# Statistics for Process Control Engineers. A Practical Approach

• ID: 4139461
• Book
• 624 Pages
• John Wiley and Sons Ltd
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The first statistics guide focussing on practical application to process control design and maintenance

Statistics for Process Control Engineers is the only guide to statistics written by and for process control professionals. It takes a wholly practical approach to the subject. Statistics are applied throughout the life of a process control scheme from assessing its economic benefit, designing inferential properties, identifying dynamic models, monitoring performance and diagnosing faults. This book addresses all of these areas and more.

The book begins with an overview of various statistical applications in the field of process control, followed by discussions of data characteristics, probability functions, data presentation, sample size, significance testing and commonly used mathematical functions. It then shows how to select and fit a distribution to data, before moving on to the application of regression analysis and data reconciliation. The book is extensively illustrated throughout with line drawings, tables and equations, and features numerous worked examples. In addition, two appendices include the data used in the examples and an exhaustive catalogue of statistical distributions. The data and a simple–to–use software tool are available for download. The reader can thus reproduce all of the examples and then extend the same statistical techniques to real problems.

• Takes a back–to–basics approach with a focus on techniques that have immediate, practical, problem–solving applications for practicing engineers, as well as engineering students
• Shows how to avoid the many common errors made by the industry in applying statistics to process control
• Describes not only the well–known statistical distributions but also demonstrates the advantages of applying the large number that are less well–known
• Inspires engineers to identify new applications of statistical techniques to the design and support of control schemes
• Provides a deeper understanding of services and products which control engineers are often tasked with assessing

This book is a valuable professional resource for engineers working in the global process industry and engineering companies, as well as students of engineering. It will be of great interest to those in the oil and gas, chemical, pulp and paper, water purification, pharmaceuticals and power generation industries, as well as for design engineers, instrument engineers and process technical support.

