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Importance Measures in Reliability, Risk, and Optimization


Importance Measures in Reliability, Risk, and Optimization

Principles and Applications
1. Aufl.

von: Way Kuo, Xiaoyan Zhu

95,99 €

Verlag: Wiley
Format: EPUB
Veröffentl.: 10.05.2012
ISBN/EAN: 9781118304174
Sprache: englisch
Anzahl Seiten: 480

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Beschreibungen

<p>This unique treatment systematically interprets a spectrum of importance measures to provide a comprehensive overview of their applications in the areas of reliability, network, risk, mathematical programming, and optimization. Investigating the precise relationships among various importance measures, it describes how they are modelled and combined with other design tools to allow users to solve readily many real-world, large-scale decision-making problems. </p> <p>Presenting the state-of-the-art in network analysis, multistate systems, and application in modern systems, this book offers a clear and complete introduction to the topic. Through describing the reliability importance and the fundamentals, it covers advanced topics such as signature of coherent systems, multi-linear functions, and new interpretation of the mathematical programming problems.</p> <p>Key highlights:</p> <ul> <li>Generalizes the concepts behind importance measures (such as sensitivity and perturbation analysis, uncertainty analysis, mathematical programming, network designs), enabling  readers to address large-scale problems within various fields effectively</li> <li>Covers a large range of importance measures, including those in binary coherent systems, binary monotone systems, multistate systems, continuum systems, repairable systems, as well as importance measures of pairs and groups of components</li> <li>Demonstrates numerical and practical applications of importance measures and the related methodologies, including risk analysis in nuclear power plants, cloud computing, software reliability and more</li> <li>Provides thorough comparisons, examples and case studies on relations of different importance measures, with conclusive results based on the authors’ own research</li> <li>Describes reliability design such as redundancy allocation, system upgrading and component assignment.</li> </ul> <p>This book will benefit researchers and practitioners interested in systems design, reliability, risk and optimization, statistics, maintenance, prognostics and operations. Readers can develop feasible approaches to solving various open-ended problems in their research and practical work. Software developers, IT analysts and reliability and safety engineers in nuclear, telecommunications, offshore and civil industries will also find the book useful.</p>
<b>Preface xv</b> <p>References xvii</p> <p><b>Acknowledgements xix</b></p> <p><b>Part One INTRODUCTION and BACKGROUND 1</b></p> <p><b>Introduction 2</b></p> <p><b>1 Introduction to Importance Measures 5</b></p> <p>References 11</p> <p><b>2 Fundamentals of Systems Reliability 13</b></p> <p>2.1 Block Diagrams 13</p> <p>2.2 Structure Functions 14</p> <p>2.3 Coherent Systems 17</p> <p>2.4 Modules within a Coherent System 18</p> <p>2.5 Cuts and Paths of a Coherent System 19</p> <p>2.6 Critical Cuts and Critical Paths of a Coherent System 21</p> <p>2.7 Measures of Performance 23</p> <p>2.7.1 Reliability for a mission time 24</p> <p>2.7.2 Reliability function (of time t) 25</p> <p>2.7.3 Availability function 27</p> <p>2.8 Stochastic Orderings 28</p> <p>2.9 Signature of Coherent Systems 28</p> <p>2.10 Multilinear Functions and Taylor (Maclaurin) Expansion 31</p> <p>2.11 Redundancy 32</p> <p>2.12 Reliability