Basic Tools and Techniques -- The Universal Generating Function in Reliability Analysis of Binary Systems -- to Multi-state Systems -- Universal Generating Function in Analysis of Series-Parallel Multi-state Systems -- Universal Generating Function in Optimization of Series-Parallel Multi-state Systems -- Universal Generating Function in Analysis and Optimization of Special Types of Multi-state System -- Universal Generating Function in Analysis and Optimization of Consecutively Connected Systems and Networks -- Universal Generating Function in Analysis and Optimization of Fault-tolerant Software.Many real-world systems in engineering are composed of multi-state components that have different performance levels and several failure modes. These have effects on the entire system’s performance. Most books on reliability theory are devoted to traditional binary models that only allow a system either 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 both binary and multi-state system reliability analysis. Features: an introduction to the basic tools used in multi-state system reliability and optimization; applications of the universal generating function in the most widely used multi-state systems; several examples of how the universal generating function can be adapted to different systems in mechanical, industrial and software engineering. The Universal Generating Function in Reliability Analysis and Optimization will be of value to all those interested in multi-state systems in industrial, electrical and nuclear engineering. The Springer Series in Reliability Engineering publishes high-quality books in important areas of current theoretical research and development in reliability, and in areas that bridge the gap between theory and application in areas of interest to practitioners in industry, laboratories, business, and government.