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Preface xiii

About the Author xix

Supplementary Material xxi

Part 1: The Basics 1

1. Introduction 3

2. Application to Process Control 5

2.1 Benefit Estimation 5

2.2 Inferential Properties 7

2.3 Controller Performance Monitoring 7

2.4 Event Analysis 8

2.5 Time Series Analysis 9

3. Process Examples 11

3.1 Debutaniser 11

3.2 De–ethaniser 11

3.3 LPG Splitter 12

3.4 Propane Cargoes 17

3.5 Diesel Quality 17

3.6 Fuel Gas Heating Value 18

3.7 Stock Level 19

3.8 Batch Blending 22

4. Characteristics of Data 23

4.1 Data Types 23

4.2 Memory 24

4.3 Use of Historical Data 24

4.4 Central Value 25

4.5 Dispersion 32

4.6 Mode 33

4.7 Standard Deviation 35

4.8 Skewness and Kurtosis 37

4.9 Correlation 46

4.10 Data Conditioning 47

5. Probability Density Function 51

5.1 Uniform Distribution 55

5.2 Triangular Distribution 57

5.3 Normal Distribution 59

5.4 Bivariate Normal Distribution 62

5.5 Central Limit Theorem 65

5.6 Generating a Normal Distribution 69

5.7 Quantile Function 70

5.8 Location and Scale 71

5.9 Mixture Distribution 73

5.10 Combined Distribution 73

5.11 Compound Distribution 75

5.12 Generalised Distribution 75

5.13 Inverse Distribution 76

5.14 Transformed Distribution 76

5.15 Truncated Distribution 77

5.16 Rectified Distribution 78

5.17 Noncentral Distribution 78

5.18 Odds 79

5.19 Entropy 80

6. Presenting the Data 83

6.1 Box and Whisker Diagram 83

6.2 Histogram 84

6.3 Kernel Density Estimation 90

6.4 Circular Plots 95

6.5 Parallel Coordinates 97

6.6 Pie Chart 98

6.7 Quantile Plot 98

7. Sample Size 105

7.1 Mean 105

7.2 Standard Deviation 106

7.3 Skewness and Kurtosis 107

7.4 Dichotomous Data 108

7.5 Bootstrapping 110

8. Significance Testing 113

8.1 Null Hypothesis 113

8.2 Confidence Interval 116

8.3 Six–Sigma 118

8.4 Outliers 119

8.5 Repeatability 120

8.6 Reproducibility 121

8.7 Accuracy 122

8.8 Instrumentation Error 123

9. Fitting a Distribution 127

9.1 Accuracy of Mean and Standard Deviation 130

9.2 Fitting a CDF 131

9.3 Fitting a QF 134

9.4 Fitting a PDF 135

9.5 Fitting to a Histogram 138

9.6 Choice of Penalty Function 141

10. Distribution of Dependent Variables 147

10.1 Addition and Subtraction 147

10.2 Division and Multiplication 148

10.3 Reciprocal 153

10.4 Logarithmic and Exponential Functions 153

10.5 Root Mean Square 162

10.6 Trigonometric Functions 164

11. Commonly Used Functions 165

11.1 Euler s Number 165

11.2 Euler Mascheroni Constant 166

11.3 Logit Function 166

11.4 Logistic Function 167

11.5 Gamma Function 168

11.6 Beta Function 174

11.7 Pochhammer Symbol 174

11.8 Bessel Function 176

11.9 Marcum Q–Function 178

11.10 Riemann Zeta Function 180

11.11 Harmonic Number 180

11.12 Stirling Approximation 182

11.13 Derivatives 183

12. Selected Distributions 185

12.1 Lognormal 186

12.2 Burr 189

12.3 Beta 191

12.4 Hosking 195

12.5 Student t 204

12.6 Fisher 208

12.7 Exponential 210

12.8 Weibull 213

12.9 Chi–Squared 216

12.10 Gamma 221

12.11 Binomial 225

12.12 Poisson 231

13. Extreme Value Analysis 235

14. Hazard Function 245

15. CUSUM 253

16. Regression Analysis 259

16.1 F Test 275

16.2 Adjusted R2 278

16.3 Akaike Information Criterion 279

16.4 Artificial Neural Networks 281

16.5 Performance Index 286

17. Autocorrelation 291

18. Data Reconciliation 299

19. Fourier Transform 305

Part 2: Catalogue of Distributions 315

20. Normal Distribution 317

20.1 Skew–Normal 317

20.2 Gibrat 320

20.3 Power Lognormal 320

20.4 Logit–Normal 321

20.5 Folded Normal 321

20.6 Lévy 323

20.7 Inverse Gaussian 325

20.8 Generalised Inverse Gaussian 329

20.9 Normal Inverse Gaussian 330

20.10 Reciprocal Inverse Gaussian 332

20.11 Q–Gaussian 334

20.12 Generalised Normal 338

20.13 Exponentially Modified Gaussian 345

20.14 Moyal 347

21. Burr Distribution 349

21.1 Type I 349

21.2 Type II 349

21.3 Type III 349

