Details

System Reliability Theory


System Reliability Theory

Models, Statistical Methods, and Applications
Wiley Series in Probability and Statistics 3. Aufl.

von: Marvin Rausand, Anne Barros, Arnljot Hoyland

134,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 08.10.2020
ISBN/EAN: 9781119374015
Sprache: englisch
Anzahl Seiten: 864

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

<p><b>Handbook and reference for industrial statisticians and system reliability engineers</b> </p> <p><i>System Reliability Theory: Models, Statistical Methods, and Applications, Third Edition</i> presents an updated and revised look at system reliability theory, modeling, and analytical methods.  The new edition is based on feedback to the second edition from numerous students, professors, researchers, and industries around the world.  New sections and chapters are added together with new real-world industry examples, and standards and problems are revised and updated. </p> <p><i>System Reliability Theory</i> covers a broad and deep array of system reliability topics, including: </p> <p>·         In depth discussion of failures and failure modes </p> <p>·         The main system reliability assessment methods </p> <p>·         Common-cause failure modeling </p> <p>·         Deterioration modeling </p> <p>·         Maintenance modeling and assessment using Python code </p> <p>·         Bayesian probability and methods </p> <p>·         Life data analysis using R </p> <p>Perfect for undergraduate and graduate students taking courses in reliability engineering, this book also serves as a reference and resource for practicing statisticians and engineers.  </p> <p>Throughout, the book has a practical focus, incorporating industry feedback and real-world industry problems and examples. </p> <p> </p>
<p>Preface xxiii</p> <p>About the Companion Website xxix</p> <p><b>1 Introduction </b><b>1</b></p> <p>1.1 What is Reliability? 1</p> <p>1.1.1 Service Reliability 2</p> <p>1.1.2 Past and Future Reliability 3</p> <p>1.2 The Importance of Reliability 3</p> <p>1.2.1 Related Applications 4</p> <p>1.3 Basic Reliability Concepts 6</p> <p>1.3.1 Reliability 6</p> <p>1.3.2 Maintainability and Maintenance 8</p> <p>1.3.3 Availability 8</p> <p>1.3.4 Quality 9</p> <p>1.3.5 Dependability 9</p> <p>1.3.6 Safety and Security 10</p> <p>1.3.7 RAM and RAMS 10</p> <p>1.4 Reliability Metrics 11</p> <p>1.4.1 Reliability Metrics for a Technical Item 11</p> <p>1.4.2 Reliability Metrics for a Service 12</p> <p>1.5 Approaches to Reliability Analysis 12</p> <p>1.5.1 The Physical Approach to Reliability 13</p> <p>1.5.2 Systems Approach to Reliability 13</p> <p>1.6 Reliability Engineering 15</p> <p>1.6.1 Roles of the Reliability Engineer 16</p> <p>1.6.2 Timing of Reliability Studies 17</p> <p>1.7 Objectives, Scope, and Delimitations of the Book 17</p> <p>1.8 Trends and Challenges 19</p> <p>1.9 Standards and Guidelines 20</p> <p>1.10 History of System Reliability 20</p> <p>1.11 Problems 26</p> <p>References 27</p> <p><b>2 The Study Object and its Functions </b><b>31</b></p> <p>2.1 Introduction 31</p> <p>2.2 System and System Elements 31</p> <p>2.2.1 Item 32</p> <p>2.2.2 Embedded Item 33</p> <p>2.3 Boundary Conditions 33</p> <p>2.3.1 Closed and Open Systems 34</p> <p>2.4 Operating Context 35</p> <p>2.5 Functions and Performance Requirements 35</p> <p>2.5.1 Functions 35</p> <p>2.5.2 Performance Requirements 36</p> <p>2.5.3 Classification of Functions 37</p> <p>2.5.4 