This introductory book equips the reader to apply the core concepts and methods of network reliability analysis to real-life problems. It explains the modeling and critical analysis of systems and probabilistic networks, and requires only a minimal background in probability theory and computer programming.

Based on the lecture notes of eight courses taught by the authors, the book is also self-contained, with no theory needed beyond the lectures. The primary focus is on essential "modus operandi," which are illustrated in numerous examples and presented separately from the more difficult theoretical material.

1. Probability and Statistics: a short reminder.

       Basic laws of probability.

       Discrete and Continuous random variables.

       Density function. Cumulative distribution function.

       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