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Data Uncertainty and Important Measures [Hardback]

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  • Formāts: Hardback, 256 pages, height x width x depth: 239x163x20 mm, weight: 499 g
  • Izdošanas datums: 09-Jan-2018
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1848219938
  • ISBN-13: 9781848219939
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Data Uncertainty and Important MeasuresPalielināt
  • Formāts: Hardback, 256 pages, height x width x depth: 239x163x20 mm, weight: 499 g
  • Izdošanas datums: 09-Jan-2018
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1848219938
  • ISBN-13: 9781848219939
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781848219939.html
Keywords:

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.

Foreword xi
Acknowledgments xiii
Chapter 1 Why and Where Uncertainties 1(8)
1.1 Sources and forms of uncertainty
1(2)
1.2 Types of uncertainty
3(1)
1.3 Sources of uncertainty
3(3)
1.4 Conclusion
6(3)
Chapter 2 Models and Language of Uncertainty 9(38)
2.1 Introduction
9(2)
2.2 Probability theory
11(4)
2.2.1 Interpretations
11(2)
2.2.2 Fundamental notions
13(2)
2.2.3 Discussion
15(1)
2.3 Belief functions theory
15(6)
2.3.1 Representation of beliefs
16(2)
2.3.2 Combination rules
18(2)
2.3.3 Extension and marginalization
20(1)
2.3.4 Pignistic transformation
20(1)
2.3.5 Discussion
21(1)
2.4 Fuzzy set theory
21(4)
2.4.1 Basic definitions
22(1)
2.4.2 Operations on fuzzy sets
22(1)
2.4.3 Fuzzy relations
23(2)
2.5 Fuzzy arithmetic
25(4)
2.5.1 Fuzzy numbers
26(2)
2.5.2 Fuzzy probabilities
28(1)
2.5.3 Discussion
29(1)
2.6 Possibility theory
29(3)
2.6.1 Definitions
30(1)
2.6.2 Possibility and necessity measures
30(2)
2.6.3 Operations on possibility and necessity measures
32(1)
2.7 Random set theory
32(4)
2.7.1 Basic definitions
33(1)
2.7.2 Expectation of random sets
34(1)
2.7.3 Random intervals
35(1)
2.7.4 Confidence interval
35(1)
2.7.5 Discussion
36(1)
2.8 Confidence structures or c-boxes
36(4)
2.8.1 Basic notions
36(1)
2.8.2 Confidence distributions
37(1)
2.8.3 P-boxes and C-boxes
38(2)
2.8.4 Discussion
40(1)
2.9 Imprecise probability theory
40(4)
2.9.1 Definitions
41(1)
2.9.2 Basic properties
42(2)
2.9.3 Discussion
44(1)
2.10 Conclusion
44(3)
Chapter 3 Risk Graphs and Risk Matrices: Application of Fuzzy Sets and Belief Reasoning 47(36)
3.1 SIL allocation scheme
48(6)
3.1.1 Safety instrumented systems (SIS)
48(1)
3.1.2 Conformity to standards ANSUISA S84.01-1996 and IEC 61508
49(1)
3.1.3 Taxonomy of risk/SIL assessment methods
50(1)
3.1.4 Risk assessment
50(2)
3.1.5 SIL allocation process
52(1)
3.1.6 The use of experts' opinions
53(1)
3.2 SIL allocation based on possibility theory
54(11)
3.2.1 Eliciting the experts' opinions
54(1)
3.2.2 Rating scales for parameters
55(1)
3.2.3 Subjective elicitation of the risk parameters
56(3)
3.2.4 Calibration of experts' opinions
59(2)
3.2.5 Aggregation of the opinions
61(4)
3.3 Fuzzy risk graph
65(7)
3.3.1 Input fuzzy partition and fuzzification
65(1)
3.3.2 Risk/SIL graph logic by fuzzy inference system
66(1)
3.3.3 Output fuzzy partition and defuzzification
67(2)
3.3.4 Illustration case
69(3)
3.4 Risk/SIL graph: belief functions reasoning
72(3)
3.4.1 Elicitation of expert opinions in the belief functions theory
72(1)
3.4.2 Aggregation of expert opinions
73(2)
3.5 Evidential risk graph
75(2)
3.6 Numerical illustration
77(4)
3.6.1 Clustering of experts' opinions
77(1)
3.6.2 Aggregation of preferences
78(1)
3.6.3 Evidential risk/SIL graph
79(2)
3.7 Conclusion
