Data Uncertainty and Important Measures
1st Edition
Published on 19. January 2018
256 pages
978-1-119-48935-1 (ISBN)
Description
The first part of the book defines the concept of uncertainties and the mathematical frameworks that will be used for uncertainty modeling. The application to system reliability assessment illustrates the concept. In the second part, evidential networks as a new tool to model uncertainty in reliability and risk analysis is proposed and described. Then it is applied on SIS performance assessment and in risk analysis of a heat sink. In the third part, Bayesian and evidential networks are used to deal with important measures evaluation in the context of uncertainties.
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Christophe Simon | Philippe Weber | Mohamed Sallak
Data Uncertainty and Important Measures
Book
01/2018
1st Edition
Wiley-ISTE
€164.50
Shipment within 15-20 days
Persons
Christophe Simon, Université de Lorraine, Centre de Recherche en Automatique de Nancy, France.
Philippe Weber, Université de Lorraine, Centre de Recherche en Automatique de Nancy, France.
Mohamed Sallak, PhD, Associate Professor University of Technologies of Compiègne, France.
Philippe Weber, Université de Lorraine, Centre de Recherche en Automatique de Nancy, France.
Mohamed Sallak, PhD, Associate Professor University of Technologies of Compiègne, France.
Content
1 - Cover [Seite 1]
2 - Half-Title Page [Seite 3]
3 - Title Page [Seite 5]
4 - Copyright Page [Seite 6]
5 - Contents [Seite 7]
6 - Foreword [Seite 13]
7 - Acknowledgments [Seite 15]
8 - 1. Why and Where Uncertainties [Seite 17]
8.1 - 1.1. Sources and forms of uncertainty [Seite 17]
8.2 - 1.2. Types of uncertainty [Seite 19]
8.3 - 1.3. Sources of uncertainty [Seite 19]
8.4 - 1.4. Conclusion [Seite 22]
9 - 2. Models and Language of Uncertainty [Seite 25]
9.1 - 2.1. Introduction [Seite 25]
9.2 - 2.2. Probability theory [Seite 27]
9.2.1 - 2.2.1. Interpretations [Seite 27]
9.2.2 - 2.2.2. Fundamental notions [Seite 29]
9.2.3 - 2.2.3. Discussion [Seite 31]
9.3 - 2.3. Belief functions theory [Seite 31]
9.3.1 - 2.3.1. Representation of beliefs [Seite 32]
9.3.2 - 2.3.2. Combination rules [Seite 34]
9.3.3 - 2.3.3. Extension and marginalization [Seite 36]
9.3.4 - 2.3.4. Pignistic transformation [Seite 36]
9.3.5 - 2.3.5. Discussion [Seite 37]
9.4 - 2.4. Fuzzy set theory [Seite 37]
9.4.1 - 2.4.1. Basic definitions [Seite 38]
9.4.2 - 2.4.2. Operations on fuzzy sets [Seite 38]
9.4.3 - 2.4.3. Fuzzy relations [Seite 39]
9.5 - 2.5. Fuzzy arithmetic [Seite 41]
9.5.1 - 2.5.1. Fuzzy numbers [Seite 42]
9.5.2 - 2.5.2. Fuzzy probabilities [Seite 44]
9.5.3 - 2.5.3. Discussion [Seite 45]
9.6 - 2.6. Possibility theory [Seite 45]
9.6.1 - 2.6.1. Definitions [Seite 46]
9.6.2 - 2.6.2. Possibility and necessity measures [Seite 46]
9.6.3 - 2.6.3. Operations on possibility and necessity measures [Seite 48]
9.7 - 2.7. Random set theory [Seite 48]
9.7.1 - 2.7.1. Basic definitions [Seite 49]
9.7.2 - 2.7.2. Expectation of random sets [Seite 50]
