Ilʹja B. Gercbach Livres

This book is devoted to the probabilistic description of the behavior of a network in the process of random removal of its components (links, nodes) appearing as a result of technical failures, natural disasters or intentional attacks. It is focused on a practical approach to network reliability and resilience evaluation, based on applications of Monte Carlo methodology to numerical approximation of network combinatorial invariants, including so-called multidimensional destruction spectra. This allows to develop a probabilistic follow-up analysis of the network in the process of its gradual destruction, to identify most important network components and to develop efficient heuristic algorithms for network optimal design. Our methodology works with satisfactory accuracy and efficiency for most applications of reliability theory to real –life problems in networks.

The material in this book was initially presented as a graduate course in Measurement Theory for M. Sc. students at Ben Gurion University during the 2000/2001 academic year. It focuses on the statistical analysis of data from measurement processes, emphasizing general issues in processing measurement data rather than specific measurement techniques. The text does not delve into how to measure particular physical parameters, such as ohmic resistance or temperature, nor does it analyze the accuracy of specific measurement devices. The Introduction (Chapter 1) provides a concise overview of the measurement process, defines the measurand, and outlines various types of measurement errors. Chapter 2 covers point and interval estimation of population mean and standard deviation (variance), discussing normal and uniform distributions, which are the most commonly used in measurement contexts. It also reviews fundamental rules for handling means and variances of sums of random variables, crucial for integrating measurement results from diverse sources. Additionally, this chapter includes a brief overview of graphical tools for sample data analysis and presents round-off rules for data presentation.

The material in this book originated from a one-semester course on Reliability Theory and Preventive Maintenance for M. Sc. students at Ben Gurion University during the 1997/98 and 1998/99 academic years. Engineering students primarily focus on the applied aspects of this theory. The effectiveness of preventive maintenance theory hinges on the handling of statistical reliability data, which is often challenging due to the nature of system lifetime data collection. Typically, the available data is incomplete and heavily censored. To enhance the applicability of the course material, topics such as modeling system lifetime distributions and maximum likelihood techniques for processing lifetime data are included. A prior course in statistics is required, as standard courses often overlook essential techniques. Chapter 3 provides a brief overview of these techniques, including commonly used probability plotting. Chapter 4 discusses popular models of preventive maintenance and replacement, addressing practical aspects like managing data uncertainty, the impact of data contamination, and the opportunistic scheduling of maintenance activities. This structured approach aims to equip students with the necessary tools to apply reliability theory effectively in real-world scenarios.