Phase‐type distribution closure properties are utilized to devise algorithms for generating reliability functions of systems with basic structures. These structures include series, parallel, K‐out‐of‐N, and standby structures with perfect/imperfect switch. The algorithms form a method for system reliability modeling and analysis based on the relationship between the system lifetime and component lifetimes for general structures. The proposed method is suitable for functional system reliability analysis, which can produce reliability functions of systems with independent components instead of only system reliability values. Once the system reliability function is obtained, other reliability measures such as the system's hazard function and mean time to failure can be obtained efficiently using only matrix algebra. Dimensional and numerical comparisons with computerized symbolic processing are also presented to show the superiority of the proposed method.

中文翻译：

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使用相位类型分布闭合特性对系统可靠性进行建模和分析

相态分布闭包特性用于设计算法，以生成具有基本结构的系统的可靠性函数。这些结构包括串联，并联ķ -Out-OF- Ñ以及具有完美/不完美开关的待机结构。该算法基于系统寿命与一般结构的组件寿命之间的关系，形成了用于系统可靠性建模和分析的方法。所提出的方法适用于功能系统可靠性分析，可以产生具有独立组件的系统的可靠性函数，而不仅仅是系统可靠性值。获得系统可靠性函数后，仅使用矩阵代数就可以有效地获得其他可靠性度量，例如系统的危险函数和平均失效时间。还提出了与计算机符号处理进行的尺寸和数值比较，以显示该方法的优越性。