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Optimal Resource Allocation: With Practical Statistical Applications and Theory by Igor A. Ushakov

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CHAPTER 1

Basic Mathematical Redundancy Models

A series system of independent subsystems is usually considered as a starting point for optimal redundancy problems. The most common case is when one considers a group of redundant units as a subsystem. The reliability objective function of a series system is usually expressed as a product of probabilities of successful operation of its subsystems. The cost objective function is usually assumed as a linear function of the number of system's units.

There are also more complex models (multi-purpose systems and multi-constraint problems) or more complex objective functions, such as average performance or the mean time to failure. However, we don't limit ourselves to pure reliability models. The reader will find a number of examples with various networks as well as examples of resource allocation in counter-terrorism protection.

In this book we consider main practical cases, describe various methods of solutions of optimal redundancy problems, and demonstrate solving the problems with numerical examples. Finally, several case studies are presented that reflect the author's personal experience and can demonstrate practical applications of methodology.

1.1 Types of Models

A number of mathematical models of systems with redundancy have been developed during the roughly half a century of modern reliability theory. Some of these models are rather specific and some of them are even “extravagant.” We limit ourselves in this discussion to the ...

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