81(2)
Chapter 4 Dependability Assessment Considering Interval-valued Probabilities 83(36)
4.1 Interval arithmetic
84(6)
4.1.1 Interval-valued parameters
84(1)
4.1.2 Interval-valued reliability
85(1)
4.1.3 Assessing the imprecise average probability of failure on demand
86(4)
4.2 Constraint arithmetic
90(3)
4.3 Fuzzy arithmetic
93(6)
4.3.1 Application example
95(2)
4.3.2 Monte Carlo sampling approach
97(2)
4.4 Discussion
99(6)
4.4.1 Markov chains
100(1)
4.4.2 Multiphase Markov chains
101(1)
4.4.3 Markov chains with fuzzy numbers
102(2)
4.4.4 Fuzzy modeling of SIS characteristic parameters
104(1)
4.5 Illustration
105(10)
4.5.1 Epistemic approach
106(7)
4.5.2 Enhanced Markov analysis
113(2)
4.6 Decision-making under uncertainty
115(2)
4.7 Conclusion
117(2)
Chapter 5 Evidential Networks 119(52)
5.1 Main concepts
119(9)
5.1.1 Temporal dimension
121(2)
5.1.2 Computing believe and plausibility measures as bounds
123(1)
5.1.3 Inference
124(2)
5.1.4 Modeling imprecision and ignorance in nodes
126(2)
5.1.5 Conclusion
128(1)
5.2 Evidential Network to model and compute Fuzzy probabilities
128(3)
5.2.1 Fuzzy probability and basic probability assignment
128(1)
5.2.2 Nested interval-valued probabilities to fuzzy probability
129(1)
5.2.3 Computation mechanism
130(1)
5.3 Evidential Networks to compute p-box
131(5)
5.3.1 Connection between p-boxes and BPA
132(1)
5.3.2 P-boxes and interval-valued probabilities
133(1)
5.3.3 P-boxes and precise probabilities
133(1)
5.3.4 Time-dependent p-boxes
134(1)
5.3.5 Computation mechanism
134(2)
5.4 Modeling some reliability problems
136(9)
5.4.1 BPA for reliability problems
136(1)
5.4.2 Building Boolean CMT (AND, OR)
137(1)
5.4.3 Conditional mass table for more than two inputs (k-out-of-n:G gate)
138(2)
5.4.4 Nodes for Pls and Bel in the binary case
140(1)
5.4.5 Modeling reliability with p-boxes
140(5)
5.5 Illustration by application of Evidential Networks
145(24)
5.5.1 Reliability assessment of system
145(8)
5.5.2 Inference for failure isolation
153(2)
5.5.3 Assessing the fuzzy reliability of systems
155(7)
5.5.4 Assessing the p-box reliability by EN
162(7)
5.6 Conclusion
169(2)
Chapter 6 Reliability Uncertainty and Importance Factors 171(36)
6.1 Introduction
171(2)
6.2 Hypothesis and notation
173(1)
6.3 Probabilistic importance measures of components
174(5)
6.3.1 Birnbaum importance measure
175(1)
6.3.2 Component criticality measure
176(1)
6.3.3 Diagnostic importance measure
176(1)
6.3.4 Reliability achievement worth (RAW)
177(1)
6.3.5 Reliability reduction worth (RRW)
177(1)
6.3.6 Observations and limitations
178(1)
6.3.7 Importance measures computation
179(1)
6.4 Probabilistic importance measures of pairs and groups of components
179(5)
6.4.1 Measures on minimum cutsets/pathsets/groups
181(1)
6.4.2 Extension of RAW and RRW to pairs
182(1)
6.4.3 Joint reliability importance factor (JR)
182(2)
6.5 Uncertainty importance measures
184(4)
6.5.1 Uncertainty probabilistic importance measures
184(2)
6.5.2 Importance factors with imprecision
186(2)
6.6 Importance measures with fuzzy probabilities
188(3)
6.6.1 Fuzzy importance measures
189(1)
6.6.2 Fuzzy uncertainty measures
190(1)
6.7 Illustration
191(15)
6.7.1 Importance factors on a simple system
192(3)
6.7.2 Importance factors in a complex case
195(2)
6.7.3 Illustration of group importance measures
197(3)
6.7.4 Uncertainty importance factors
200(3)
6.7.5 Fuzzy importance measures
203(3)
6.8 Conclusion
206(1)
Conclusion 207(4)
Bibliography 211(14)
Index 225
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 Compičgne, France.