[eBook Code] Reliability Analysis for Asset Management of Electric Power Grids (eBook Code, 1st)

Preface xvii

Acknowledgements xxi

List of Symbols and Abbreviations xxiii

About the Companion website xxix

1 Introduction 1

1.1 Electric Power Grids 1

1.2 Asset Management of Electric Power Grids 2

1.3 Maintenance Styles 4

1.4 Incident Management 20

1.5 Summary 21

2 Basics of Statistics and Probability 25

2.1 Outcomes, Sample Space and Events 26

2.2 Probability of Events 29

2.3 Probability versus Statistical Distributions 30

2.4 Fundamental Statistical Functions 33

2.5 Mixed Distributions 38

2.6 Multivariate Distributions and Power Law 49

2.7 Summary 59

3 Measures in Statistics 63

3.1 Expected Values and Moments 63

3.2 Median and Other Quantiles 73

3.3 Mode 75

3.4 Merits of Mean, Median and Modal Value 75

3.5 Measures for Comparing Distributions 77

3.6 Similarity of Distributions 82

3.7 Compliance 96

3.8 Summary 97

4 Specific Distributions 101

4.1 Fractions and Ranking 101

4.2 Extreme Value Statistics 112

4.3 Mean and Variance Statistics 124

4.4 Frequency and Hit Statistics 134

4.5 Summary 152

5 Graphical Data Analysis 157

5.1 Data Quality 158

5.3 Model-Based or Parametric Graphs 176

5.4 Weibull Plot 178

5.5 Exponential Plot 188

5.6 Normal Distribution 193

5.7 Power Law Reliability Growth 197

5.8 Summary 202

6 Parameter Estimation 207

6.1 General Aspects with Parameter Estimation 207

6.2 Maximum Likelihood Estimators 212

6.3 Linear Regression 223

6.4 Summary 263

7 System and Component Reliability 267

7.1 The Basics of System Reliability 267

7.2 Block Diagrams 268

7.3 Series Systems 269

7.4 Parallel Systems and Redundancy 272

7.5 Combined Series and Parallel Systems, Common Cause 273

7.6 EXTRA: Reliability and Expected Life of k-out-of-n Systems 276

7.7 Analysis of Complex Systems 277

7.8 Summary 285

8 System States, Reliability and Availability 291

8.1 States of Components and Systems 291

8.2 States and Transition Rates of One-Component Systems 292

8.3 System State Probabilities via Markov Chains 297

8.4 Markov–Laplace Method for Reliability and Availability 303

8.5 Lifetime with Absorbing States and Spare Parts 306

8.6 Mean Lifetimes MTTFF and MTBF 310

8.7 Availability and Steady-State Situations 312

8.8 Summary 314

9 Application to Asset and Incident Management 317

9.1 Maintenance Styles 317

9.1.1 Period-Based Maintenance Optimization for Lowest Costs 317

9.2 Health Index 334

9.3 Testing and Quality Assurance 338

9.4 Incident Management (Determining End of Trouble) 342

10 Miscellaneous Subjects 367

10.1 Basics of Combinatorics 367

10.2 Power Functions and Asymptotic Behaviour 369

10.3 Regression Analysis 380

10.4 Sampling from a Population and Simulations 386

10.5 Hypothesis Testing 407

10.6 Approximations for the Normal Distribution 408

10.6.1 Power Series 409

10.6.2 Power Series Times Density f (y) 409

10.6.3 Inequalities for Boxing R(y) and h(y) for Large y 410

10.6.4 Polynomial Expression for F(y) 410

10.6.5 Power Function for the Reliability Function R(y) 410

10.6.6 Wrap-up of Approximations 412

Appendix A Weibull Plot 413

Appendix B Laplace Transforms 415

Appendix C Taylor Series 417

Appendix D SI Prefixes 419

Appendix E Greek Characters 421

Appendix F Standard Weibull and Exponential Distribution 423

Appendix G Standardized Normal Distribution 429

Appendix H Standardized Lognormal Distribution 435

Appendix I Gamma Function 441

Appendix J Plotting Positions 447

References 469

Index 473