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Gregory Levitin

Bio: Gregory Levitin is an academic researcher from Southwest Jiaotong University. The author has contributed to research in topics: Reliability (statistics) & Redundancy (engineering). The author has an hindex of 50, co-authored 363 publications receiving 10729 citations. Previous affiliations of Gregory Levitin include Technion – Israel Institute of Technology & University of Electronic Science and Technology of China.


Papers
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Book
01 Jan 2003
TL;DR: Basic concepts of Multi-State Systems (MSS) Boolean methods extension for MSS reliability analysis basic random process methods for M SS reliability assessment Universal Generating Function (UGF) models MSSreliability optimization application problems.
Abstract: Basic concepts of Multi-State Systems (MSS) Boolean methods extension for MSS reliability analysis basic random process methods for MSS reliability assessment Universal Generating Function (UGF) models MSS reliability optimization application problems.

850 citations

Book
15 Sep 2008
TL;DR: The Universal Generating Function in Reliability Analysis and Optimization (UGO) as discussed by the authors is a comprehensive description of the universal generating function technique and its applications in binary and multi-state system reliability analysis.
Abstract: Many real systems are composed of multi-state components with different performance levels and several failure modes. These affect the whole system's performance. Most books on reliability theory cover binary models that allow a system only to function perfectly or fail completely. "The Universal Generating Function in Reliability Analysis and Optimization" is the first book that gives a comprehensive description of the universal generating function technique and its applications in binary and multi-state system reliability analysis. Features:- an introduction to basic tools of multi-state system reliability and optimization;- applications of the universal generating function in widely used multi-state systems;- examples of the adaptation of the universal generating function to different systems in mechanical, industrial and software engineering. This monograph will be of value to anyone interested in system reliability, performance analysis and optimization in industrial, electrical and nuclear engineering.

352 citations

Journal ArticleDOI
TL;DR: In this paper, the redundancy optimization problem is generalized to multi-state systems, where the system and its components have a range of performance levels-from perfect functioning to complete failure-and the redundancy for each component can be used.
Abstract: This paper generalizes a redundancy optimization problem to multi-state systems, where the system and its components have a range of performance levels-from perfect functioning to complete failure. The components are: (1) chosen from a list of products available in the market; and (2) characterized by their nominal performance level, availability and cost. System availability is represented by a multi-state availability function, which extends the binary-state availability. To satisfy the required multi-state system availability, the redundancy for each component can be used. A procedure which determines the minimal-cost series-parallel system structure subject to a multi-state availability constraint is proposed. A fast procedure is developed, based on a universal generating function, to evaluate the multi-state system availability. Two important types of systems are considered and special operators for the universal generating function determination are introduced. A genetic algorithm is used as an optimization technique. Examples are given.

305 citations

Journal ArticleDOI
TL;DR: Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure.

203 citations

Journal ArticleDOI
TL;DR: This paper generalizes a preventive maintenance optimization problem to multi-state systems, which have a range of performance levels and an algorithm is developed which obtains the sequence of maintenance actions providing system functioning with the desired level of reliability during its lifetime by minimum maintenance cost.

202 citations


Cited by
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Journal ArticleDOI
TL;DR: A review of more than 90 published papers is presented here to analyze the applicability of various methods discussed and it is observed that Analytical Hierarchy Process is the most popular technique followed by outranking techniques PROMETHEE and ELECTRE.
Abstract: Multi-Criteria Decision Making (MCDM) techniques are gaining popularity in sustainable energy management. The techniques provide solutions to the problems involving conflicting and multiple objectives. Several methods based on weighted averages, priority setting, outranking, fuzzy principles and their combinations are employed for energy planning decisions. A review of more than 90 published papers is presented here to analyze the applicability of various methods discussed. A classification on application areas and the year of application is presented to highlight the trends. It is observed that Analytical Hierarchy Process is the most popular technique followed by outranking techniques PROMETHEE and ELECTRE. Validation of results with multiple methods, development of interactive decision support systems and application of fuzzy methods to tackle uncertainties in the data is observed in the published literature.

1,715 citations

01 Jan 2011
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

1,296 citations

Proceedings Article
01 Jan 2003

1,212 citations

Journal ArticleDOI
TL;DR: The main logistics processes and operations in container terminals are described and classified and a survey of methods for their optimization is presented.
Abstract: In the last four decades the container as an essential part of a unit-load-concept has achieved undoubted importance in international sea freight transportation. With ever increasing containerization the number of seaport container terminals and competition among them have become quite remarkable. Operations are nowadays unthinkable without effective and efficient use of information technology as well as appropriate optimization (operations research) methods. In this paper we describe and classify the main logistics processes and operations in container terminals and present a survey of methods for their optimization.

1,158 citations