9.7.3 - 2.7.3. Random intervals [Seite 51]
9.7.4 - 2.7.4. Confidence interval [Seite 51]
9.7.5 - 2.7.5. Discussion [Seite 52]
9.8 - 2.8. Confidence structures or c-boxes [Seite 52]
9.8.1 - 2.8.1. Basic notions [Seite 52]
9.8.2 - 2.8.2. Confidence distributions [Seite 53]
9.8.3 - 2.8.3. P-boxes and C-boxes [Seite 54]
9.8.4 - 2.8.4. Discussion [Seite 56]
9.9 - 2.9. Imprecise probability theory [Seite 56]
9.9.1 - 2.9.1. Definitions [Seite 57]
9.9.2 - 2.9.2. Basic properties [Seite 58]
9.9.3 - 2.9.3. Discussion [Seite 60]
9.10 - 2.10. Conclusion [Seite 60]
10 - 3. Risk Graphs and Risk Matrices: Application of Fuzzy Sets and Belief Reasoning [Seite 63]
10.1 - 3.1. SIL allocation scheme [Seite 64]
10.1.1 - 3.1.1. Safety instrumented systems (SIS) [Seite 64]
10.1.2 - 3.1.2. Conformity to standards ANSI/ISA S84.01-1996 and IEC 61508 [Seite 65]
10.1.3 - 3.1.3. Taxonomy of risk/SIL assessment methods [Seite 66]
10.1.4 - 3.1.4. Risk assessment [Seite 66]
10.1.5 - 3.1.5. SIL allocation process [Seite 68]
10.1.6 - 3.1.6. The use of experts' opinions [Seite 69]
10.2 - 3.2. SIL allocation based on possibility theory [Seite 70]
10.2.1 - 3.2.1. Eliciting the experts' opinions [Seite 70]
10.2.2 - 3.2.2. Rating scales for parameters [Seite 71]
10.2.3 - 3.2.3. Subjective elicitation of the risk parameters [Seite 72]
10.2.4 - 3.2.4. Calibration of experts' opinions [Seite 75]
10.2.5 - 3.2.5. Aggregation of the opinions [Seite 77]
10.3 - 3.3. Fuzzy risk graph [Seite 81]
10.3.1 - 3.3.1. Input fuzzy partition and fuzzification [Seite 81]
10.3.2 - 3.3.2. Risk/SIL graph logic by fuzzy inference system [Seite 82]
10.3.3 - 3.3.3. Output fuzzy partition and defuzzification [Seite 83]
10.3.4 - 3.3.4. Illustration case [Seite 85]
10.4 - 3.4. Risk/SIL graph: belief functions reasoning [Seite 88]
10.4.1 - 3.4.1. Elicitation of expert opinions in the belief functions theory [Seite 88]
10.4.2 - 3.4.2. Aggregation of expert opinions [Seite 89]
10.5 - 3.5. Evidential risk graph [Seite 91]
10.6 - 3.6. Numerical illustration [Seite 93]
10.6.1 - 3.6.1. Clustering of experts' opinions [Seite 93]
10.6.2 - 3.6.2. Aggregation of preferences [Seite 94]
10.6.3 - 3.6.3. Evidential risk/SIL graph [Seite 95]
10.7 - 3.7. Conclusion [Seite 97]
11 - 4. Dependability Assessment Considering Interval-valued Probabilities [Seite 99]
11.1 - 4.1. Interval arithmetic [Seite 100]
11.1.1 - 4.1.1. Interval-valued parameters [Seite 100]
11.2 - 4.2. Constraint arithmetic [Seite 106]
11.3 - 4.3. Fuzzy arithmetic [Seite 109]
11.3.1 - 4.3.1. Application example [Seite 111]
11.3.2 - 4.3.2. Monte Carlo sampling approach [Seite 113]
11.4 - 4.4. Discussion [Seite 115]
11.4.1 - 4.4.1. Markov chains [Seite 116]
11.4.2 - 4.4.2. Multiphase Markov chains [Seite 117]
11.4.3 - 4.4.3. Markov chains with fuzzy numbers [Seite 118]
11.4.4 - 4.4.4. Fuzzy modeling of SIS characteristic parameters [Seite 120]
11.5 - 4.5. Illustration [Seite 121]
11.5.1 - 4.5.1. Epistemic approach [Seite 122]
11.5.2 - 4.5.2. Enhanced Markov analysis [Seite 129]
