Preface ................................................... xiii
Acknowledgements .......................................... xvii
Abbreviations .............................................. xix
Symbols .................................................... xxi
Nomenclature ............................................. xxiii
Introduction ............................................... xxv
PART I FUNDAMENTALS OF MULTIVARIATE STATISTICAL PROCESS
CONTROL ......................................................... 1
1 Motivation for multivariate statistical process control ...... 3
1.1 Summary of statistical process control .................. 3
1.1.1 Roots and evolution of statistical process
control .......................................... 4
1.1.2 Principles of statistical process control ........ 5
1.1.3 Hypothesis testing, Type I and II errors ........ 12
1.2 Why multivariate statistical process control ........... 15
1.2.1 Statistically uncorrelated variables ............ 16
1.2.2 Perfectly correlated variables .................. 17
1.2.3 Highly correlated variables ..................... 19
1.2.4 Type I and II errors and dimension reduction .... 24
1.3 Tutorial session ....................................... 26
2 Multivariate data modeling methods ....................... 28
2.1 Principal component analysis ........................... 30
2.1.1 Assumptions for underlying data structure ....... 30
2.1.2 Geometric analysis of data structure ............ 33
2.1.3 A simulation example ............................ 34
2.2 Partial least squares .................................. 38
2.2.1 Assumptions for underlying data structure ........... 39
2.2.2 Deflation procedure for estimating data models .. 41
2.2.3 A simulation example ............................ 43
2.3 Maximum redundancy partial least squares ............... 49
2.3.1 Assumptions for underlying data structure ....... 49
2.3.2 Source signal estimation ........................ 50
2.3.3 Geometric analysis of data structure ............ 52
2.3.4 A simulation example ............................ 58
2.4 Estimating the number of source signals ................ 65
2.4.1 Stopping rules for PCA models ................... 65
2.4.2 Stopping rules for PLS models ................... 76
2.5 Tutorial Session ....................................... 79
3 Process monitoring charts ................................... 81
3.1 Fault detection ........................................ 83
3.1.1 Scatter diagrams ................................ 84
3.1.2 Non-negative quadratic monitoring statistics .... 85
3.2 Fault isolation and identification ..................... 93
3.2.1 Contribution charts ............................. 95
3.2.2 Residual-based tests ............................ 98
3.2.3 Variable reconstruction ........................ 100
3.3 Geometry of variable projections ...................... 111
3.3.1 Linear dependency of projection residuals ...... 111
3.3.2 Geometric analysis of variable reconstruction .. 112
3.4 Tutorial session ...................................... 119
PART II APPLICATION STUDIES .................................. 121
4 Application to a chemical reaction process ................. 123
4.1 Process description ................................... 123
4.2 Identification of a monitoring model .................. 124
4.3 Diagnosis of a fault condition ........................ 133
5 Application to a distillation process ................... 141
5.1 Process description ................................... 141
5.2 Identification of a monitoring model .................. 144
5.3 Diagnosis of a fault condition ........................ 153
PART III ADVANCES IN MULTIVARIATE STATISTICAL PROCESS
CONTROL ....................................................... 165
6 Further modeling issues .................................... 167
6.1 Accuracy of estimating PCA models .................... 168
6.1.1 Revisiting the eigendecomposition of SZoZ(j .... 168
6.1.2 Two illustrative examples ...................... 171
6.1.3 Maximum likelihood PCA for known SBB ........... 172
6.1.4 Maximum likelihood PCA for unknown SgB ......... 177
6.1.5 A simulation example ........................... 182
6.1.6 A stopping rale for maximum likelihood PCA
models ......................................... 187
6.1.7 Properties of model and residual subspace
estimates ...................................... 189
6.1.8 Application to a chemical reaction process -
revisited ...................................... 194
6.2 Accuracy of estimating PLS models ..................... 202
6.2.1 Bias and variance of parameter estimation ...... 203
6.2.2 Comparing accuracy of PLS and OLS regression
models ......................................... 205
6.2.3 Impact of error-in-variables structure upon
PLS models ..................................... 212
6.2.4 Error-in-variable estimate for known Sec ....... 218
6.2.5 Error-in-variable estimate for unknown See ..... 219
6.2.6 Application to a distillation process -
revisited ...................................... 223