Functional Modeling and Analysis 38</p> <p>2.5.5 Function Trees 38</p> <p>2.5.6 SADT and IDEF 0 39</p> <p>2.6 System Analysis 41</p> <p>2.6.1 Synthesis 41</p> <p>2.7 Simple, Complicated, and Complex Systems 42</p> <p>2.8 System Structure Modeling 44</p> <p>2.8.1 Reliability Block Diagram 44</p> <p>2.8.2 Series Structure 46</p> <p>2.8.3 Parallel Structure 46</p> <p>2.8.4 Redundancy 47</p> <p>2.8.5 Voted Structure 47</p> <p>2.8.6 Standby Structure 48</p> <p>2.8.7 More Complicated Structures 48</p> <p>2.8.8 Two Different System Functions 49</p> <p>2.8.9 Practical Construction of RBDs 50</p> <p>2.9 Problems 51</p> <p>References 52</p> <p><b>3 Failures and Faults </b><b>55</b></p> <p>3.1 Introduction 55</p> <p>3.1.1 States and Transitions 56</p> <p>3.1.2 Operational Modes 56</p> <p>3.2 Failures 57</p> <p>3.2.1 Failures in a State 58</p> <p>3.2.2 Failures During Transition 59</p> <p>3.3 Faults 60</p> <p>3.4 Failure Modes 60</p> <p>3.5 Failure Causes and Effects 62</p> <p>3.5.1 Failure Causes 62</p> <p>3.5.2 Proximate Causes and Root Causes 63</p> <p>3.5.3 Hierarchy of Causes 64</p> <p>3.6 Classification of Failures and Failure Modes 64</p> <p>3.6.1 Classification According to Local Consequence 65</p> <p>3.6.2 Classification According to Cause 65</p> <p>3.6.3 Failure Mechanisms 70</p> <p>3.6.4 Software Faults 71</p> <p>3.6.5 Failure Effects 71</p> <p>3.7 Failure/Fault Analysis 72</p> <p>3.7.1 Cause and Effect Analysis 73</p> <p>3.7.2 Root Cause Analysis 74</p> <p>3.8 Problems 76</p> <p>References 77</p> <p><b>4 Qualitative System Reliability Analysis </b><b>79</b></p> <p>4.1 Introduction 79</p> <p>4.1.1 Deductive Versus Inductive Analysis 80</p> <p>4.2 FMEA/FMECA 80</p> <p>4.2.1 Types of FMECA 81</p> <p>4.2.2 Objectives of FMECA 82</p> <p>4.2.3 FMECA Procedure 83</p> <p>4.2.4 Applications 87</p> <p>4.3 Fault Tree Analysis 88</p> <p>4.3.1 Fault Tree Symbols and Elements 88</p> <p>4.3.2 Definition of the Problem and the Boundary Conditions 91</p> <p>4.3.3 Constructing the Fault Tree 92</p> <p>4.3.4 Identification of Minimal Cut and Path Sets 95</p> <p>4.3.5 MOCUS 96</p> <p>4.3.6 Qualitative Evaluation of the Fault Tree 98</p> <p>4.3.7 Dynamic Fault Trees 101</p> <p>4.4 Event Tree Analysis 103</p> <p>4.4.1 Initiating Event 104</p> <p>4.4.2 Safety Functions 105</p> <p>4.4.3 Event Tree Construction 106</p> <p>4.4.4 Description of Resulting Event Sequences 106</p> <p>4.5 Fault Trees versus Reliability Block Diagrams 109</p> <p>4.5.1 Recommendation 111</p> <p>4.6 Structure Function 111</p> <p>4.6.1 Series Structure 112</p> <p>4.6.2 Parallel Structure 112</p> <p>4.6.3 <i>k</i>oo<i>n</i>:G Structure 113</p> <p>4.6.4 Truth Tables 114</p> <p>4.7 System Structure Analysis 114</p> <p>4.7.1 Single Points of Failure 115</p> <p>4.7.2 Coherent Structures 115</p> <p>4.7.3 General Properties of Coherent Structures 117</p> <p>4.7.4 Structures Represented by Paths and Cuts 119</p> <p>4.7.5 Pivotal Decomposition 123</p> <p>4.7.6 Modules of Coherent Structures 124</p> <p>4.8 Bayesian Networks 127</p> <p>4.8.1 Illustrative Examples 128</p> <p>4.9 Problems 131</p> <p>References 138</p> <p><b>5 Probability Distributions in Reliability Analysis </b><b>141</b></p> <p>5.1 Introduction 141</p> <p>5.1.1 State Variable 142</p> <p>5.1.2 Time-to-Failure 142</p> <p>5.2 A Dataset 143</p> <p>5.2.1 Relative Frequency Distribution 143</p> <p>5.2.2 Empirical Distribution and Survivor Function 144</p> <p>5.3 General Characteristics of Time-to-Failure