11.6 - 4.6. Decision-making under uncertainty [Seite 131]
11.7 - 4.7. Conclusion [Seite 133]
12 - 5. Evidential Networks [Seite 135]
12.1 - 5.1. Main concepts [Seite 135]
12.1.1 - 5.1.1. Temporal dimension [Seite 137]
12.1.2 - 5.1.2. Computing believe and plausibility measures as bounds [Seite 139]
12.1.3 - 5.1.3. Inference [Seite 140]
12.1.4 - 5.1.4. Modeling imprecision and ignorance in nodes [Seite 142]
12.1.5 - 5.1.5. Conclusion [Seite 144]
12.2 - 5.2. Evidential Network to model and compute Fuzzy probabilities [Seite 144]
12.2.1 - 5.2.1. Fuzzy probability and basic probability assignment [Seite 144]
12.2.2 - 5.2.2. Nested interval-valued probabilities to fuzzy probability [Seite 145]
12.2.3 - 5.2.3. Computation mechanism [Seite 146]
12.3 - 5.3. Evidential Networks to compute p-box [Seite 147]
12.3.1 - 5.3.1. Connection between p-boxes and BPA [Seite 148]
12.3.2 - 5.3.2. P-boxes and interval-valued probabilities [Seite 149]
12.3.3 - 5.3.3. P-boxes and precise probabilities [Seite 149]
12.3.4 - 5.3.4. Time-dependent p-boxes [Seite 150]
12.3.5 - 5.3.5. Computation mechanism [Seite 150]
12.4 - 5.4. Modeling some reliability problems [Seite 152]
12.4.1 - 5.4.1. BPA for reliability problems [Seite 152]
12.4.2 - 5.4.2. Building Boolean CMT (AND, OR) [Seite 153]
12.4.3 - 5.4.3. Conditional mass table for more than two inputs (k-out-of-n:G gate) [Seite 154]
12.4.4 - 5.4.4. Nodes for Pls and Bel in the binary case [Seite 156]
12.4.5 - 5.4.5. Modeling reliability with p-boxes [Seite 156]
12.5 - 5.5. Illustration by application of Evidential Networks [Seite 161]
12.5.1 - 5.5.1. Reliability assessment of system [Seite 161]
12.5.2 - 5.5.2. Inference for failure isolation [Seite 169]
12.5.3 - 5.5.3. Assessing the fuzzy reliability of systems [Seite 171]
12.5.4 - 5.5.4. Assessing the p-box reliability by EN [Seite 178]
12.6 - 5.6. Conclusion [Seite 185]
13 - 6. Reliability Uncertainty and Importance Factors [Seite 187]
13.1 - 6.1. Introduction [Seite 187]
13.2 - 6.2. Hypothesis and notation [Seite 189]
13.3 - 6.3. Probabilistic importance measures of components [Seite 190]
13.3.1 - 6.3.1. Birnbaum importance measure [Seite 191]
13.3.2 - 6.3.2. Component criticality measure [Seite 192]
13.3.3 - 6.3.3. Diagnostic importance measure [Seite 192]
13.3.4 - 6.3.4. Reliability achievement worth (RAW) [Seite 193]
13.3.5 - 6.3.5. Reliability reduction worth (RRW) [Seite 193]
13.3.6 - 6.3.6. Observations and limitations [Seite 194]
13.3.7 - 6.3.7. Importance measures computation [Seite 195]
13.4 - 6.4. Probabilistic importance measures of pairs and groups of components [Seite 195]
13.4.1 - 6.4.1. Measures on minimum cutsets/pathsets/groups [Seite 197]
13.4.2 - 6.4.2. Extension of RAW and RRW to pairs [Seite 198]
13.4.3 - 6.4.3. Joint reliability importance factor (JR) [Seite 198]
13.5 - 6.5. Uncertainty importance measures [Seite 200]
13.5.1 - 6.5.1. Uncertainty probabilistic importance measures [Seite 200]
13.5.2 - 6.5.2. Importance factors with imprecision [Seite 202]
13.6 - 6.6. Importance measures with fuzzy probabilities [Seite 204]
