Process analysis by statistical methods:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Wiley
1970
|
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XI, 463 S. zahlr. graph. Darst. |
ISBN: | 047139985X |
Internformat
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Datensatz im Suchindex
_version_ | 1805071486675845120 |
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adam_text |
1 Introduction
1.1 Terminology and Classification of Models. . 3
1.2 Stochastic Variables and Models . 5
Supplementary References 8
Problems 8
2 Probability Distributions and Sample Statistics
2.1 Probability Density Functions and Probability
Distributions 10
2.2 Ensemble Averages: The Mean, Variance, and
Correlation Coefficient 14
2.2 1 Mean 16
2.2 2 Autocorrelation Function . 17
2.2 3 Variance 18
2.2 4 Crosscorrelation Function . 19
2.2 5 Crosscovariance and Correlation Co¬
efficient 21
2.2 6 Moments of a Random Variable . . 22
2.3 The Normal and x2 Probability Distributions 23
2.3 1 The Normal Probability Distribution . 23
2.3 2 The xz Distribution 29
2.4 Sample Statistics and Their Distributions . . 30
2.4 1 The Sample Mean and Variance . 31
2.4 2 The t Distribution 34
2.4 3 Distribution of the Variance Ratio . . 35
2.4 4 "Propagation of Error" . 36
2.4 5 Sample Correlation Coefficient . 40
Supplementary References 42
Problems 42
PART II DEVELOPMENT AND Al
4 Linear Models With One Independent Variable
4.1 How to Select a Functional Relationship . . 105
4.2 Least Squares Parameter Estimation . . . 107
4.3 Estimation With Constant Error Variance. . 111
4.3 1 Least Squares Estimate 111
4.3 2 Maximum Likelihood Estimate . . 112
4.3 3 Expected Values and Variance of Esti¬
mators and Analysis of Variance . . 112
3 Statistical Inference and Applications
3.1 Introduction 49
3.2 Parameter Estimation Techniques . 50
3.2 1 Method of Maximum Likelihood . . 50
3.2 2 Method of Moments 51
3.2 3 Bayes' Estimates 52
3.3 Interval Estimation 53
3.4 Hypothesis Testing 56
3.4 1 Sequential Testing 60
3.5 Hypothesis Tests for Means 61
3.6 Hypothesis Tests for Variability . 64
3.7 Nonparametric (Distribution Free) Tests . . 68
3.7 1 Sign Test for Median Difference in
Paired Observations 68
3.7 2 Mann Whitney £/* Test 69
3.7 3 Siegel Tukey Test for Dispersion . . 71
3.7 4 Tests for Stationarity 71
3.7 5 Tests for Randomness 74
3.7 6 Tests for Goodness of Fit and In¬
dependence 74
3.8 Detection and Elimination of Outliers . 77
3.9 Process Control Charts 78
3.9 1 Shewhart Control Charts . 80
3.9 2 Acceptance Control Charts . 84
3.9 3 Geometric Moving Average Control
Chart 86
3.9 4 Cumulative Sum Control Charts . . 86
3.9 5 Control Charts for Several Variables . 93
Supplementary References 94
Problems 95
S1ALYSIS OF EMPIRICAL MODELS
4.3 4 Confidence Interval and Confidence
Region 118
4.3 5 The Estimated Regression Equation in
Reverse 120
4.4 Estimation With Error Variance a Function of
the Independent Variable 126
4.5 Estimation With Both Independent and De¬
pendent Variables Stochastic 128
4.6 Estimation When Measurement Errors Are Not
Independent 130
4.6 1 Cumulative Data 130
4.6 2 Correlated Residuals 132
4.7 Detection and Removal of Outliers. . . . 135
Supplementary References 136
Problems 137
5 Linear Models With Several Independent Variables
5.1 Estimation of Parameters 143
5.1 1 Least Squares Estimation . 143
5.1 2 Maximum Likelihood Estimation . . 146
5.1 3 Correlation and Bias in the Estimates 147
5.1 4 Sensitivity of the Estimates . 147
5.1 5 Computational Problems . 148