Distributions 145</p> <p>5.3.1 Survivor Function 147</p> <p>5.3.2 Failure Rate Function 148</p> <p>5.3.3 Conditional Survivor Function 153</p> <p>5.3.4 Mean Time-to-Failure 154</p> <p>5.3.5 Additional Probability Metrics 155</p> <p>5.3.6 Mean Residual Lifetime 157</p> <p>5.3.7 Mixture of Time-to-Failure Distributions 160</p> <p>5.4 Some Time-to-Failure Distributions 161</p> <p>5.4.1 The Exponential Distribution 161</p> <p>5.4.2 The Gamma Distribution 168</p> <p>5.4.3 TheWeibull Distribution 173</p> <p>5.4.4 The Normal Distribution 180</p> <p>5.4.5 The Lognormal Distribution 183</p> <p>5.4.6 Additional Time-to-Failure Distributions 188</p> <p>5.5 Extreme Value Distributions 188</p> <p>5.5.1 The Gumbel Distribution of the Smallest Extreme 190</p> <p>5.5.2 The Gumbel Distribution of the Largest Extreme 191</p> <p>5.5.3 TheWeibull Distribution of the Smallest Extreme 191</p> <p>5.6 Time-to-Failure Models With Covariates 193</p> <p>5.6.1 Accelerated Failure Time Models 194</p> <p>5.6.2 The Arrhenius Model 195</p> <p>5.6.3 Proportional Hazards Models 198</p> <p>5.7 Additional Continuous Distributions 198</p> <p>5.7.1 The Uniform Distribution 198</p> <p>5.7.2 The Beta Distribution 199</p> <p>5.8 Discrete Distributions 200</p> <p>5.8.1 Binomial Situation 200</p> <p>5.8.2 The Binomial Distribution 201</p> <p>5.8.3 The Geometric Distribution 201</p> <p>5.8.4 The Negative Binomial Distribution 202</p> <p>5.8.5 The Homogeneous Poisson Process 203</p> <p>5.9 Classes of Time-to-Failure Distributions 205</p> <p>5.9.1 IFR and DFR Distributions 206</p> <p>5.9.2 IFRA and DFRA Distributions 208</p> <p>5.9.3 NBU and NWU Distributions 208</p> <p>5.9.4 NBUE and NWUE Distributions 209</p> <p>5.9.5 Some Implications 209</p> <p>5.10 Summary of Time-to-Failure Distributions 210</p> <p>5.11 Problems 210</p> <p>References 218</p> <p><b>6 System Reliability Analysis </b><b>221</b></p> <p>6.1 Introduction 221</p> <p>6.1.1 Assumptions 222</p> <p>6.2 System Reliability 222</p> <p>6.2.1 Reliability of Series Structures 223</p> <p>6.2.2 Reliability of Parallel Structures 224</p> <p>6.2.3 Reliability of <i>k</i>oo<i>n </i>Structures 225</p> <p>6.2.4 Pivotal Decomposition 226</p> <p>6.2.5 Critical Component 227</p> <p>6.3 Nonrepairable Systems 228</p> <p>6.3.1 Nonrepairable Series Structures 228</p> <p>6.3.2 Nonrepairable Parallel Structures 230</p> <p>6.3.3 Nonrepairable 2oo3 Structures 234</p> <p>6.3.4 A Brief Comparison 235</p> <p>6.3.5 Nonrepairable <i>k</i>oo<i>n </i>Structures 236</p> <p>6.4 Standby Redundancy 237</p> <p>6.4.1 Passive Redundancy, Perfect Switching, No Repairs 238</p> <p>6.4.2 Cold Standby, Imperfect Switch, No Repairs 240</p> <p>6.4.3 Partly Loaded Redundancy, Imperfect Switch, No Repairs 241</p> <p>6.5 Single Repairable Items 242</p> <p>6.5.1 Availability 243</p> <p>6.5.2 Average Availability with Perfect Repair 244</p> <p>6.5.3 Availability of a Single Item with Constant Failure and Repair Rates 246</p> <p>6.5.4 Operational Availability 247</p> <p>6.5.5 Production Availability 248</p> <p>6.5.6 Punctuality 249</p> <p>6.5.7 Failure Rate of Repairable Items 249</p> <p>6.6 Availability of Repairable Systems 252</p> <p>6.6.1 The MUT and MDT of Repairable Systems 253</p> <p>6.6.2 Computation Based on Minimal Cut Sets 258</p> <p>6.6.3 Uptimes and Downtimes for Reparable Systems 260</p> <p>6.7 Quantitative Fault Tree Analysis 262</p> <p>6.7.1 Terminology and Symbols 263</p> <p>6.7.2 Delimitations and Assumptions 263</p> <p>6.7.3 