A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems. Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features: An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithms Optimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.

A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATIONOptimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems.Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features:* An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology* Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection* The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems* Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithmsOptimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.

Preface xi1 BASIC MATHEMATICAL REDUNDANCY MODELS 11.1 Types of Models 21.2 Non-repairable Redundant Group with Active Redundant Units31.3 Non-repairable Redundant Group with Standby Redundant Units71.4 Repairable Redundant Group with Active Redundant Units101.5 Repairable Redundant Group with Standby Redundant Units131.6 Multi-level Systems and System Performance Estimation 151.7 Brief Review of Other Types of Redundancy 161.8 Time Redundancy 241.9 Some Additional Optimization Problems 27Chronological Bibliography of Main Monographs on ReliabilityTheory (with topics on Optimization) 302 FORMULATION OF OPTIMAL REDUNDANCY PROBLEMS 332.1 Problem Description 332.2 Formulation of the Optimal Redundancy Problem with a SingleRestriction 352.3 Formulation of Optimal Redundancy Problems with MultipleConstraints 392.4 Formulation of Multi-Criteria Optimal Redundancy Problems43Chronological Bibliography 453 METHOD OF LAGRANGE MULTIPLIERS 48Chronological Bibliography 554 STEEPEST DESCENT METHOD 564.1 The Main Idea of SDM 564.2 Description of the Algorithm 574.3 The Stopping Rule 604.5 Approximate Solution 66Chronological Bibliography 685 DYNAMIC PROGRAMMING 695.1 Bellman's Algorithm 695.2 Kettelle's Algorithm 73Chronological Bibliography 846 UNIVERSAL GENERATING FUNCTIONS 856.1 Generating Function 856.2 Universal GF (U-function) 87Chronological Bibliography 947 GENETIC ALGORITHMS 967.1 Introduction 967.2 Structure of Steady-State Genetic Algorithms 1007.3 Related Techniques 102Chronological Bibliography 1048 MONTE CARLO SIMULATION 1078.1 Introductory Remarks 1078.2 Formulation of Optimal Redundancy Problems in StatisticalTerms 1088.3 Algorithm for Trajectory Generation 1088.4 Description of the Idea of the Solution 1118.5 Inverse Optimization Problem 1148.6 Direct Optimization Problem 124Chronological Bibliography 1299 COMMENTS ON CALCULATION METHODS 1309.1 Comparison of Methods 1309.2 Sensitivity Analysis of Optimal Redundancy Solutions 13510 OPTIMAL REDUNDANCY WITH SEVERAL LIMITING FACTORS14210.1 Method of "Weighing Costs" 14210.2 Method of Generalized Generating Functions 146Chronological Bibliography 14911 OPTIMAL REDUNDANCY IN MULTISTATE SYSTEMS 150Chronological Bibliography 17012 CASE STUDIES 17212.1 Spare Supply System for Worldwide Telecommunication SystemGlobalstar 17212.2 Optimal Capacity Distribution of Telecommunication BackboneNetwork Resources 17912.3 Optimal Spare Allocation for Mobile Repair Station 183Chronological Bibliography 19013 COUNTER-TERRORISM: PROTECTION RESOURCES ALLOCATION19113.1 Introduction 19113.2 Written Description of the Problem 19213.3 Evaluation of Expected Loss 19513.4 Algorithm of Resource Allocation 19713.5 Branching System Protection 20113.6 Fictional Case Study 21013.7 Measures of Defense, Their Effectiveness, and RelatedExpenses 21713.8 Antiterrorism Resource Allocation under Fuzzy SubjectiveEstimates 22313.9 Conclusion 232Chronological Bibliography 232About the author 235