13.6.1 - 6.6.1. Fuzzy importance measures [Seite 205]
13.6.2 - 6.6.2. Fuzzy uncertainty measures [Seite 206]
13.7 - 6.7. Illustration [Seite 207]
13.7.1 - 6.7.1. Importance factors on a simple system [Seite 208]
13.7.2 - 6.7.2. Importance factors in a complex case [Seite 211]
13.7.3 - 6.7.3. Illustration of group importance measures [Seite 213]
13.7.4 - 6.7.4. Uncertainty importance factors [Seite 216]
13.7.5 - 6.7.5. Fuzzy importance measures [Seite 219]
13.8 - 6.8. Conclusion [Seite 222]
14 - Conclusion [Seite 223]
15 - Bibliography [Seite 227]
16 - Index [Seite 241]
17 - Other titles from iSTE in Systems and Industrial Engineering - Robotics [Seite 243]
18 - EULA [Seite 252]
2 - Half-Title Page [Seite 3]
3 - Title Page [Seite 5]
4 - Copyright Page [Seite 6]
5 - Contents [Seite 7]
6 - Foreword [Seite 13]
7 - Acknowledgments [Seite 15]
8 - 1. Why and Where Uncertainties [Seite 17]
8.1 - 1.1. Sources and forms of uncertainty [Seite 17]
8.2 - 1.2. Types of uncertainty [Seite 19]
8.3 - 1.3. Sources of uncertainty [Seite 19]
8.4 - 1.4. Conclusion [Seite 22]
9 - 2. Models and Language of Uncertainty [Seite 25]
9.1 - 2.1. Introduction [Seite 25]
9.2 - 2.2. Probability theory [Seite 27]
9.2.1 - 2.2.1. Interpretations [Seite 27]
9.2.2 - 2.2.2. Fundamental notions [Seite 29]
9.2.3 - 2.2.3. Discussion [Seite 31]
9.3 - 2.3. Belief functions theory [Seite 31]
9.3.1 - 2.3.1. Representation of beliefs [Seite 32]
9.3.2 - 2.3.2. Combination rules [Seite 34]
9.3.3 - 2.3.3. Extension and marginalization [Seite 36]
9.3.4 - 2.3.4. Pignistic transformation [Seite 36]
9.3.5 - 2.3.5. Discussion [Seite 37]
9.4 - 2.4. Fuzzy set theory [Seite 37]
9.4.1 - 2.4.1. Basic definitions [Seite 38]
9.4.2 - 2.4.2. Operations on fuzzy sets [Seite 38]
9.4.3 - 2.4.3. Fuzzy relations [Seite 39]
9.5 - 2.5. Fuzzy arithmetic [Seite 41]
9.5.1 - 2.5.1. Fuzzy numbers [Seite 42]
9.5.2 - 2.5.2. Fuzzy probabilities [Seite 44]
9.5.3 - 2.5.3. Discussion [Seite 45]
9.6 - 2.6. Possibility theory [Seite 45]
9.6.1 - 2.6.1. Definitions [Seite 46]
9.6.2 - 2.6.2. Possibility and necessity measures [Seite 46]
9.6.3 - 2.6.3. Operations on possibility and necessity measures [Seite 48]
9.7 - 2.7. Random set theory [Seite 48]
9.7.1 - 2.7.1. Basic definitions [Seite 49]
9.7.2 - 2.7.2. Expectation of random sets [Seite 50]
9.7.3 - 2.7.3. Random intervals [Seite 51]
9.7.4 - 2.7.4. Confidence interval [Seite 51]
9.7.5 - 2.7.5. Discussion [Seite 52]
9.8 - 2.8. Confidence structures or c-boxes [Seite 52]
9.8.1 - 2.8.1. Basic notions [Seite 52]
9.8.2 - 2.8.2. Confidence distributions [Seite 53]
9.8.3 - 2.8.3. P-boxes and C-boxes [Seite 54]
9.8.4 - 2.8.4. Discussion [Seite 56]
9.9 - 2.9. Imprecise probability theory [Seite 56]
9.9.1 - 2.9.1. Definitions [Seite 57]
9.9.2 - 2.9.2. Basic properties [Seite 58]
9.9.3 - 2.9.3. Discussion [Seite 60]
9.10 - 2.10. Conclusion [Seite 60]
10 - 3. Risk Graphs and Risk Matrices: Application of Fuzzy Sets and Belief Reasoning [Seite 63]
10.1 - 3.1. SIL allocation scheme [Seite 64]