Fault Trees with a Single AND-Gate 264</p> <p>6.7.4 Fault Tree with a Single OR-Gate 265</p> <p>6.7.5 The Upper Bound Approximation Formula for <i>Q</i>0(<i>t</i>) 265</p> <p>6.7.6 The Inclusion–Exclusion Principle 267</p> <p>6.7.7 ROCOF of a Minimal Cut Parallel Structure 271</p> <p>6.7.8 Frequency of the TOP Event 271</p> <p>6.7.9 Binary Decision Diagrams 273</p> <p>6.8 Event Tree Analysis 275</p> <p>6.9 Bayesian Networks 277</p> <p>6.9.1 Influence and Cause 278</p> <p>6.9.2 Independence Assumptions 278</p> <p>6.9.3 Conditional Probability Table 279</p> <p>6.9.4 Conditional Independence 280</p> <p>6.9.5 Inference and Learning 282</p> <p>6.9.6 BN and Fault Tree Analysis 282</p> <p>6.10 Monte Carlo Simulation 284</p> <p>6.10.1 Random Number Generation 285</p> <p>6.10.2 Monte Carlo Next Event Simulation 287</p> <p>6.10.3 Simulation of Multicomponent Systems 289</p> <p>6.11 Problems 291</p> <p>References 296</p> <p><b>7 Reliability Importance Metrics </b><b>299</b></p> <p>7.1 Introduction 299</p> <p>7.1.1 Objectives of Reliability Importance Metrics 300</p> <p>7.1.2 Reliability Importance Metrics Considered 300</p> <p>7.1.3 Assumptions and Notation 301</p> <p>7.2 Critical Components 302</p> <p>7.3 Birnbaum’s Metric for Structural Importance 304</p> <p>7.4 Birnbaum’s Metric of Reliability Importance 305</p> <p>7.4.1 Birnbaum’s Metric in Fault Tree Analysis 307</p> <p>7.4.2 A Second Definition of Birnbaum’s Metric 308</p> <p>7.4.3 A Third Definition of Birnbaum’s Metric 310</p> <p>7.4.4 Computation of Birnbaum’s Metric for Structural Importance 312</p> <p>7.4.5 Variants of Birnbaum’s Metric 312</p> <p>7.5 Improvement Potential 313</p> <p>7.5.1 Relation to Birnbaum’s Metric 314</p> <p>7.5.2 A Variant of the Improvement Potential 314</p> <p>7.6 Criticality Importance 315</p> <p>7.7 Fussell–Vesely’s Metric 317</p> <p>7.7.1 Derivation of Formulas for Fussell–Vesely’s Metric 317</p> <p>7.7.2 Relationship to Other Metrics for Importance 320</p> <p>7.8 Differential Importance Metric 323</p> <p>7.8.1 Option 1 323</p> <p>7.8.2 Option 2 324</p> <p>7.9 Importance Metrics for Safety Features 326</p> <p>7.9.1 Risk AchievementWorth 327</p> <p>7.9.2 Risk ReductionWorth 329</p> <p>7.9.3 Relationship with the Improvement Potential 330</p> <p>7.10 Barlow–Proschan’s Metric 331</p> <p>7.11 Problems 333</p> <p>References 335</p> <p><b>8 Dependent Failures </b><b>337</b></p> <p>8.1 Introduction 337</p> <p>8.1.1 Dependent Events and Variables 337</p> <p>8.1.2 Correlated Variables 338</p> <p>8.2 Types of Dependence 340</p> <p>8.3 Cascading Failures 340</p> <p>8.3.1 Tight Coupling 342</p> <p>8.4 Common-Cause Failures 342</p> <p>8.4.1 Multiple Failures that Are Not a CCF 344</p> <p>8.4.2 Causes of CCF 344</p> <p>8.4.3 Defenses Against CCF 345</p> <p>8.5 CCF Models and Analysis 346</p> <p>8.5.1 Explicit Modeling 347</p> <p>8.5.2 Implicit Modeling 348</p> <p>8.5.3 Modeling Approach 348</p> <p>8.5.4 Model Assumptions 349</p> <p>8.6 Basic Parameter Model 349</p> <p>8.6.1 Probability of a Specific Multiplicity 350</p> <p>8.6.2 Conditional Probability of a Specific Multiplicity 351</p> <p>8.7 Beta-Factor Model 352</p> <p>8.7.1 Relation to the BPM 354</p> <p>8.7.2 Beta-Factor Model in System Analysis 354</p> <p>8.7.3 Beta-Factor Model for Nonidentical Components 358</p> <p>8.7.4 <i>C</i>-Factor Model 360</p> <p>8.8 Multi-parameter Models 360</p> <p>8.8.1 Binomial Failure Rate Model 360</p> <p>8.8.2 Multiple Greek Letter Model 362</p> <p>8.8.3 Alpha-Factor Model 364</p> <p>8.8.4 Multiple Beta-Factor Model 365</p> <p>8.9 Problems 366</p> <p>References 368</p> <p><b>9 Maintenance and Maintenance Strategies </b><b>371</b></p> <p>9.1 Introduction 371</p> <p>9.1.1 What is Maintenance? 