中文摘要：

复杂斜坡被大量失败模式，或由在失败模式之间的统计依赖描绘，切了集合或连接集合。为如此的斜坡，一个系统的量的方法，或基于矩阵的系统可靠性方法，为他们的可靠性分析被描述并且改善。事件向量 c 的一个构造公式<啜class=“ a-plus-plus ”> E 被建议解决在样品空间，和系统事件的事件向量 c 识别任何部件 E 的困难能基于它被计算，然后，系统失败概率的界限能与给定的概率信息被获得。改进方法与系统失败可能性的多重失败模式，和界限为四个铜矿斜坡被说明被自我编的节目在软件 MATLAB 的平台上计算。在从基于矩阵的系统可靠性方法和二个通用系统方法的结果的比较建议如果仅仅在斜坡系统有一些失败模式，那相同精确性能被所有方法获得。否则，由 Ditlevsen 方法的界限或科内尔方法随失败模式的增加显然被扩展，当从建议方法的结果仍然是足够精确的时，他们的精确几乎不能满足实际工程的要求。

英文摘要：

Complex slopes are characterized by large numbers of failure modes, cut sets or link sets, or by statistical dependence between the failure modes. For such slopes, a systematic quantitative method, or matrix-based system reliability method, was described and improved for their reliability analysis. A construction formula of event vector ce was suggested to solve the difficulty of identifying any component E in sample space, and event vector c of system events can be calculated based on it, then the bounds of system failure probability can be obtained with the given probability information. The improved method was illustrated for four copper mine slopes with multiple failure modes, and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB. Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system. Otherwise, the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.