ESTIMATION USING TOLERANCE INTERVALS 254
5.4. Further generalizations 256
5.5. Accuracy of the predicted mean value and variance in mass
production 260
5.5.1. INFLUENCE OF THE REGRESSION MODEL STRUCTURE 260
5.5.2. INFLUENCE OF HIGH ORDER ERROR DISTRIBUTION MOMENTS
AND HIGH ORDER TERMS ON THE VARIANCE MODEL 262
5.5 3. INFLUENCE OF THE INACCURACY OF ESTIMATION 265
5.6. Bibliography 275
Appendix A.5.1. Derivation of mean value and variance models for second
order polynomials with m factors 275
Appendix A.5.2. Unbiased estimation of variance in mass production 280
Appendix A.5.3. Derivation of matrix ¥ for a full second order polynomial
model 283
6. OPTIMIZATION PROCEDURES FOR ROBUST DESIGN OF
PRODUCTS AND PROCESSES WITH ERRORS IN THE FACTORS 287
6.1. Introduction 287
6.2. Optimality criteria for robust process and product design 288
6 2 1. LOSS FUNCTION MINIMIZATION 288
6 2 2. CONDITIONAL MINIMIZATION OF THE VARIANCE 290
6 2 3. MAXIMIZATION OF SIGNAL TO NOISE RATIO 291
6.3. Robustness against errors in product parameters: the larger the better
and the smaller the better cases 292
6 3 1. DEFINING THE PROBLEM 292
6 3 2. A SIMPLE CASE: SINGLE PARAMETER PRODUCT 294
63 3 MULTIVARIABLE ANALYTICAL SOLUTION 297
6.4. Model based product design in cases when a specific target value
is best 300
6 4 1 ANALYTICAL SOLUTION FOR SECOND REGRESSION MODELS 300
6 4 2. A SPECIAL CASE: ERROR FREE PRODUCT PARAMETERS 305
6.5. Model based decision making in quality improvement 311
6.5.1. PRODUCTS WITH SEVERAL PERFORMANCE
xi
CHARACTERISTICS 311
6.5.2. USE OF NUMERICAL OPTIMIZATION PROCEDURES 315
6.5.3. PRACTICAL PROBLEMS 318
6.6. Model based tolerance design 325
6.7. Summary of the model based approach to quality
improvement through reduction of the transmitted error 328
6.8. Friction welding example 328
6.9. Bibliography 338
Appendix A.6.1. Development of the algorithm of subsection 6.4.1 338
Appendix A.6.2. Development of the algorithm of subsection 6.4.2 342
7. ROBUSTNESS AGAINST BOTH ERRORS IN PRODUCT
PARAMETERS AND EXTERNAL NOISE FACTORS 344
7.1. Introduction 344
7.2. Design of experiments 346
7.3. Model building 349
7.3.1. MODELS OF MEAN VALUE AND VARIANCE IN MASS
PRODUCTION BASED ON SECOND ORDER MODELS 349
7 3.2. MODELS WITH ERROR FREE PRODUCT PARAMETERS 352
7 3.3. GENERAL SECOND ORDER MODELS REVISITED 363
7.4. Optimization procedures 367
7.4.1 PROBLEM FORMULATION 367
7 4.2. OPTIMIZATION BY LAGRANGE MULTIPLIERS 369
Introduction 369
Unconstrained optimization by Lagrange multipliers 369
Constrained optimization by Lagrange multipliers in a spherical region
of interest 374
7.4.3. NUMERICAL OPTIMIZATION PROCEDURES 375
7.5. Bibliography 380
Appendix A.7.1. Development of models for mean value and variance with both
errors in product parameters and external noise factors 381
Appendix A.7.2. Derivation of algorithm for unconstrained optimization by
Lagrange multipliers 385
8. QUALITY IMPROVEMENT THROUGH MECHANISTIC MODELS 388
8.1. Introduction 388
8.2. Computing performance characteristic s mean value and
variance using mechanistic models 390
82 1 CASE WITH ERRORS ONLY IN PRODUCT PARAMETERS 390
8 2 2 PERFORMANCE CHARACTERISTIC S VARIATIONS DUE
TO BOTH ERRORS IN FACTORS AND EXTERNAL NOISES 397
8.3. Mixed models for mean value and variance 399
8.4. Response surface approach based on polynomial approximations 404
8.5. Other methods for quality improvement based on mechanistic
xii
models 408
8.5.1. USING COMBINED ARRAYS AND OPTIMIZING LOSS
STATISTICS VIA MODELLING THE UNDERLYING RESPONSE 408
8.5.2. MONTE CARLO EXPERIMENTS 409
8.5.3. USE OF TAGUCHI METHOD WITH MECHANISTIC MODELS 409
8.6. Specific problems of quality improvement based on
mechanistic models 409
8.7. Bibliography 412
Appendix A.8.1. Derivation of formulae (8.4) and (8.6) 412
Appendix A. 8.2. Development of formulae (8.11) and (8.12) 416
Appendix A.8.3. Derivation of mean and variance models for third order
polynomials 419
9. QUALITY IMPROVEMENT OF PRODUCTS DEPENDING ON
BOTH QUALITATIVE AND QUANTITATIVE FACTORS 422
9.1. Introduction 422
9.2. Models of performance characteristics depending on both
qualitative and quantitative factors 423
9.2.1. DUMMY VARIABLES 423
9.2.2. REGRESSION MODELS WITH BOTH QUALITATIVE AND
QUANTITATIVE FACTORS 423
Models without external noise factors 424
Models with external noise factors 427
9.3. Design and analysis of experiments with both qualitative and
