随着可靠性系统的日益大型化和复杂化，系统多性能水平和多失效模式的特点使得针对系统结构的建模与分析变得困难。多状态Signature理论是解决该问题的关键，也是目前Signature研究领域的重点和难点。本项目将基于Signature理论深入研究多状态系统的可靠性问题。首先，基于实际系统的特性，建立多状态/多状态联合/多状态次序（生存）Signature指标。其次，分析指标的随机性质，深入刻画多状态可靠性系统的结构特性。然后，推导指标的转换公式，给出部件数不同的多状态系统结构之间简单有效的比较方法。最后，针对部件两状态系统多状态、部件多状态系统两状态和系统由模块构成这三种不同情形，分别提出有效通用的指标计算方法。本项目的研究成果不仅是对Signature理论的必要补充与完善，对于提高复杂系统的可靠性也具有重要的现实意义。

As the size and complexity of reliability systems improve continuously, multiple performance levels and multiple failure modes of these system structures make related modeling and analysis more difficult. Multi-state Signature theory is the key to dealing with this problem and also an important and difficult point in the research field of Signature nowadays. The present project will go deep into reliability problems of multi-state systems basing on Signature theory. First, indexes such as multi-state/multi-state joint/multi-state ordered (survival) Signature will be proposed based on characteristics of practical systems. Next, stochastic properties of these indexes will be analyzed to describe structural characteristics of multi-state reliability systems deeply. Then, transformation formulas of these indexes will be derived to provide a simple and efficient way to compare multi-state system structures of different sizes. Finally, effective general computation methods will be presented for three different situations respectively, namely multi-state systems with binary-state components, binary-state systems with multi-state components, and systems with modules. Results of this project are not only an essential supplement and improvement to Signature theory, but also of great practical significance to reliability improvements of complex systems.