372</p> <p>9.2 Maintainability 372</p> <p>9.3 Maintenance Categories 374</p> <p>9.3.1 Completeness of a Repair Task 377</p> <p>9.3.2 Condition Monitoring 377</p> <p>9.4 Maintenance Downtime 378</p> <p>9.4.1 Downtime Caused by Failures 379</p> <p>9.4.2 Downtime of a Series Structure 381</p> <p>9.4.3 Downtime of a Parallel Structure 381</p> <p>9.4.4 Downtime of a General Structure 382</p> <p>9.5 Reliability Centered Maintenance 382</p> <p>9.5.1 What is RCM? 383</p> <p>9.5.2 Main Steps of an RCM Analysis 384</p> <p>9.6 Total Productive Maintenance 396</p> <p>9.7 Problems 398</p> <p>References 399</p> <p><b>10 Counting Processes </b><b>401</b></p> <p>10.1 Introduction 401</p> <p>10.1.1 Counting Processes 401</p> <p>10.1.2 Basic Concepts 406</p> <p>10.1.3 Martingale Theory 408</p> <p>10.1.4 Four Types of Counting Processes 409</p> <p>10.2 Homogeneous Poisson Processes 410</p> <p>10.2.1 Main Features of the HPP 411</p> <p>10.2.2 Asymptotic Properties 412</p> <p>10.2.3 Estimate and Confidence Interval 412</p> <p>10.2.4 Sum and Decomposition of HPPs 413</p> <p>10.2.5 Conditional Distribution of Failure Time 414</p> <p>10.2.6 Compound HPPs 415</p> <p>10.3 Renewal Processes 417</p> <p>10.3.1 Basic Concepts 417</p> <p>10.3.2 The Distribution of <i>Sn </i>418</p> <p>10.3.3 The Distribution of <i>N</i>(<i>t</i>) 420</p> <p>10.3.4 The Renewal Function 421</p> <p>10.3.5 The Renewal Density 423</p> <p>10.3.6 Age and Remaining Lifetime 427</p> <p>10.3.7 Bounds for the Renewal Function 431</p> <p>10.3.8 Superimposed Renewal Processes 433</p> <p>10.3.9 Renewal Reward Processes 434</p> <p>10.3.10 Delayed Renewal Processes 436</p> <p>10.3.11 Alternating Renewal Processes 438</p> <p>10.4 Nonhomogeneous Poisson Processes 447</p> <p>10.4.1 Introduction and Definitions 447</p> <p>10.4.2 Some Results 449</p> <p>10.4.3 Parametric NHPP Models 452</p> <p>10.4.4 Statistical Tests of Trend 454</p> <p>10.5 Imperfect Repair Processes 455</p> <p>10.5.1 Brown and Proschan’s model 456</p> <p>10.5.2 Failure Rate Reduction Models 458</p> <p>10.5.3 Age Reduction Models 461</p> <p>10.5.4 Trend Renewal Process 462</p> <p>10.6 Model Selection 464</p> <p>10.7 Problems 466</p> <p>References 470</p> <p><b>11 Markov Analysis </b><b>473</b></p> <p>11.1 Introduction 473</p> <p>11.1.1 Markov Property 475</p> <p>11.2 Markov Processes 476</p> <p>11.2.1 Procedure to Establish the Transition Rate Matrix 479</p> <p>11.2.2 Chapman–Kolmogorov Equations 482</p> <p>11.2.3 Kolmogorov Differential Equations 483</p> <p>11.2.4 State Equations 484</p> <p>11.3 Asymptotic Solution 487</p> <p>11.3.1 System Performance Metrics 492</p> <p>11.4 Parallel and Series Structures 495</p> <p>11.4.1 Parallel Structures of Independent Components 495</p> <p>11.4.2 Series Structures of Independent Components 497</p> <p>11.4.3 Series Structure of Components Where Failure of One Component Prevents Failure of the Other 499</p> <p>11.5 Mean Time to First System Failure 501</p> <p>11.5.1 Absorbing States 501</p> <p>11.5.2 Survivor Function 504</p> <p>11.5.3 Mean Time to the First System Failure 505</p> <p>11.6 Systems with Dependent Components 507</p> <p>11.6.1 Common Cause Failures 508</p> <p>11.6.2 Load-Sharing Systems 510</p> <p>11.7 Standby Systems 