5.1 6 Estimation Using Orthogonal Poly¬
nomials 151
5.2 Confidence Intervals and Hypothesis Tests . 154
5.2 1 Confidence Intervals and Region . . 154
5.2 2 Hypothesis Tests 155
5.3 Analysis of Variance 158
5.4 Estimation When Errors Are Not Independent 164
5.5 Estimation for Multiresponse Models . . . 166
5.6 Estimation When Both Independent and
Dependent Variables are Stochastic . . . 167
Supplementary References 168
Problems 170
6 Nonlinear Models
6.1 Introduction 176
6.2 Nonlinear Estimation by Least Squares . . 177
6.2 1 Direct Search Methods 178
6.2 2 Flexible Geometric Simplex Method . 181
6.2 3 Linearization of the Model . . . . 186
6.2 4 Linearization of the Objective Function 191
6.3 Resolution of Certain Practical Difficulties in
Nonlinear Estimation 193
6.4 Hypothesis Tests and the Confidence Region . 197
6.4 1 Linearization of the Model in the Re¬
gion About the Minimum Sum of the
Squares 197
6.4 2 The Williams Method 199
6.4 3 The Method of Hartley and Booker . 200
6.5 Transformations to Linear Form . 200
PART III ESTIMATION USING MODELS BASE
9 Parameter Estimation in Process Models Represented
by Ordinary Differential Equations
9.1 Process Models and Introduction of Error . 295
9.1 1 Process Models and Response Error . 296
9.1 2 Unobservable Error Added to Deriva¬
tives 298
9.1 3 Differentiation of Process Data. . . 298
6.6 Estimation With the Parameters and/or Vari¬
ables Subject to Constraints 201
Supplementary References 202
Problems 203
7 Identification of the Best Model(s)
7.1 Analysis of Residuals 208
7.2 Stepwise Regression 212
7.3 A Graphical Procedure for Screening Models. 214
7.4 Comparison of Two Regression Equations . 216
7.5 Comparison Among Several Regression Equa¬
tions 218
Supplementary References 221
Problems 222
8 Strategy for Efficient Experimentation
8.1 Response Surface Methods 230
8.1 1 One Dimensional Models . . . .231
8.1 2 Two Dimensional Models and Experi¬
mental Designs 234
8.1 3 Three (and Higher) Dimensional
Models and Experimental Designs . . 239
8.1 4 Blocking 242
8.1 5 Practical Considerations . 245
8.2 Canonical Analysis 245
8.3 Strategies for Process Optimization by Experi¬
mentation 252
8.3 1 The Box Wilson (Gradient) Method . 253
8.3 2 Evolutionary Operation (EVOP) . . 257
8.3 3 Simplex Designs 259
8.3 4 Optimization by Direct Search . . . 260
8.4 Sequential Designs to Reduce Uncertainty in
Parameter Estimates 263
8.4 1 Processes With a Single Response . . 263
8.4 2 Multiresponse Processes 271
8.5 Sequential Designs to Discriminate Among
Models 274
8.5 1 Model Discrimination Using one Re¬
sponse 275
8.5 2 Model Discrimination in the Case of
Multiple Responses 278
8.5 3 Sequential Designs for Simultaneous
Discrimination and Parameter Estima¬
tion 280
Supplementary References 282
Problems 283
¦D ON TRANSPORT PHENOMENA PRINCIPLES
9.2 Least Squares Estimation 299
9.2 1 Discrete Observations 300
9.2 2 Computational Problems . 300
9.2 3 Continuous Observations . 303
9.2 4 Repetitive Integration of Experimental
Data 307
9.3 Maximum Likelihood Estimation . 307
9.4 Sequential Estimation 308
9.5 Method of Quasilinearization Combined With
Least Squares 315
9.6 Estimation Using the Equation Error (Model
Residue) 318
Supplementary References 323
Problems 324
10 Parameter Estimation in Models Containing Partial
Differential Equations
10.1 Process Inputs 330
10.2 Responses to Process Inputs 332
10.3 Design of Experiments to Simplify Model
Solutions 334
10.4 Parameter Estimation Using Deterministic
Moments 339
