Multi-state system reliability analysis and evaluation

In the traditional reliability theory, a system or a component is allowed to take only two possible states: working or failed. The binary reliability theory has been well developed and has been used in various industries over the past half century. However, a system or a component may experience more than two levels of performance. The multi-state reliability theory is attracting more and more research attention in the past two decades.; This thesis provides a systematic literature review on both binary and multi-state reliability theories. The multi-state reliability theory is built on the basis of coherent structures in the same way as binary reliability theory. Many concepts in the binary case have been extended to the multi-state case. The literature review focuses on the fundamentals of the multi-state reliability theory; which include multi-state relevancy conditions, binary decomposition methods of multi-state systems, multi-state system modeling techniques, and algorithms for system performance evaluation.; Binary k-out-of-n systems and binary consecutive k-out-of-n systems are commonly used models in engineering practice. Their definitions have been extended to the multi-state case by assuming that the system has a constant k-out-of-n structure or constant consecutive- k-out-of-n structure at all system levels. In this thesis, we propose the definitions of the generalized multi-state k-out-of-n systems and the generalized consecutive k-out-of-n systems. Under the proposed definitions, the systems are allowed to have different structures at different system levels. Such models are more flexible for describing some engineering problems. Algorithms for system performance evaluation or bounding techniques are developed.; Since the state space of a multi-state system is usually complex, it is difficult to evaluate the probabilities for the system to be in different states. An approach for multi-state system performance evaluation is to extend binary algorithms to the multi-state context. In this thesis, we investigate the internal relationship between binary systems and multi-state systems and then propose a definition of the dominant multi-state system. A dominant system has some binary properties and can be bounded by two binary structures. A dominant system with binary image can be treated like a binary system. Various properties of dominant systems are explored. The proposed definition has excellent potential for multi-state system performance evaluation.; In summary, this thesis contributes to multi-state system modeling technique, system analysis, and performance evaluation. The proposed generalized multi-state k-out-of-n systems and multi-state consecutive k-out-of-n systems are more flexible than the models proposed by other researchers. The definition of the dominant system provides a new tool for classifying multi-state systems and evaluating or bounding the system performance indexes.