10.1.1 - 3.1.1. Safety instrumented systems (SIS) [Seite 64]
10.1.2 - 3.1.2. Conformity to standards ANSI/ISA S84.01-1996 and IEC 61508 [Seite 65]
10.1.3 - 3.1.3. Taxonomy of risk/SIL assessment methods [Seite 66]
10.1.4 - 3.1.4. Risk assessment [Seite 66]
10.1.5 - 3.1.5. SIL allocation process [Seite 68]
10.1.6 - 3.1.6. The use of experts' opinions [Seite 69]
10.2 - 3.2. SIL allocation based on possibility theory [Seite 70]
10.2.1 - 3.2.1. Eliciting the experts' opinions [Seite 70]
10.2.2 - 3.2.2. Rating scales for parameters [Seite 71]
10.2.3 - 3.2.3. Subjective elicitation of the risk parameters [Seite 72]
10.2.4 - 3.2.4. Calibration of experts' opinions [Seite 75]
10.2.5 - 3.2.5. Aggregation of the opinions [Seite 77]
10.3 - 3.3. Fuzzy risk graph [Seite 81]
10.3.1 - 3.3.1. Input fuzzy partition and fuzzification [Seite 81]
10.3.2 - 3.3.2. Risk/SIL graph logic by fuzzy inference system [Seite 82]
10.3.3 - 3.3.3. Output fuzzy partition and defuzzification [Seite 83]
10.3.4 - 3.3.4. Illustration case [Seite 85]
10.4 - 3.4. Risk/SIL graph: belief functions reasoning [Seite 88]
10.4.1 - 3.4.1. Elicitation of expert opinions in the belief functions theory [Seite 88]
10.4.2 - 3.4.2. Aggregation of expert opinions [Seite 89]
10.5 - 3.5. Evidential risk graph [Seite 91]
10.6 - 3.6. Numerical illustration [Seite 93]
10.6.1 - 3.6.1. Clustering of experts' opinions [Seite 93]
10.6.2 - 3.6.2. Aggregation of preferences [Seite 94]
10.6.3 - 3.6.3. Evidential risk/SIL graph [Seite 95]
10.7 - 3.7. Conclusion [Seite 97]
11 - 4. Dependability Assessment Considering Interval-valued Probabilities [Seite 99]
11.1 - 4.1. Interval arithmetic [Seite 100]
11.1.1 - 4.1.1. Interval-valued parameters [Seite 100]
11.2 - 4.2. Constraint arithmetic [Seite 106]
11.3 - 4.3. Fuzzy arithmetic [Seite 109]
11.3.1 - 4.3.1. Application example [Seite 111]
11.3.2 - 4.3.2. Monte Carlo sampling approach [Seite 113]
11.4 - 4.4. Discussion [Seite 115]
11.4.1 - 4.4.1. Markov chains [Seite 116]
11.4.2 - 4.4.2. Multiphase Markov chains [Seite 117]
11.4.3 - 4.4.3. Markov chains with fuzzy numbers [Seite 118]
11.4.4 - 4.4.4. Fuzzy modeling of SIS characteristic parameters [Seite 120]
11.5 - 4.5. Illustration [Seite 121]
11.5.1 - 4.5.1. Epistemic approach [Seite 122]
11.5.2 - 4.5.2. Enhanced Markov analysis [Seite 129]
11.6 - 4.6. Decision-making under uncertainty [Seite 131]
11.7 - 4.7. Conclusion [Seite 133]
12 - 5. Evidential Networks [Seite 135]
12.1 - 5.1. Main concepts [Seite 135]
12.1.1 - 5.1.1. Temporal dimension [Seite 137]
12.1.2 - 5.1.2. Computing believe and plausibility measures as bounds [Seite 139]
12.1.3 - 5.1.3. Inference [Seite 140]
12.1.4 - 5.1.4. Modeling imprecision and ignorance in nodes [Seite 142]
12.1.5 - 5.1.5. Conclusion [Seite 144]
12.2 - 5.2. Evidential Network to model and compute Fuzzy probabilities [Seite 144]
12.2.1 - 5.2.1. Fuzzy probability and basic probability assignment [Seite 144]
12.2.2 - 5.2.2. Nested interval-valued probabilities to fuzzy probability [Seite 145]
12.2.3 - 5.2.3. Computation mechanism [Seite 146]