10.4 1 Models of Axial Dispersion . 339
10.4 2 Models of Axial and Radial Dispersion 345
Supplementary References 350
Problems 350
11 Parameter Estimation in Transfer Functions
11.1 The Transfer Function as a Process Model . 354
11.2 Least Squares Estimation of Parameters . . 357
APPE]
A. Concepts of Probability
Supplementary References 400
B. Mathematical Tools
B.I Properties and Characteristics of Linear
Equations 401
B.2 Linear and Nonlinear Operators . 401
B.3 Linear Systems 402
B.4 Matrix Algebra 402
B.4 1 Solution of Algebraic Equations . . 404
B.4 2 Eigenvalues and Eigenvectors . . 405
B.4 3 Normalization 406
B.4 4 Transformation to Canonical Form . 406
B.4 5 Solution of Nonlinear Sets of Equa¬
tions 409
B.5 Solutions of Single Ordinary Differential
Equations 409
B.5 1 Single Second and Higher Order
Linear Equations 410
11.2 1 Estimation in the Time Domain by
Inversion of the Transfer Function . 357
11.2 2 Estimation in Laplace Transform Space
by Transforming Observations . . . 360
11.3 Orthogonal Product Methods 361
11.4 Estimation for Sampled Data 365
11.4 1 The z Transform 365
11.4 2 Introduction of Error 366
11.4 3 "Equation Error" Estimation . . . 366
11.4 4 Maximum Likelihood Estimates . . 367
Supplementary References 370
Problems 371
12 Estimation in the Frequency Domain
12.1 The Process Model in the Frequency Domain. 374
12.2 Estimation Using Deterministic Inputs. . . 376
12.3 Estimation Using Stochastic Inputs . . . 378
12.3 1 Power Spectrum 379
12.3 2 Experimental Design for Random Proc¬
ess Inputs 380
12.3 3 Estimation of Spectral Densities . . 382
12.3 4 Precision of Transfer Function Esti¬
mates 386
Supplementary References 394
Problems 394
MDIX
B.5 2 Special Linear Equations With Vari¬
able Coefficients 411
B.5 3 Nonlinear Equations 411
B.6 Solution of Sets of Linear Ordinary Differen¬
tial Equations With Constant Coefficients . 411
B.7 Solutions of Single Partial Differential
Equations 416
B.8 Laplace Transforms 416
B.9 Generalized Functions 420
B.10 Use of Lagrangian Multipliers to Determine
an Optimum 421
Supplementary References 422
C. Tables 423
D. Notation 449
Author Index 457
Subject Index 459 |
any_adam_object | 1 |
author | Himmelblau, David M. 1923-2011 |
author_GND | (DE-588)140664122 |
author_facet | Himmelblau, David M. 1923-2011 |
author_role | aut |
author_sort | Himmelblau, David M. 1923-2011 |
author_variant | d m h dm dmh |
building | Verbundindex |
bvnumber | BV002277978 |
callnumber-first | T - Technology |
callnumber-label | TP155 |
callnumber-raw | TP155.7 |
callnumber-search | TP155.7 |
callnumber-sort | TP 3155.7 |
callnumber-subject | TP - Chemical Technology |
classification_rvk | SK 830 |
classification_tum | CIT 310f |
ctrlnum | (OCoLC)636627495 (DE-599)BVBBV002277978 |
dewey-full | 660/.284/01519 |
dewey-hundreds | 600 - Technology (Applied sciences) |
dewey-ones | 660 - Chemical engineering |
dewey-raw | 660/.284/01519 |
dewey-search | 660/.284/01519 |
dewey-sort | 3660 3284 41519 |
dewey-tens | 660 - Chemical engineering |
discipline | Chemie / Pharmazie Chemie-Ingenieurwesen Mathematik |
format | Book |
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id | DE-604.BV002277978 |
illustrated | Illustrated |
indexdate | 2024-07-20T04:38:36Z |
institution | BVB |
isbn | 047139985X |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001496677 |
oclc_num | 636627495 |
open_access_boolean | |
owner | DE-91G DE-BY-TUM DE-29T DE-83 DE-188 |
owner_facet | DE-91G DE-BY-TUM DE-29T DE-83 DE-188 |
physical | XI, 463 S. zahlr. graph. Darst. |
