IGOR USHAKOV, DrSci, was previously a professor at both The George Washington University and the University of California, San Diego; chair of the Department of Large Scale Systems at the Moscow Institute of Physics and Technology; and a principal engineer at Qualcomm. In addition, he is founder of the International Group on Reliability's Gnedenko Forum and has authored or edited dozens of books and published more than 300 journal papers on reliability engineering, logistics, and quality assurance.

• Preface xi1 BASIC MATHEMATICAL REDUNDANCY MODELS 11.1 Types of Models 21.2 Non-repairable Redundant Group with Active Redundant Units 31.3 Non-repairable Redundant Group with Standby Redundant Units 71.4 Repairable Redundant Group with Active Redundant Units 101.5 Repairable Redundant Group with Standby Redundant Units 131.6 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 Reliability Theory (with topics on Optimization) 302 FORMULATION OF OPTIMAL REDUNDANCY PROBLEMS 332.1 Problem Description 332.2 Formulation of the Optimal Redundancy Problem with a Single Restriction 352.3 Formulation of Optimal Redundancy Problems with Multiple Constraints 392.4 Formulation of Multi-Criteria Optimal Redundancy Problems 43Chronological 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 Statistical Terms 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 FACTORS 14210.1 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 System Globalstar 17212.2 Optimal Capacity Distribution of Telecommunication Backbone Network Resources 17912.3 Optimal Spare Allocation for Mobile Repair Station 183Chronological Bibliography 19013 COUNTER-TERRORISM: PROTECTION RESOURCES ALLOCATION 19113.1 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 Related Expenses 21713.8 Antiterrorism Resource Allocation under Fuzzy Subjective Estimates 22313.9 Conclusion 232Chronological Bibliography 232About the author 235

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