512</p> <p>11.7.1 Parallel System with Cold Standby and Perfect Switching 513</p> <p>11.7.2 Parallel System with Cold Standby and Perfect Switching (Item <i>A </i>is the Main Operating Item) 515</p> <p>11.7.3 Parallel System with Cold Standby and Imperfect Switching (Item <i>A </i>is the Main Operating Item) 517</p> <p>11.7.4 Parallel System with Partly Loaded Standby and Perfect Switching (Item <i>A </i>is the Main Operating Item) 518</p> <p>11.8 Markov Analysis in Fault Tree Analysis 519</p> <p>11.8.1 Cut Set Information 520</p> <p>11.8.2 System Information 521</p> <p>11.9 Time-Dependent Solution 521</p> <p>11.9.1 Laplace Transforms 522</p> <p>11.10 Semi-Markov Processes 524</p> <p>11.11 Multiphase Markov Processes 526</p> <p>11.11.1 Changing the Transition Rates 526</p> <p>11.11.2 Changing the Initial State 527</p> <p>11.12 Piecewise Deterministic Markov Processes 528</p> <p>11.12.1 Definition of PDMP 529</p> <p>11.12.2 State Probabilities 529</p> <p>11.12.3 A Specific Case 530</p> <p>11.13 Simulation of a Markov Process 532</p> <p>11.14 Problems 536</p> <p>References 543</p> <p><b>12 Preventive Maintenance </b><b>545</b></p> <p>12.1 Introduction 545</p> <p>12.2 Terminology and Cost Function 546</p> <p>12.3 Time-Based Preventive Maintenance 548</p> <p>12.3.1 Age Replacement 549</p> <p>12.3.2 Block Replacement 553</p> <p>12.3.3 <i>P</i>–<i>F </i>Intervals 557</p> <p>12.4 Degradation Models 564</p> <p>12.4.1 Remaining Useful Lifetime 565</p> <p>12.4.2 Trend Models; Regression-Based Models 567</p> <p>12.4.3 Models with Increments 569</p> <p>12.4.4 Shock Models 571</p> <p>12.4.5 Stochastic Processes with Discrete States 573</p> <p>12.4.6 Failure Rate Models 574</p> <p>12.5 Condition-Based Maintenance 574</p> <p>12.5.1 CBM Strategy 575</p> <p>12.5.2 Continuous Monitoring and Finite Discrete State Space 576</p> <p>12.5.3 Continuous Monitoring and Continuous State Space 581</p> <p>12.5.4 Inspection-Based Monitoring and Finite Discrete State Space 583</p> <p>12.5.5 Inspection-Based Monitoring and Continuous State Space 586</p> <p>12.6 Maintenance of Multi-Item Systems 587</p> <p>12.6.1 System Model 587</p> <p>12.6.2 Maintenance Models 589</p> <p>12.6.3 An Illustrative Example 591</p> <p>12.7 Problems 595</p> <p>References 601</p> <p><b>13 Reliability of Safety Systems </b><b>605</b></p> <p>13.1 Introduction 605</p> <p>13.2 Safety-Instrumented Systems 606</p> <p>13.2.1 Main SIS Functions 607</p> <p>13.2.2 Testing of SIS Functions 608</p> <p>13.2.3 Failure Classification 609</p> <p>13.3 Probability of Failure on Demand 611</p> <p>13.3.1 Probability of Failure on Demand 612</p> <p>13.3.2 Approximation Formulas 617</p> <p>13.3.3 Mean Downtime in a Test Interval 618</p> <p>13.3.4 Mean Number of Test Intervals Until First Failure 619</p> <p>13.3.5 Staggered Testing 620</p> <p>13.3.6 Nonnegligible Repair Time 621</p> <p>13.4 Safety Unavailability 622</p> <p>13.4.1 Probability of Critical Situation 623</p> <p>13.4.2 Spurious Trips 623</p> <p>13.4.3 Failures Detected by Diagnostic Self-Testing 625</p> <p>13.5 Common Cause Failures 627</p> <p>13.5.1 Diagnostic Self-Testing and CCFs 629</p> <p>13.6 CCFs Between Groups and Subsystems 631</p> <p>13.6.1 CCFs Between Voted Groups 632</p> <p>13.6.2 CCFs Between Subsystems 632</p> <p>13.7 IEC 61508 632</p> <p>13.7.1 Safety Lifecycle 633</p> <p>13.7.2 Safety Integrity Level 634</p> <p>13.7.3 Compliance with IEC 61508 635</p> <p>13.8 The PDS Method 638</p> <p>13.9 Markov Approach 639</p> <p>13.9.1 