中文摘要：

鉴于组成系统单元的多状态单调关联性特征,将多元离散函数理论引入描述系统状态结构函数,发展了控制状态等价类主导状态向量的状态等价类主控边界点的逻辑方法,推导了多态单调关联系统的状态结构函数、可靠性和期望状态表达式;面向顾客的需求偏好,将负效用函数嵌入系统平均性能效用模型;鉴于元件状态引起的计算复杂性,提出了集合运算的德摩根律法和新型的框图式算法,简化了系统可靠度的表达式。结合某型航空发动机的简化演算,验证了主导等价类向量方法和框图算法的合理性与有效性,为工程系统的可靠性设计和可靠性管理提供理论依据。

英文摘要：

Considering the monotone and coherence of the multi-state system,the multiple discrete function theory is introduced to describe the structure function of system state.The logic approaches for the equivalence class of the component state which control the state vector of system are proposed,and the expressions for the state structure function,reliability and expected states are derived for the multi-state coherent system.To avoid the complexity of computation caused by the number of the state,the Demogen law and the new block diagram algorithm are developed to simplify the expression for the system reliability.An illustrative example of a certain type of aero engine verifies the effectiveness of the logic vector measure controlling the state equivalence class and the block diagram algorithm.It provides theoretical basis for reliability design and reliability management of system engineering.