Optimization and Complexity 33</p> <p>2.13 Consecutive-k-out-of-n Systems 34</p> <p>2.14 Assumptions 35</p> <p>References 36</p> <p><b>Part Two PRINCIPLES of IMPORTANCE MEASURES 39</b></p> <p><b>Introduction 40</b></p> <p><b>3 The Essence of Importance Measures 43</b></p> <p>3.1 ImportanceMeasures in Reliability 43</p> <p>3.2 Classifications 44</p> <p>3.3 <i>c</i>-type and <i>p</i>-type ImportanceMeasures 45</p> <p>3.4 ImportanceMeasures of a Minimal Cut and a Minimal Path 45</p> <p>3.5 Terminology 45</p> <p>References 46</p> <p><b>4 Reliability Importance Measures 47</b></p> <p>4.1 The B-reliability Importance 47</p> <p>4.1.1 The B-reliability importance for system functioning and for system failure 52</p> <p>4.1.2 The criticality reliability importance 52</p> <p>4.1.3 The Bayesian reliability importance 53</p> <p>4.2 The FV Reliability Importance 53</p> <p>4.2.1 The c-type FV (c-FV) reliability importance 54</p> <p>4.2.2 The p-type FV (p-FV) reliability importance 54</p> <p>4.2.3 Decomposition of state vectors 54</p> <p>4.2.4 Properties 56</p> <p>References 57</p> <p><b>5 Lifetime Importance Measures 59</b></p> <p>5.1 The B-time-dependent-lifetime Importance 59</p> <p>5.1.1 The criticality time-dependent lifetime importance 61</p> <p>5.2 The FV Time-dependent Lifetime Importance 61</p> <p>5.2.1 The c-FV time-dependent lifetime importance 61</p> <p>5.2.2 The p-FV time-dependent lifetime importance 63</p> <p>5.2.3 Decomposition of state vectors 64</p> <p>5.3 The BP Time-independent Lifetime Importance 64</p> <p>5.4 The BP Time-dependent Lifetime Importance 69</p> <p>5.5 Numerical Comparisons of Time-dependent Lifetime ImportanceMeasures 69</p> <p>5.6 Summary 71</p> <p>References 72</p> <p><b>6 Structure Importance Measures 73</b></p> <p>6.1 The B-i.i.d. Importance and B-structure Importance 73</p> <p>6.2 The FV Structure Importance 76</p> <p>6.3 The BP Structure Importance 76</p> <p>6.4 Structure ImportanceMeasures Based on the B-i.i.d. importance 79</p> <p>6.5 The Permutation Importance and Permutation Equivalence 80</p> <p>6.5.1 Relations to minimal cuts and minimal paths 81</p> <p>6.5.2 Relations to systems reliability 83</p> <p>6.6 The Domination Importance 85</p> <p>6.7 The Cut Importance and Path Importance 86</p> <p>6.7.1 Relations to the B-i.i.d. importance 87</p> <p>6.7.2 Computation 89</p> <p>6.8 The Absoluteness Importance 91</p> <p>6.9 The Cut-path Importance,Min-cut Importance, and Min-path Importance 92</p> <p>6.10 The First-term Importance and Rare-event Importance 93</p> <p>6.11 c-type and p-type of Structure ImportanceMeasures 93</p> <p>6.12 Structure ImportanceMeasures for Dual Systems 94</p> <p>6.13 Dominant Relations among ImportanceMeasures 96</p> <p>6.13.1 The absoluteness importance with the domination importance 96</p> <p>6.13.2 The domination importance with the permutation importance 96</p> <p>6.13.3 The domination importance with the min-cut importance and min-path importance 96</p> <p>6.13.4 The permutation importance with the FV importance 96</p> <p>6.13.5 The permutation importance with the cut-path importance, min-cut importance,</p> <p>and min-path importance 100</p> <p>6.13.6 The cut-path importance with the cut importance and path importance 101</p> <p>6.13.7 The cut-path importance with the B-i.i.d. importance 101</p> <p>6.13.8 The B-i.i.d. importance with the BP importance 102</p> <p>6.14 Summary 102</p> <p>References 105</p> <p><b>7 ImportanceMeasures of Pairs and Groups of Components 107</b></p> <p>7.1 The Joint Reliability Importance and Joint Failure Importance 107</p> <p>7.1.1 The joint reliability importance of dependent components 110</p> <p>7.1.2 The joint reliability importance of two gate events 