12.3 - 5.3. Evidential Networks to compute p-box [Seite 147]
12.3.1 - 5.3.1. Connection between p-boxes and BPA [Seite 148]
12.3.2 - 5.3.2. P-boxes and interval-valued probabilities [Seite 149]
12.3.3 - 5.3.3. P-boxes and precise probabilities [Seite 149]
12.3.4 - 5.3.4. Time-dependent p-boxes [Seite 150]
12.3.5 - 5.3.5. Computation mechanism [Seite 150]
12.4 - 5.4. Modeling some reliability problems [Seite 152]
12.4.1 - 5.4.1. BPA for reliability problems [Seite 152]
12.4.2 - 5.4.2. Building Boolean CMT (AND, OR) [Seite 153]
12.4.3 - 5.4.3. Conditional mass table for more than two inputs (k-out-of-n:G gate) [Seite 154]
12.4.4 - 5.4.4. Nodes for Pls and Bel in the binary case [Seite 156]
12.4.5 - 5.4.5. Modeling reliability with p-boxes [Seite 156]
12.5 - 5.5. Illustration by application of Evidential Networks [Seite 161]
12.5.1 - 5.5.1. Reliability assessment of system [Seite 161]
12.5.2 - 5.5.2. Inference for failure isolation [Seite 169]
12.5.3 - 5.5.3. Assessing the fuzzy reliability of systems [Seite 171]
12.5.4 - 5.5.4. Assessing the p-box reliability by EN [Seite 178]
12.6 - 5.6. Conclusion [Seite 185]
13 - 6. Reliability Uncertainty and Importance Factors [Seite 187]
13.1 - 6.1. Introduction [Seite 187]
13.2 - 6.2. Hypothesis and notation [Seite 189]
13.3 - 6.3. Probabilistic importance measures of components [Seite 190]
13.3.1 - 6.3.1. Birnbaum importance measure [Seite 191]
13.3.2 - 6.3.2. Component criticality measure [Seite 192]
13.3.3 - 6.3.3. Diagnostic importance measure [Seite 192]
13.3.4 - 6.3.4. Reliability achievement worth (RAW) [Seite 193]
13.3.5 - 6.3.5. Reliability reduction worth (RRW) [Seite 193]
13.3.6 - 6.3.6. Observations and limitations [Seite 194]
13.3.7 - 6.3.7. Importance measures computation [Seite 195]
13.4 - 6.4. Probabilistic importance measures of pairs and groups of components [Seite 195]
13.4.1 - 6.4.1. Measures on minimum cutsets/pathsets/groups [Seite 197]
13.4.2 - 6.4.2. Extension of RAW and RRW to pairs [Seite 198]
13.4.3 - 6.4.3. Joint reliability importance factor (JR) [Seite 198]
13.5 - 6.5. Uncertainty importance measures [Seite 200]
13.5.1 - 6.5.1. Uncertainty probabilistic importance measures [Seite 200]
13.5.2 - 6.5.2. Importance factors with imprecision [Seite 202]
13.6 - 6.6. Importance measures with fuzzy probabilities [Seite 204]
13.6.1 - 6.6.1. Fuzzy importance measures [Seite 205]
13.6.2 - 6.6.2. Fuzzy uncertainty measures [Seite 206]
13.7 - 6.7. Illustration [Seite 207]
13.7.1 - 6.7.1. Importance factors on a simple system [Seite 208]
13.7.2 - 6.7.2. Importance factors in a complex case [Seite 211]
13.7.3 - 6.7.3. Illustration of group importance measures [Seite 213]
13.7.4 - 6.7.4. Uncertainty importance factors [Seite 216]
13.7.5 - 6.7.5. Fuzzy importance measures [Seite 219]
13.8 - 6.8. Conclusion [Seite 222]
14 - Conclusion [Seite 223]
15 - Bibliography [Seite 227]
16 - Index [Seite 241]
17 - Other titles from iSTE in Systems and Industrial Engineering - Robotics [Seite 243]
18 - EULA [Seite 252]