All Failures are Repaired After Each Test 643</p> <p>13.9.2 All Critical Failures Are Repaired after Each Test 644</p> <p>13.9.3 Imperfect Repair after Each Test 644</p> <p>13.10 Problems 644</p> <p>References 652</p> <p><b>14 Reliability Data Analysis </b><b>655</b></p> <p>14.1 Introduction 655</p> <p>14.1.1 Purpose of the Chapter 656</p> <p>14.2 Some Basic Concepts 656</p> <p>14.2.1 Datasets 657</p> <p>14.2.2 Survival Times 658</p> <p>14.2.3 Categories of Censored Datasets 660</p> <p>14.2.4 Field Data Collection Exercises 662</p> <p>14.2.5 At-Risk-Set 663</p> <p>14.3 Exploratory Data Analysis 663</p> <p>14.3.1 A Complete Dataset 664</p> <p>14.3.2 Sample Metrics 665</p> <p>14.3.3 Histogram 669</p> <p>14.3.4 Density Plot 670</p> <p>14.3.5 Empirical Survivor Function 671</p> <p>14.3.6 Q–Q Plot 673</p> <p>14.4 Parameter Estimation 674</p> <p>14.4.1 Estimators and Estimates 675</p> <p>14.4.2 Properties of Estimators 675</p> <p>14.4.3 Method of Moments Estimation 677</p> <p>14.4.4 Maximum Likelihood Estimation 680</p> <p>14.4.5 Exponentially Distributed Lifetimes 686</p> <p>14.4.6 Weibull Distributed Lifetimes 692</p> <p>14.5 The Kaplan–Meier Estimate 696</p> <p>14.5.1 Motivation for the Kaplan–Meier Estimate Based a Complete Dataset 696</p> <p>14.5.2 The Kaplan–Meier Estimator for a Censored Dataset 697</p> <p>14.6 Cumulative Failure Rate Plots 701</p> <p>14.6.1 The Nelson–Aalen Estimate of the Cumulative Failure Rate 703</p> <p>14.7 Total-Time-on-Test Plotting 708</p> <p>14.7.1 Total-Time-on-Test Plot for Complete Datasets 708</p> <p>14.7.2 Total-Time-on-Test Plot for Censored Datasets 721</p> <p>14.7.3 A Brief Comparison 722</p> <p>14.8 Survival Analysis with Covariates 723</p> <p>14.8.1 Proportional Hazards Model 723</p> <p>14.8.2 Cox Models 726</p> <p>14.8.3 Estimating the Parameters of the Cox Model 727</p> <p>14.9 Problems 730</p> <p>References 736</p> <p><b>15 Bayesian Reliability Analysis </b><b>739</b></p> <p>15.1 Introduction 739</p> <p>15.1.1 Three Interpretations of Probability 739</p> <p>15.1.2 Bayes’ Formula 741</p> <p>15.2 Bayesian Data Analysis 742</p> <p>15.2.1 Frequentist Data Analysis 743</p> <p>15.2.2 Bayesian Data Analysis 743</p> <p>15.2.3 Model for Observed Data 745</p> <p>15.2.4 Prior Distribution 745</p> <p>15.2.5 Observed Data 746</p> <p>15.2.6 Likelihood Function 746</p> <p>15.2.7 Posterior Distribution 747</p> <p>15.3 Selection of Prior Distribution 749</p> <p>15.3.1 Binomial Model 749</p> <p>15.3.2 Exponential Model – Single Observation 752</p> <p>15.3.3 Exponential Model – Multiple Observations 753</p> <p>15.3.4 Homogeneous Poisson Process 755</p> <p>15.3.5 Noninformative Prior Distributions 757</p> <p>15.4 Bayesian Estimation 758</p> <p>15.4.1 Bayesian Point Estimation 758</p> <p>15.4.2 Credible Intervals 760</p> <p>15.5 Predictive Distribution 761</p> <p>15.6 Models with Multiple Parameters 762</p> <p>15.7 Bayesian Analysis with R 762</p> <p>15.8 Problems 764</p> <p>References 766</p> <p><b>16 Reliability Data: Sources and Quality </b><b>767</b></p> <p>16.1 Introduction 767</p> <p>16.1.1 Categories of Input Data 767</p> <p>16.1.2 Parameters Estimates 768</p> <p>16.2 Generic Reliability Databases 769</p> <p>16.2.1 OREDA 770</p> <p>16.2.2 PDS Data Handbook 772</p> <p>16.2.3 PERD 773</p> <p>16.2.4 SERH 773</p> <p>16.2.5 NPRD, EPRD, and FMD 773</p> <p>16.2.6 GADS 774</p> <p>16.2.7 GIDEP 774</p> <p>16.2.8 FMEDA Approach 775</p> <p>16.2.9 Failure Event Databases 775</p> <p>16.3 