110</p> <p>7.1.3 The joint reliability importance for k-out-of-n systems 111</p> <p>7.1.4 The joint reliability importance of order k 111</p> <p>7.2 The Differential ImportanceMeasure 112</p> <p>7.2.1 The first-order differential importance measure 112</p> <p>7.2.2 The second-order differential importance measure 113</p> <p>7.2.3 The differential importance measure of order k 114</p> <p>7.3 The Total Order Importance 114</p> <p>7.4 The Reliability AchievementWorth and Reliability ReductionWorth 115</p> <p>References 116</p> <p><b>8 ImportanceMeasures for Consecutive-</b>k<b>-out-of-</b>n <b>Systems 119</b></p> <p>8.1 Formulas for the B-importance 119</p> <p>8.1.1 The B-reliability importance and B-i.i.d. importance 119</p> <p>8.1.2 The B-structure importance 122</p> <p>8.2 Patterns of the B-importance for Lin/Con/k/n Systems 123</p> <p>8.2.1 The B-reliability importance 123</p> <p>8.2.2 The uniform B-i.i.d. importance 124</p> <p>8.2.3 The half-line B-i.i.d. importance 126</p> <p>8.2.4 The nature of the B-i.i.d. importance patterns 126</p> <p>8.2.5 Patterns with respect to p 128</p> <p>8.2.6 Patterns with respect to n 129</p> <p>8.2.7 Disproved patterns and conjectures 131</p> <p>8.3 Structure ImportanceMeasures 135</p> <p>8.3.1 The permutation importance 135</p> <p>8.3.2 The cut-path importance 135</p> <p>8.3.3 The BP structure importance 135</p> <p>8.3.4 The first-term importance and rare-event importance 136</p> <p>References 137</p> <p><b>Part Three IMPORTANCE MEASURES for RELIABILITY DESIGN 139</b></p> <p><b>Introduction 140</b></p> <p>References 141</p> <p><b>9 Redundancy Allocation 143</b></p> <p>9.1 Redundancy ImportanceMeasures 144</p> <p>9.2 A Common Spare 145</p> <p>9.2.1 The redundancy importance measures 145</p> <p>9.2.2 The permutation importance 147</p> <p>9.2.3 The cut importance and path importance 147</p> <p>9.3 Spare Identical to the Respective Component 148</p> <p>9.3.1 The redundancy importance measures 148</p> <p>9.3.2 The permutation importance 149</p> <p>9.4 Several Spares in a k-out-of-n System 150</p> <p>9.5 Several Spares in an Arbitrary Coherent System 150</p> <p>9.6 Cold Standby Redundancy 152</p> <p>References 152</p> <p><b>10 Upgrading System Performance 155</b></p> <p>10.1 Improving Systems Reliability 156</p> <p>10.1.1 Same amount of improvement in component reliability 156</p> <p>10.1.2 A fractional change in component reliability 157</p> <p>10.1.3 Cold standby redundancy 158</p> <p>10.1.4 Parallel redundancy 158</p> <p>10.1.5 Example and discussion 158</p> <p>10.2 Improving Expected System Lifetime 159</p> <p>10.2.1 A shift in component lifetime distributions 160</p> <p>10.2.2 Exactly one minimal repair 160</p> <p>10.2.3 Reduction in the proportional hazards 167</p> <p>10.2.4 Cold standby redundancy 168</p> <p>10.2.5 A perfect component 170</p> <p>10.2.6 An imperfect repair 170</p> <p>10.2.7 A scale change in component lifetime distributions 171</p> <p>10.2.8 Parallel redundancy 171</p> <p>10.2.9 Comparisons and numerical evaluation 172</p> <p>10.3 Improving Expected System Yield 174</p> <p>10.3.1 A shift in component lifetime distributions 175</p> <p>10.3.2 Exactly one minimal repair / cold standby redundancy / a perfect component /</p> <p>parallel redundancy 180</p> <p>10.4 Discussion 182</p> <p>References 182</p> <p><b>11 Component Assignment in Coherent Systems 185</b></p> <p>11.1 Description of Component Assignment Problems 186</p> <p>11.2 Enumeration and Randomization Methods 187</p> <p>11.3 Optimal Design based on the Permutation Importance and Pairwise Exchange 188</p> <p>11.4 Invariant Optimal and InvariantWorst Arrangements 189</p> <p>11.5 Invariant Arrangements for Parallel-series and Series-parallel