6.3 Robust model estimation ............................... 226
6.3.1 Robust parameter estimation .................... 228
6.3.2 Trimming approaches ............................ 231
6.4 Small sample sets ..................................... 232
6.5 Tutorial session ...................................... 237
7 Monitoring multivariate time-varying processes ............. 240
7.1 Problem analysis ...................................... 241
7.2 Recursive principal component analysis ................ 242
7.3 Moving window principal component analysis ............ 244
7.3.1 Adapting the data correlation matrix ........... 244
7.3.2 Adapting the eigendecomposition ................ 247
7.3.3 Computational analysis of the adaptation
procedure ...................................... 251
7.3.4 Adaptation of control limits ................... 252
7.3.5 Process monitoring using an application delay .. 253
7.3.6 Minimum window length .......................... 254
7.4 A simulation example .................................. 257
7.4.1 Data generation ................................ 257
7.4.2 Application of PCA ............................. 258
7.4.3 Utilizing MWPCA based on an application delay .. 261
7.5 Application to a Fluid Catalytic Cracking Unit ........ 265
7.5.1 Process description ............................ 266
7.5.2 Data generation ................................ 268
7.5.3 Pre-analysis of simulated data ................. 272
7.5.4 Application of PCA ............................. 273
7.5.5 Application of MWPCA ........................... 275
7.6 Application to a furnace process ...................... 278
7.6.1 Process description ............................ 278
7.6.2 Description of sensor bias ..................... 279
7.6.3 Application of PCA ............................. 280
7.6.4 Utilizing MWPCA based on an application delay .. 282
7.7 Adaptive partial least squares ........................ 286
7.7.1 Recursive adaptation of SXQXQ and S^oyo ........ 287
7.7.2 Moving window adaptation of SXQXo and SWo ...... 287
7.7.3 Adapting the number of source signals .......... 287
7.7.4 Adaptation of the PLS model .................... 290
7.8 Tutorial Session ...................................... 292
8 Monitoring changes in covariance structure ................. 293
8.1 Problem analysis ...................................... 294
8.1.1 First intuitive example ........................ 294
8.1.2 Generic statistical analysis ................... 297
8.1.3 Second intuitive example ....................... 299
8.2 Preliminary discussion of related techniques .......... 304
8.3 Definition of primary and improved residuals .......... 305
8.3.1 Primary residuals for eigenvectors ............. 306
8.3.2 Primary residuals for eigenvalues .............. 307
8.3.3 Comparing both types of primary residuals ...... 307
8.3.4 Statistical properties of primary residuals .... 312
8.3.5 Improved residuals for eigenvalues ............. 315
8.4 Revisiting the simulation examples of Section 8.1 ..... 317
8.4.1 First simulation example ....................... 318
8.4.2 Second simulation example ...................... 321
8.5 Fault isolation and identification .................... 324
8.5.1 Diagnosis of step-type fault conditions ........ 325
8.5.2 Diagnosis of general deterministic fault
conditions ..................................... 328
8.5.3 A simulation example ........................... 328
8.6 Application study of a gearbox system ................. 331
8.6.1 Process description ............................ 332
8.6.2 Fault description .............................. 332
8.6.3 Identification of a monitoring model ........... 334
8.6.4 Detecting a fault condition .................... 338
8.7 Analysis of primary and improved residuals ............ 341
8.7.1 Central limit theorem .......................... 341
8.7.2 Further statistical properties of primary
residuals ...................................... 344
8.7.3 Sensitivity of statistics based on improved
residuals ...................................... 349
8.8 Tutorial session ...................................... 353
PART IV DESCRIPTION OF MODELING METHODS ...................... 355
9 Principal component analysis ............................... 357
9.1 The core algorithm .................................... 357
9.2 Summary of the PCA algorithm .......................... 362
9.3 Properties of a PCA model ............................. 363
10 Partial least squares ......................................
10.1 Preliminaries .........................................
10.2 The core algorithm .................................... 377
10.3 Summary of the PLS algorithm .......................... 380
10.4 Properties of PLS ..................................... 381
10.5 Properties of maximum redundancy PLS .................. 396
References ................................................. 410
Index ...................................................... 427
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