Reliability Prediction 775</p> <p>16.3.1 MIL-HDBK-217 Approach 776</p> <p>16.3.2 Similar Methods 778</p> <p>16.4 Common Cause Failure Data 778</p> <p>16.4.1 ICDE 779</p> <p>16.4.2 IEC 61508 Method 779</p> <p>16.5 Data Analysis and Data Quality 780</p> <p>16.5.1 Outdated Technology 780</p> <p>16.5.2 Inventory Data 781</p> <p>16.5.3 Constant Failure Rates 781</p> <p>16.5.4 Multiple Samples 783</p> <p>16.5.5 Data From Manufacturers 785</p> <p>16.5.6 Questioning the Data Quality 785</p> <p>16.6 Data Dossier 785</p> <p>16.6.1 Final Remarks 785</p> <p>References 787</p> <p><b>Appendix A Acronyms </b><b>789</b></p> <p><b>Appendix B Laplace Transforms </b><b>793</b></p> <p>B.1 Important Properties of Laplace Transforms 794</p> <p>B.2 Laplace Transforms of Some Selected Functions 794</p> <p>Author Index 797</p> <p>Subject Index 803</p>
<p><b>MARVIN RAUSAND</b> is Professor Emeritus in the department of Mechanical and Industrial Engineering at the Norwegian University of Science and Technology (NTNU), Norway, and author of <i>Risk Assessment: Theory, Methods, and Applications and Reliability of Safety-Critical Systems: Theory and Applications,</i> both published by Wiley. <p><b>ANNE BARROS, P<small>H</small>D,</b> is Professor in reliability and maintenance engineering at Ecole CentraleSupélec, University of Paris-Saclay, France. Her research focus is on degradation modeling, prognostics, condition based and predictive maintenance. She got a PHD then a professorship position at University of Technology of Troyes, France (2003 – 2014) and spent five years as a full-time professor at NTNU, Norway (2014 – 2019). She is currently heading a research group and holds an industrial chair at CentraleSupélec with the ambition to provide reliability assessment and maintenance modeling methods for systems of systems. <p>The late <b>ARNLJOT HØYLAND, P<small>H</small>D,</b> was a Professor in the Department of Mathematical Sciences at the Norwegian University of Science and Technology.
<p><b>Handbook and reference for industrial statisticians and system reliability engineers</b> <p><i>System Reliability Theory: Models, Statistical Methods, and Applications, Third Edition</i> presents an updated and revised look at system reliability theory, modeling, and analytical methods. The new edition is based on feedback to the second edition from numerous students, professors, researchers, and industries around the world. New sections and chapters are added together with new real-world industry examples, and standards and problems are revised and updated. <p><i>System Reliability Theory</i> covers a broad and deep array of system reliability topics, including: <ul> <li>In depth discussion of failures and failure modes</li> <li>The main system reliability assessment methods</li> <li>Common-cause failure modeling</li> <li>Deterioration modeling</li> <li>Maintenance modeling and assessment using Python code</li> <li>Bayesian probability and methods</li> <li>Life data analysis using R</li> </ul> <p>Perfect for undergraduate and graduate students taking courses in reliability engineering, this book also serves as a reference and resource for practicing statisticians and engineers. <p>Throughout, the book has a practical focus, incorporating industry feedback and real-world industry problems and examples.

Diese Produkte könnten Sie auch interessieren:

Statistics for Microarrays
Statistics for Microarrays
von: Ernst Wit, John McClure
PDF ebook
90,99 €