quantitative factors 430
9.4. Models of mean value and variance in mass production and
use of the product 431
9.5. Optimization procedures 433
9.5.1. INTRODUCTION 433
9 5 2. ANALYTICAL SOLUTIONS OF THE OPTIMIZATION PROBLEM
IN CASES WHEN ONLY THE ERRORS IN PRODUCT
PARAMETERS ARE TAKEN INTO ACCOUNT 433
The smaller the better and the larger the better cases 433
A specific target value is best 434
9.6. Other optimization problems 435
9.7. Examples 436
9.8. Bibliography 452
10. OTHER METHODS FOR MODEL BASED QUALITY
IMPROVEMENT 453
10 1. Introduction 453
10.2. Model building based on replicated observations 454
10.2.1. PROBLEM STATEMENT 454
10 2 2 REGRESSION MODELS FOR THE MEAN VALUE
xiii
AND VARIANCE 454
10.2.3. VARIANCE ESTIMATES BASED ON RESIDUALS 456
10.2.4. GRAPHICAL TOOLS FOR STUDYING LOCATION AND
DISPERSSION EFFECTS 462
10.3. Location and dispersion effects from non replicated observations 466
10.4. More about the optimization procedures for robust product design 473
10.5. Parameter estimation in the case with errors in factor levels 474
10.5.1. INTRODUCTION 474
10.5.2. WEIGHTED LEAST SQUARES ESTIMATION BASED ON
REPEATED OBSERVATIONS 475
10.5.3. WEIGHTED LEAST SQUARES: UNREPLICATED CASE 476
10.6 Response surface approach to robust design of signal dependent
systems 477
10.7. Bibliography 481
BIBLIOGRAPHY 482
SUBJECT INDEX 500
AUTHOR INDEX 503
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| id | DE-604.BV013948707 |
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| indexdate | 2024-07-09T18:54:55Z |
| institution | BVB |
| isbn | 0792368274 |
| language | English |
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| oclc_num | 45714784 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVI, 505 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer |
| record_format | marc |
| series | Topics in safety, reliability and quality |
| series2 | Topics in safety, reliability and quality |
| spelling | Vuchkov, Ivan N. Verfasser aut Quality improvement with design of experiments a response surface approach by Ivan N. Vuchkov and Lidia N. Boyadjieva Dordrecht [u.a.] Kluwer 2001 XVI, 505 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topics in safety, reliability and quality 7 Fertigung swd Production - Gestion - Qualité - Contrôle Qualité - Contrôle Qualitätsmanagement swd Versuchsplanung swd Production management Quality control Quality control Boyadjieva, Lidia N. Verfasser aut Topics in safety, reliability and quality 7 (DE-604)BV006188902 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009545166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vuchkov, Ivan N. Boyadjieva, Lidia N. Quality improvement with design of experiments a response surface approach Topics in safety, reliability and quality Fertigung swd Production - Gestion - Qualité - Contrôle Qualité - Contrôle Qualitätsmanagement swd Versuchsplanung swd Production management Quality control Quality control |
| title | Quality improvement with design of experiments a response surface approach |
| title_auth | Quality improvement with design of experiments a response surface approach |
| title_exact_search | Quality improvement with design of experiments a response surface approach |
| title_full | Quality improvement with design of experiments a response surface approach by Ivan N. Vuchkov and Lidia N. Boyadjieva |
| title_fullStr | Quality improvement with design of experiments a response surface approach by Ivan N. Vuchkov and Lidia N. Boyadjieva |
| title_full_unstemmed | Quality improvement with design of experiments a response surface approach by Ivan N. Vuchkov and Lidia N. Boyadjieva |
| title_short | Quality improvement with design of experiments |
| title_sort | quality improvement with design of experiments a response surface approach |
| title_sub | a response surface approach |
| topic | Fertigung swd Production - Gestion - Qualité - Contrôle Qualité - Contrôle Qualitätsmanagement swd Versuchsplanung swd Production management Quality control Quality control |
| topic_facet | Fertigung Production - Gestion - Qualité - Contrôle Qualité - Contrôle Qualitätsmanagement Versuchsplanung Production management Quality control Quality control |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009545166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV006188902 |
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