Ilya Gertsbakh – författare

Ternary means “based on three”. This book deals with reliability investigations of networks whose components subject to failures can be in three states –up, down and middle (mid), contrary to traditionally considered networks having only binary (up/down) components. Extending binary case to ternary allows to consider more realistic and flexible models for communication, flow and supply networks

The emphasis of this textbook is on industrial applications of Statistical Measurement Theory. It deals with the principal issues of measurement theory, is concise and intelligibly written, and to a wide extent self-contained. Difficult theoretical issues are separated from the mainstream presentation. Each topic starts with an informal introduction followed by an example, the rigorous problem formulation, solution method, and a detailed numerical solution. Each chapter concludes with a set of exercises of increasing difficulty, mostly with solutions. The book is meant as a text for graduate students and a reference for researchers and industrial experts specializing in measurement and measurement data analysis for quality control, quality engineering and industrial process improvement using statistical methods. Knowledge of calculus and fundamental probability and statistics is required for the understanding of its contents.

The increase in the requirements on the reliability of units makes it necessary to analyze the relationship between mathematicalmeth­ ods of calculating reliability and the physical nature of fail­ ures. The difficulty of such an analysis is obvious. On the one hand, in making a representation of the physical picture of a phe­ nomenon, one can make an error in the direction of excessive sim­ plification. On the other hand, in the mathematical treatment of the physical scheme, it may be necessary to use extremely complex and fine analytical methods, and their simplified exposition bor­ ders on vulgarization. Without the aid of a large number of specialists working in the field of analysis and calculation of systems reliability, an ex­ posi tion of models of failures and their mathematical treatment would be unobtainable. The authors take this opportunity to express their gratitude to Academicians N. G. B r u y vic e h and Y u. V. Lin n i k conversations with whom clarified a number of problems treated, to active member of the Academy of Sciences of the UkrSSR B. V.

This textbook on Reliability Theory focusses on Applications in Preventive Maintenance (PM). All models are presented in connection with the relevant statistical material. Short and simply written the book is almost self-contained. The reader needs not more than basic knowledge of calculus, probability and statistics. Each chapter is concluded by a series of exercices with detailed solutions. Numerical solutions are elaborated with Mathematica software. Novel topics are discussed, like PM with learning, choice of the best time-scale for PM, handling multidimensional state description, dealing with uncertainty in data. The book is meant for graduate students, researchers and engineers specializing in Quality Control, Logistics, Reliability and Maintenance Engineering.

The material in this book was first presented as a one-semester graduate course in Measurement Theory for M.Sc. students of the Industrial Engineering De­ partment of Ben Gurion University in the 2000/2001 academic year. The book is devoted to various aspects of the statistical analysis of data arising in the process of measurement. We would like to stress that the book is devoted to general problems arising in processing measurement data and does not deal with various aspects of special measurement techniques. For example, we do not go into the details of how special physical parameters, say ohmic resistance or temperature, should be measured. We also omit the accuracy analysis of particular measurement devices. The Introduction (Chapter 1) gives a general and brief description of the measurement process, defines the measurand and describes different kinds of the measurement error. Chapter 2 is devoted to the point and interval estimation of the popula­ tion mean and standard deviation (variance). It also discusses the normal and uniform distributions, the two most widely used distributions in measurement. We give an overview of the basic rules for operating with means and variances of sums of random variables. This information is particularly important for combining measurement results obtained from different sources. There is a brief description of graphical tools for analyzing sampIe data. This chapter also presents the round-off rules for data presentation.

This textbook on Reliability Theory focusses on Applications in Preventive Maintenance (PM). All models are presented in connection with the relevant statistical material. Short and simply written the book is almost self-contained. The reader needs not more than basic knowledge of calculus, probability and statistics. Each chapter is concluded by a series of exercices with detailed solutions. Numerical solutions are elaborated with Mathematica software. Novel topics are discussed, like PM with learning, choice of the best time-scale for PM, handling multidimensional state description, dealing with uncertainty in data. The book is meant for graduate students, researchers and engineers specializing in Quality Control, Logistics, Reliability and Maintenance Engineering.

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.