Systems 191</p> <p>11.6 Consistent B-i.i.d. Importance Ordering and Invariant Arrangements 192</p> <p>11.7 Optimal Design based on the B-reliability Importance 194</p> <p>11.8 Optimal Assembly Problems 196</p> <p>References 197</p> <p><b>12 Component Assignment in Consecutive-</b>k<b>-out-of-</b>n <b>and Its Variant Systems 199</b></p> <p>12.1 Invariant Arrangements for Con/k/n Systems 199</p> <p>12.1.1 Invariant optimal arrangements for Lin/Con/k/n systems 200</p> <p>12.1.2 Invariant optimal arrangements for Cir/Con/k/n systems 200</p> <p>12.1.3 Consistent B-i.i.d. importance ordering and invariant arrangements 202</p> <p>12.2 Necessary Conditions for Component Assignment in Con/k/n Systems 204</p> <p>12.3 Sequential Component Assignment Problems in Con/2/n:F Systems 206</p> <p>12.4 Consecutive-2 Failure Systems on Graphs 207</p> <p>12.4.1 Consecutive-2 failure systems on trees 208</p> <p>12.5 Series Con/k/n Systems 208</p> <p>12.5.1 Series Con/2/n:F systems 209</p> <p>12.5.2 Series Lin/Con/k/n:G systems 209</p> <p>12.6 Consecutive-k-out-of-r-from-n Systems 211</p> <p>12.7 Two-dimensional and Redundant Con/k/n Systems 213</p> <p>12.7.1 Con/(r, k)/(r, n) systems 214</p> <p>12.8 Miscellaneous 216</p> <p>References 217</p> <p><b>13 B-importance based Heuristics for Component Assignment 219</b></p> <p>13.1 The Kontoleon Heuristic 219</p> <p>13.2 The LK Type Heuristics 221</p> <p>13.2.1 The LKA heuristic 221</p> <p>13.2.2 Another three LK type heuristics 221</p> <p>13.2.3 Relation to invariant optimal arrangements 221</p> <p>13.2.4 Numerical comparisons of the LK type heuristics 224</p> <p>13.3 The ZK Type Heuristics 225</p> <p>13.3.1 Four ZK type heuristics 225</p> <p>13.3.2 Relation to invariant optimal arrangements 227</p> <p>13.3.3 Comparisons of initial arrangements 227</p> <p>13.3.4 Numerical comparisons of the ZK type heuristics 229</p> <p>13.4 The B-importance based Two-stage Approach 229</p> <p>13.4.1 Numerical comparisons with the GAMS/CoinBomin solver and enumeration</p> <p>method 230</p> <p>13.4.2 Numerical comparisons with the randomization method 230</p> <p>13.5 The B-importance based Genetic Local Search 231</p> <p>13.5.1 The description of algorithm 232</p> <p>13.5.2 Numerical comparisons with the B-importance based two-stage approach and a</p> <p>genetic algorithm 235</p> <p>13.6 Summary and Discussion 236</p> <p>References 238</p> <p><b>Part Four RELATIONS and GENERALIZATIONS 241</b></p> <p><b>Introduction 242</b></p> <p><b>14 Comparisons of Importance Measures 245</b></p> <p>14.1 Relations to the B-importance 245</p> <p>14.2 Rankings of Reliability ImportanceMeasures 247</p> <p>14.2.1 Using the permutation importance 247</p> <p>14.2.2 Using the permutation importance and joint reliability importance 249</p> <p>14.2.3 Using the domination importance 250</p> <p>14.2.4 Summary 250</p> <p>14.3 ImportanceMeasures for Some Special Systems 250</p> <p>14.4 Computation of ImportanceMeasures 251</p> <p>References 253</p> <p><b>15 Generalizations of Importance Measures 255</b></p> <p>15.1 Noncoherent Systems 255</p> <p>15.1.1 Binary monotone systems 256</p> <p>15.2 Multistate Coherent Systems 257</p> <p>15.2.1 The μ, _ B-importance 258</p> <p>15.2.2 The μ, _ cut importance 259</p> <p>15.3 Multistate Monotone Systems 261</p> <p>15.3.1 The permutation importance 261</p> <p>15.3.2 The utility B-reliability importance 262</p> <p>15.3.3 The utility-decomposition reliability importance 262</p> <p>15.3.4 The utility B-structure importance, joint structure importance, and joint reliability</p> <p>importance 263</p> <p>15.3.5 The B-importance, FV importance, reliability achievement worth, and reliability</p> <p>reduction worth with respect