Reliability measures the ability of a system performing its intended functions. It is one of the most critical performance measures of today’s complex systems, such as transportation systems, power systems, communication systems and aircraft systems, and has been emphasized more and more by academia, industry and government. Reliability of a system needs to be evaluated accurately, and it can be improved through design optimization.

In traditional binary reliability framework, both systems and components can only take two possible states:​ completely working and totally failed. However, engineering systems typically have multiple partial failure states in addition to the above-mentioned completely working and totally failed states. Reliability analysis considering multiple possible states is known as multi-state reliability analysis. Multi-state reliability analysis recognizes the multiple possible states of engineering systems, and enables more accurate system reliability analysis.

Efficient methods were not available for some types of multi-state systems, such as multi-state fc-out-of-n systems and multi-state network systems. Without such efficient methods, it is time-consuming, sometimes impossible, to evaluate the reliability of complex systems, and approximation approaches have to be used. Efficient reliability evaluation methods are also required in reliability based system design, which typically involves many iterations of system R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. reliability evaluation.

This dissertation documents research contributions to multi-state system reliability theory, including reliability modeling, evaluation and optimal design of multi-state system. The contributions are summarized as follows:​

1. Efficient methods have been developed for reliability evaluation of multistate systems with fc-out-of-n structures.
2. An efficient method has been developed for reliability evaluation of multi-state two-terminal networks given all minimal path vectors.
3. The recursive computation principle is the common principle in all system reliability evaluation algorithms proposed in this work.
4. An effective method has been developed for dealing with multiple objectives typically involved in the optimal design of multi-state series-parallel systems.
5. A joint reliability and redundancy optimization method has been developed for multi-state series-parallel systems.

With efficient reliability evaluation methods and effective reliability based design approaches for multi-state engineering systems, the research results out of this work provides useful tools for achieving highly reliable and cost effective engineering systems.