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Probabilistic Reliability Models [Kõva köide]

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(SOTAS, Inc. and George Washington University)
  • Formaat: Hardback, 248 pages, kõrgus x laius x paksus: 236x158x20 mm, kaal: 544 g
  • Ilmumisaeg: 06-Nov-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111834183X
  • ISBN-13: 9781118341834
Teised raamatud teemal:
Probabilistic Reliability ModelsSuurem pilt
  • Formaat: Hardback, 248 pages, kõrgus x laius x paksus: 236x158x20 mm, kaal: 544 g
  • Ilmumisaeg: 06-Nov-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 111834183X
  • ISBN-13: 9781118341834
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781118341834.html
Märksõnad:
Practical Approaches to Reliability Theory in Cutting-Edge Applications

Probabilistic Reliability Models helps readers understand and properly use statistical methods

and optimal resource allocation to solve engineering problems.

The author supplies engineers with a deeper understanding of mathematical models while also

equipping mathematically oriented readers with a fundamental knowledge of the engineeringrelated

applications at the center of model building. The book showcases the use of probability

theory and mathematical statistics to solve common, real-world reliability problems. Following

an introduction to the topic, subsequent chapters explore key systems and models including:

Unrecoverable objects and recoverable systems

Methods of direct enumeration

Markov models and heuristic models

Performance effectiveness

Time redundancy

System survivability

Aging units and their related systems

Multistate systems

Detailed case studies illustrate the relevance of the discussed methods to real-world technical

projects including software failure avalanches, gas pipelines with underground storage, and

intercontinental ballistic missile (ICBM) control systems. Numerical examples and detailed

explanations accompany each topic, and exercises throughout allow readers to test their

comprehension of the presented material.

Probabilistic Reliability Models is an excellent book for statistics, engineering, and operations

research courses on applied probability at the upper-undergraduate and graduate levels. The

book is also a valuable reference for professionals and researchers working in industry who