psigel | TUB-nvmb |
publishDate | 1970 |
publishDateSearch | 1970 |
publishDateSort | 1970 |
publisher | Wiley |
record_format | marc |
spelling | Himmelblau, David M. 1923-2011 Verfasser (DE-588)140664122 aut Process analysis by statistical methods David M. Himmelblau New York [u.a.] Wiley 1970 XI, 463 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chemische technologie gtt Lineaire modellen gtt Procesbeheersing gtt Statistische methoden gtt Mathematisches Modell Chemical engineering Statistical methods Chemical processes Mathematical models Transportprozess (DE-588)4185932-7 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Deterministisches System (DE-588)4426832-4 gnd rswk-swf Berechnung (DE-588)4120997-7 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Prozessanalyse (DE-588)4136607-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Prozessanalyse (DE-588)4136607-4 s Statistik (DE-588)4056995-0 s DE-604 Bewertung (DE-588)4006340-9 s 1\p DE-604 Berechnung (DE-588)4120997-7 s 2\p DE-604 Deterministisches System (DE-588)4426832-4 s 3\p DE-604 Modell (DE-588)4039798-1 s 4\p DE-604 Simulation (DE-588)4055072-2 s 5\p DE-604 Transportprozess (DE-588)4185932-7 s 6\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001496677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Himmelblau, David M. 1923-2011 Process analysis by statistical methods Chemische technologie gtt Lineaire modellen gtt Procesbeheersing gtt Statistische methoden gtt Mathematisches Modell Chemical engineering Statistical methods Chemical processes Mathematical models Transportprozess (DE-588)4185932-7 gnd Simulation (DE-588)4055072-2 gnd Bewertung (DE-588)4006340-9 gnd Deterministisches System (DE-588)4426832-4 gnd Berechnung (DE-588)4120997-7 gnd Modell (DE-588)4039798-1 gnd Prozessanalyse (DE-588)4136607-4 gnd Statistik (DE-588)4056995-0 gnd |
subject_GND | (DE-588)4185932-7 (DE-588)4055072-2 (DE-588)4006340-9 (DE-588)4426832-4 (DE-588)4120997-7 (DE-588)4039798-1 (DE-588)4136607-4 (DE-588)4056995-0 |
title | Process analysis by statistical methods |
title_auth | Process analysis by statistical methods |
title_exact_search | Process analysis by statistical methods |
title_full | Process analysis by statistical methods David M. Himmelblau |
title_fullStr | Process analysis by statistical methods David M. Himmelblau |
title_full_unstemmed | Process analysis by statistical methods David M. Himmelblau |
title_short | Process analysis by statistical methods |
title_sort | process analysis by statistical methods |
topic | Chemische technologie gtt Lineaire modellen gtt Procesbeheersing gtt Statistische methoden gtt Mathematisches Modell Chemical engineering Statistical methods Chemical processes Mathematical models Transportprozess (DE-588)4185932-7 gnd Simulation (DE-588)4055072-2 gnd Bewertung (DE-588)4006340-9 gnd Deterministisches System (DE-588)4426832-4 gnd Berechnung (DE-588)4120997-7 gnd Modell (DE-588)4039798-1 gnd Prozessanalyse (DE-588)4136607-4 gnd Statistik (DE-588)4056995-0 gnd |
topic_facet | Chemische technologie Lineaire modellen Procesbeheersing Statistische methoden Mathematisches Modell Chemical engineering Statistical methods Chemical processes Mathematical models Transportprozess Simulation Bewertung Deterministisches System Berechnung Modell Prozessanalyse Statistik |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001496677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT himmelblaudavidm processanalysisbystatisticalmethods |