21.4 Type IV 350

21.5 Type V 351

21.6 Type VI 351

21.7 Type VII 353

21.8 Type VIII 354

21.9 Type IX 354

21.10 Type X 355

21.11 Type XI 356

21.12 Type XII 356

21.13 Inverse 357

22. Logistic Distribution 361

22.1 Logistic 361

22.2 Half–Logistic 364

22.3 Skew–Logistic 365

22.4 Log–Logistic 367

22.5 Paralogistic 369

22.6 Inverse Paralogistic 370

22.7 Generalised Logistic 371

22.8 Generalised Log–Logistic 375

22.9 Exponentiated Kumaraswamy Dagum 376

23. Pareto Distribution 377

23.1 Pareto Type I 377

23.2 Bounded Pareto Type I 378

23.3 Pareto Type II 379

23.4 Lomax 381

23.5 Inverse Pareto 381

23.6 Pareto Type III 382

23.7 Pareto Type IV 383

23.8 Generalised Pareto 383

23.9 Pareto Principle 385

24. Stoppa Distribution 389

24.1 Type I 389

24.2 Type II 389

24.3 Type III 391

24.4 Type IV 391

24.5 Type V 392

25. Beta Distribution 393

25.1 Arcsine 393

25.2 Wigner Semicircle 394

25.3 Balding Nichols 395

25.4 Generalised Beta 396

25.5 Beta Type II 396

25.6 Generalised Beta Prime 399

25.7 Beta Type IV 400

25.8 PERT 401

25.9 Beta Rectangular 403

25.10 Kumaraswamy 404

25.11 Noncentral Beta 407

26. Johnson Distribution 409

26.1 SN 409

26.2 SU 410

26.3 SL 412

26.4 SB 412

26.5 Summary 413

27. Pearson Distribution 415

27.1 Type I 416

27.2 Type II 416

27.3 Type III 417

27.4 Type IV 418

27.5 Type V 424

27.6 Type VI 425

27.7 Type VII 429

27.8 Type VIII 433

27.9 Type IX 433

27.10 Type X 433

27.11 Type XI 434

27.12 Type XII 434

28. Exponential Distribution 435

28.1 Generalised Exponential 435

28.2 Gompertz Verhulst 435

28.3 Hyperexponential 436

28.4 Hypoexponential 437

28.5 Double Exponential 438

28.6 Inverse Exponential 439

28.7 Maxwell Jüttner 439

28.8 Stretched Exponential 440

28.9 Exponential Logarithmic 441

28.10 Logistic Exponential 442

28.11 Q–Exponential 442

28.12 Benktander 445

29. Weibull Distribution 447

29.1 Nukiyama Tanasawa 447

29.2 Q–Weibull 447

30. Chi Distribution 451

30.1 Half–Normal 451

30.2 Rayleigh 452

30.3 Inverse Rayleigh 454

30.4 Maxwell 454

30.5 Inverse Chi 458

30.6 Inverse Chi–Squared 459

30.7 Noncentral Chi–Squared 460

31. Gamma Distribution 463

31.1 Inverse Gamma 463

31.2 Log–Gamma 463

31.3 Generalised Gamma 467

31.4 Q–Gamma 468

32. Symmetrical Distributions 471

32.1 Anglit 471

32.2 Bates 472

32.3 Irwin Hall 473

32.4 Hyperbolic Secant 475

32.5 Arctangent 476

32.6 Kappa 477

32.7 Laplace 478

32.8 Raised Cosine 479

32.9 Cardioid 481

32.10 Slash 481

32.11 Tukey Lambda 483

32.12 Von Mises 486

33. Asymmetrical Distributions 487

33.1 Benini 487

33.2 Birnbaum Saunders 488

33.4 Champernowne 491

33.5 Davis 492

33.6 Fréchet 494

33.7 Gompertz 496

33.8 Shifted Gompertz 497

33.9 Gompertz Makeham 498

33.10 Gamma–Gompertz 499

33.11 Hyperbolic 499

33.12 Asymmetric Laplace 502

33.13 Log–Laplace 504

33.14 Lindley 506

33.15 Lindley–Geometric 507

33.16 Generalised Lindley 509

33.17 Mielke 509

33.18 Muth 510

33.19 Nakagami 512

33.20 Power 513

33.21 Two–Sided Power 514

33.22 Exponential Power 516

33.23 Rician 517

33.24 Topp Leone 517

33.25 Generalised Tukey Lambda 519

33.26 Wakeby 521

34. Amoroso Distribution 525

35. Binomial Distribution 529

35.1 Negative–Binomial 529

35.2 Pülya 531

35.3 Geometric 531

35.4 Beta–Geometric 535

35.5 Yule Simon 536

35.6 Beta–Binomial 538

35.7 Beta–Negative Binomial 540

35.8 Beta–Pascal 541

35.9 Gamma–Poisson 542

35.10 Conway Maxwell Poisson 543

35.11 Skellam 546

36. Other Discrete Distributions 549

36.1 Benford 549

36.2 Borel Tanner 552

36.3 Consul 555

36.4 Delaporte 556

36.5 Flory Schulz 558

36.6 Hypergeometric 559

36.7 Negative Hypergeometric 561

36.8 Logarithmic 561

36.9 Discrete Weibull 563

36.10 Zeta 564

36.11 Zipf 565

36.12 Parabolic Fractal 567

Appendix 1 Data Used in Examples 569

Appendix 2 Summary of Distributions 577

References 591

Index 593

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