would like a mathematical review of reliability models and the relevant applications.
Preface xiii
Acronyms and Notations xv
1 What Is Reliability?
1(8)
1.1 Reliability as a Property of Technical Objects
1(1)
1.2 Other "Ilities"
2(3)
1.3 Hierarchical Levels of Analyzed Objects
5(1)
1.4 How Can Reliability Be Measured?
5(2)
1.5 Software Reliability
7(2)
1.5.1 Case Study: Avalanche of Software Failures
8(1)
2 Unrecoverable Objects
9(31)
2.1 Unit
9(2)
2.1.1 Probability of Failure-Free Operation
9(1)
2.1.2 Mean Time to Failure
10(1)
2.2 Series Systems
11(3)
2.2.1 Probability of Failure-Free Operation
11(2)
2.2.2 Mean Time to Failure
13(1)
2.3 Parallel System
14(6)
2.3.1 Probability of Failure-Free Operation
14(4)
2.3.2 Mean Time to Failure
18(2)
2.4 Structure of Type "k-out-of-n"
20(2)
2.5 Realistic Models of Loaded Redundancy
22(6)
2.5.1 Unreliable Switching Process
23(1)
2.5.2 Non-Instant Switching
23(1)
2.5.3 Unreliable Switch
24(1)
2.5.4 Switch Serving as Interface
25(1)
2.5.5 Incomplete Monitoring of the Operating Unit
26(2)
2.5.6 Periodical Monitoring of the Operating Unit
28(1)
2.6 Reducible Structures
28(2)
2.6.1 Parallel-Series and Series-Parallel Structures
28(1)
2.6.2 General Case of Reducible Structures
29(1)
2.7 Standby Redundancy
30(4)
2.7.1 Simple Redundant Group
30(3)
2.7.2 Standby Redundancy of Type "k-out-of-n"
33(1)
2.8 Realistic Models of Unloaded Redundancy
34(6)
2.8.1 Unreliable Switching Process
34(1)
2.8.2 Non-Instant Switching
35(1)
2.8.3 Unreliable Switch
35(2)
2.8.4 Switch Serving as Interface
37(1)
2.8.5 Incomplete Monitoring of the Operating Unit
38(2)
3 Recoverable Systems: Markov Models
40(32)
3.1 Unit
40(7)
3.1.1 Markov Model
41(6)
3.2 Series System
47(6)
3.2.1 Turning Off System During Recovery
47(2)
3.2.2 System in Operating State During Recovery: Unrestricted Repair
49(2)
3.2.3 System in Operating State During Recovery: Restricted Repair
51(2)
3.3 Dubbed System
53(12)
3.3.1 General Description
53(1)
3.3.2 Nonstationary Availability Coefficient
54(4)
3.3.3 Stationary Availability Coefficient
58(1)
3.3.4 Probability of Failure-Free Operation
59(3)
3.3.5 Stationary Coefficient of Interval Availability
62(1)
3.3.6 Mean Time to Failure
63(1)
3.3.7 Mean Time Between Failures
63(2)
3.3.8 Mean Recovery Time
65(1)
3.4 Parallel Systems
65(1)
3.5 Structures of Type "m-out-of-n"
66(6)
4 Recoverable Systems: Heuristic Models
72(23)
4.1 Preliminary Notes
72(3)
4.2 Poisson Process
75(3)
4.3 Procedures over Poisson Processes
78(2)
4.3.1 Thinning Procedure
78(2)
4.3.2 Superposition Procedure
80(1)
4.4 Asymptotic Thinning Procedure over Stochastic Point Process
80(2)
4.5 Asymptotic Superposition of Stochastic Point Processes
82(2)
4.6 Intersection of Flows of Narrow Impulses
84(3)
4.7 Heuristic Method for Reliability Analysis of Series Recoverable Systems
87(1)
4.8 Heuristic Method for Reliability Analysis of Parallel Recoverable Systems
87(6)
4.8.1 Influence of Unreliable Switching Procedure
88(1)
4.8.2 Influence of Switch's Unreliability
89(1)
4.8.3 Periodical Monitoring of the Operating Unit
90(1)
4.8.4 Partial Monitoring of the Operating Unit
91(2)
4.9 Brief Historical Overview and Related Sources
93(2)
5 Time Redundancy
95(8)
5.1 System with Possibility of Restarting Operation
95(3)
5.2 Systems with "Admissibly Short Failures"
98(1)
5.3 Systems with Time Accumulation
99(1)
5.4 Case Study: Gas Pipeline with an Underground Storage
100(2)
5.5 Brief Historical Overview and Related Sources
102(1)
6 "Aging" Units and Systems of "Aging" Units
103(20)
6.1 Chebyshev Bound
103(1)
6.2 "Aging" Unit
104(1)
6.3 Bounds for Probability of Failure-Free Operations
105(3)
6.4 Series System Consisting of "Aging" Units
108(2)
6.4.1 Preliminary Lemma
108(2)
6.5 Series System
110(4)
6.5.1 Probability of Failure-Free Operation
110(2)
6.5.2 Mean Time to Failure of a Series System
112(2)
6.6 Parallel System
114(5)
6.6.1 Probability of Failure-Free Operation
114(3)
6.6.2 Mean Time to Failure
117(2)
6.7 Bounds for the Coefficient of Operational Availability
119(2)
6.8 Brief Historical Overview and Related Sources
121(2)
7 Two-Pole Networks
123(20)
7.1 General Comments
123(4)
7.1.1 Method of Direct Enumeration
125(2)
7.2 Method of Boolean Function Decomposition
127(3)
7.3 Method of Paths and Cuts
130(10)
7.3.1 Esary-Proschan Bounds
130(3)
7.3.2 "Improvements" of Esary-Proschan Bounds
133(2)
7.3.3 Litvak-Ushakov Bounds
135(4)
7.3.4 Comparison of the Two Methods
139(1)
7.4 Brief Historical Overview and Related Sources
140(3)
8 Performance Effectiveness
143(19)
8.1 Effectiveness Concepts
143(2)
8.2 General Idea of Effectiveness Evaluation
145(5)
8.2.1 Conditional Case Study: Airport Traffic Control System
147(3)
8.3 Additive Type of System Units' Outcomes
150(1)
8.4 Case Study: ICBM Control System
151(2)
8.5 Systems with Intersecting Zones of Action
153(5)
8.6 Practical Recommendation
158(2)
8.7 Brief Historical Overview and Related Sources
160(2)
9 System Survivability
162(7)
9.1 Illustrative Example
166(1)
9.2 Brief Historical Overview and Related Sources
167(2)
10 Multistate Systems
169(26)
10.1 Preliminary Notes
169(1)
10.2 Generating Function
169(3)
10.3 Universal Generating Function
172(2)
10.4 Multistate Series System
174(7)
10.4.1 Series Connection of Piping Runs
174(3)
10.4.2 Series Connection of Resistors
177(2)
10.4.3 Series Connections of Capacitors
179(2)
10.5 Multistate Parallel System
181(2)
10.5.1 Parallel Connection of Piping Runs
181(1)
10.5.2 Parallel Connection of Resistors
182(1)
10.5.3 Parallel Connections of Capacitors
182(1)
10.6 Reducible Systems
183(7)
10.7 Conclusion
190(1)
10.8 Brief Historical Overview and Related Sources
190(5)
Appendix A Main Distributions Related to Reliability Theory
195(14)
A.1 Discrete Distributions
195(6)
A.1.1 Degenerate Distribution
195(1)
A.1.2 Bernoulli Distribution
196(1)
A.1.3 Binomial Distribution
197(1)
A.1.4 Poisson Distribution
198(2)
A.1.5 Geometric Distribution
200(1)
A.2 Continuous Distributions
201(8)
A.2.1 Intensity Function
201(1)
A.2.2 Continuous Uniform Distribution
202(1)
A.2.3 Exponential Distribution
203(1)
A.2.4 Erlang Distribution
204(1)
A.2.5 Hyperexponential Distribution
205(2)
A.2.6 Normal Distribution
207(1)
A.2.7 Weibull-Gnedenko Distribution
207(2)
Appendix B Laplace Transformation
209(5)
Appendix C Markov Processes
214(13)
C.1 General Markov Process
214(9)
C.1.1 Nonstationary Availability Coefficient
216(2)
C.1.2 Probability of Failure-Free Operation
218(2)
C.1.3 Stationary Availability Coefficient
220(1)
C.1.4 Mean Time to Failure and Mean Time Between Failures
221(1)
C.1.5 Mean Recovery Time
222(1)
C.2 Birth-Death Process
223(4)
Appendix D General Bibliography
227(4)
Index 231
IGOR USHAKOV, PhD, is Senior Consultant at Advanced Logistics Developments in Tel Aviv, Israel. He has published extensively in his areas of research interest, which include operations research, applied statistics, and probabilistic modeling. Dr. Ushakov is the author of Handbook of Reliability Engineering as well as the coauthor of Probabilistic Reliability Engineering and Statistical Reliability Engineering, all published by Wiley.