to system mean unavailability and mean performance 265</p> <p>15.4 Binary Type Multistate Monotone Systems 266</p> <p>15.4.1 The B-t.d.l. importance, BP t.i.l. importance, and L1 t.i.l. importance 267</p> <p>15.5 Summary of ImportanceMeasures for Multistate Systems 268</p> <p>15.6 Continuum Systems 270</p> <p>15.7 Repairable Systems 272</p> <p>15.7.1 The B-availability importance 272</p> <p>15.7.2 The c-FV unavailability importance 273</p> <p>15.7.3 The BP availability importance 273</p> <p>15.7.4 The L1 t.i.l. importance 274</p> <p>15.7.5 Simulation-based importance measures 275</p> <p>15.8 Applications in the Power Industry 276</p> <p>References 277</p> <p><b>Part Five BROAD IMPLICATIONS to RISK and MATHEMATICAL</b></p> <p><b>PROGRAMMING 281</b></p> <p><b>Introduction 282</b></p> <p>References 283</p> <p><b>16 Networks 285</b></p> <p>16.1 Network Flow Systems 285</p> <p>16.1.1 The edge importance measures in a network flow system 286</p> <p>16.1.2 The edge importance measures for a binary monotone system 288</p> <p>16.1.3 The B-reliability importance, FV reliability importance, reliability reduction</p> <p>worth, and reliability achievement worth 289</p> <p>16.1.4 The flow-based importance and impact-based importance 290</p> <p>16.2 K-terminal Networks 291</p> <p>16.2.1 Importance measures of an edge 293</p> <p>16.2.2 A K-terminal optimization problem 295</p> <p>References 295</p> <p><b>17 Mathematical Programming 297</b></p> <p>17.1 Linear Programming 297</p> <p>17.1.1 Basic concepts 298</p> <p>17.1.2 The simplex algorithm 300</p> <p>17.1.3 Sensitivity analysis 301</p> <p>17.2 Integer Programming 303</p> <p>17.2.1 Basic concepts and branch-and-bound algorithm 303</p> <p>17.2.2 Branch-and-bound using linear programming relaxations 306</p> <p>17.2.3 Mixed integer nonlinear programming 309</p> <p>References 309</p> <p><b>18 Sensitivity Analysis 311</b></p> <p>18.1 Local Sensitivity and Perturbation Analysis 311</p> <p>18.1.1 The B-reliability importance 311</p> <p>18.1.2 The multidirectional sensitivity measure 312</p> <p>18.1.3 The multidirectional differential importance measure and total order importance 317</p> <p>18.1.4 Perturbation analysis 318</p> <p>18.2 Global Sensitivity Analysis 319</p> <p>18.2.1 ANOVA-decomposition based global sensitivity measures 320</p> <p>18.2.2 Elementary effect methods and derivative-based global sensitivity measures 323</p> <p>18.2.3 Relationships between the ANOVA-decomposition-based and the derivativebased</p> <p>sensitivity measures 326</p> <p>18.2.4 The case of random input variables 327</p> <p>18.2.5 Moment-independent sensitivity measures 328</p> <p>18.3 Systems reliability subject to uncertain component reliability 330</p> <p>18.3.1 Software Reliability 332</p> <p>18.4 Broad applications 335</p> <p>References 336</p> <p><b>19 Risk and Safety in Nuclear Power Plants 339</b></p> <p>19.1 Introduction to Probabilistic Risk Analysis and Probabilistic Safety Assessment 339</p> <p>19.2 Probabilistic (Local) ImportanceMeasures 340</p> <p>19.3 Uncertainty and Global Sensitivity Measures 342</p> <p>19.4 A Case Study 343</p> <p>19.5 Review of Applications 345</p> <p>19.6 System Fault Diagnosis and Maintenance 347</p> <p>References 348</p> <p><b>Afterword 350</b></p> <p>References 354</p> <p><b>APPENDIX 355</b></p> <p><b>A Proofs 357</b></p> <p>A.1 Proof of Theorem 8.2.7 357</p> <p>A.2 Proof of Theorem 10.2.10 358</p> <p>A.3 Proof of Theorem 10.2.17 359</p>
<p>“It will definitely be very useful for those interested in studying various structures.”  (<i>Computing Reviews</i>, 5 November 2012)</p> <p> </p>
