Network Reliability: A Lecture Course

ISBN-13: 9789811514579 / Angielski / Miękka / 2020 / 90 str.

Ilya Gertsbakh; Yoseph Shpungin

Spis treści

1. Probability and Statistics: a short reminder.

       Basic laws of probability.

       Discrete and Continuous random variables.

       Density function. Cumulative distribution function.

       Expected value of random variable. Variance, standard deviation.

       Population. Random Sample. Sample mean, Variance of the sample mean.

       Point estimation. Unbiased Estimator.

 

2. The concept of network.

       General description. Network topology.

       Different criteria for performance of Networks.

       Reliability indices.

 

3. Network Static and Dynamic Reliability.

       Definitions of static and dynamic Network Reliability

       Reliability straightforward computation. Examples.

       Minimal Path-set and Cut-set methods. Examples.

    Structure function and Network Reliability. Examples.               

       Burtin-Pittel approximation to Network Reliability. Examples.

 

4. Monte Carlo method for evaluating network reliability.

       Basic Monte Carlo notions.

       Pseudocode for network reliability evaluation by CMC. Examples.

       Why CMC is not sufficient for all cases?

 

5.  Lomonosov’s “Turnip” for Network Reliability evaluation.

        In which cases the approach most applicable?

        The idea of the turnip.  Example.

        Network reliability evaluation by turnip.

        Pseudocode for the appropriate algorithm.

 

6. Destruction and Construction  spectrum and Network Reliability.

      In which cases the approach most applicable?

      The idea of the method.

      Examples for some criterions.

      Pseudocode for network reliability evaluation using spectra.

 

7. Importance Measure and spectrum.

       What is Birnbaum Importance Measure?

       Examples of straightforward computation of BIM.

       BIM-spectrum. Examples.

       Computation of BIM by BIM-spectrum. Examples.

       Pseudocode of BIM evaluation.

 

8. Appendix    sintax, convolution

 

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O autorze

Ilya B. Gertsbakh is Professor Emeritus in the Department of Mathematics at Ben-Gurion University of the Negev, Israel. He is author or coauthor of seven books, the recent of which is “Ternary networks: Reliability and Monte Carlo” (with Yoseph Shpungin and Radislav Vaisman), published by Springer in 2014. Ilya Gertsbakh has published some 100 papers on topics in operations research, reliability, applied probability and applied statistics. He received M.Sc degrees in mechanical engineering and mathematics (1961) from Latvian State University in Riga, Latvia, and the Ph.D. degree (1964) in applied probability and statistics from Latvian Academy of Sciences, also in Riga.

  

  Yoseph Shpungin is Professor Emeritus in the Software Engineering Department, at Shamoon College of Engineering, Beer Sheva, Israel. He is a coauthor of three books and numerous publications in international scientific journals. He received his M.Sc degree in mathematics (1969) from Latvian State University in Riga, Latvia, and Ph.D. degree (1997) in mathematics from Ben Gurion University, Beer Sheva, Israel.