<p><strong>Professor Way Kuo, City University of Hong Kong</strong><br />Professor Kuo is President and Distinguished Professor of City University of Hong Kong. He served as Distinguished Professor and Dean of Engineering at the University of Tennessee between 2003 and 2008, and between 2000 and 2003 he held the Wisenbaker Chair of Engineering in Innovation and was the Executive Associate Dean of Engineering at Texas A&M University. Professor Kuo is recipient of the IEEE Reliability Society Lifetime Achievement Award, and now serves as the Editor-in-Chief of <em>IEEE Transactions on Reliability</em>. He has co-authored six textbooks and is a member of the U.S. National Academy of Engineering, Academia Sinica (Taiwan), ad International Academy for Quality. He is a fellow of ASQ, ASA, IEEE, INFORMS and IIE. <p><strong>Professor Xiaoyan Zhu, University of Tennessee, USA</strong><br />Professor Zhu is an assistant professor in the Department of Industrial and Information Engineering at University of Tennessee, Knoxville. She has taught both undergraduate and graduate courses in mathematical programming and operations research, for example Operations Research I (Linear Programming), Inventory Control, Production Planning, and Advanced Nonlinear Programming. Professor Zhu has published several papers related to importance measures, and she is a member of INFORMS, IIE, and IEEE.
<p>This unique treatment systematically interprets a spectrum of importance measures to provide a comprehensive overview of their applications in the areas of reliability, network, risk, mathematical programming, and optimization. Investigating the precise relationships among various importance measures, it describes how they are modelled and combined with other design tools to allow users to solve readily many real-world, large-scale decision-making problems. </p> <p>Presenting the state-of-the-art in network analysis, multistate systems, and application in modern systems, this book offers a clear and complete introduction to the topic. Through describing the reliability importance and the fundamentals, it covers advanced topics such as signature of coherent systems, multi-linear functions, and new interpretation of the mathematical programming problems.</p> <p>Key highlights:</p> <ul> <li>Generalizes the concepts behind importance measures (such as sensitivity and perturbation analysis, uncertainty analysis, mathematical programming, network designs), enabling  readers to address large-scale problems within various fields effectively</li> <li>Covers a large range of importance measures, including those in binary coherent systems, binary monotone systems, multistate systems, continuum systems, repairable systems, as well as importance measures of pairs and groups of components</li> <li>Demonstrates numerical and practical applications of importance measures and the related methodologies, including risk analysis in nuclear power plants, cloud computing, software reliability and more</li> <li>Provides thorough comparisons, examples and case studies on relations of different importance measures, with conclusive results based on the authors’ own research</li> <li>Describes reliability design such as redundancy allocation, system upgrading and component assignment.</li> </ul> <p>This book will benefit researchers and practitioners interested in systems design, reliability, risk and optimization, statistics, maintenance, prognostics and operations. Readers can develop feasible approaches to solving various open-ended problems in their research and practical work. Software developers, IT analysts and reliability and safety engineers in nuclear, telecommunications, offshore and civil industries will also find the book useful.</p>

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