In many real-world applications, phased-mission systems (PMSs) often have time redundancy in the form of that mission task failed in one phase can be re-executed in a backup phase with change of its configurations. In this case, a new kind of dependence among phase tasks is involved: the success or failure of a phase task may result in a different configuration of its backup phases, and the original task in the backup phase may be either cooperated with or replaced by the failed task. It is essential to consider such redundancy as a more precise result for system mission reliability evaluation is required. This article proposes a combinatorial method to model the mission reliability of PMS with such phase backups. A compressed event tree containing only failure branches is constructed, each branch describing a mission failure cause as an execution sequence of a set of dependent phase tasks. Each phase task is supported by a kind of phase configuration, whose failure causes are modeled by a fault tree illustrating the logic relations of component malfunctions. A binary decision diagram-based method is applied on this combinatorial model to calculate the mission failure probability, and always has a better performance than other alternative solutions. Examples are analyzed for illustration, and the results show the effectiveness of the proposed approach.

中文翻译：

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一种具有阶段备份的分阶段任务系统任务可靠性的组合建模方法

在许多实际应用中，分阶段任务系统 (PMS) 通常具有时间冗余，即在一个阶段失败的任务任务可以在备份阶段通过更改其配置重新执行。在这种情况下，涉及阶段任务之间的一种新的依赖：阶段任务的成功或失败可能导致其备份阶段的不同配置，备份阶段中的原始任务可能会被合作或替代失败的任务。由于需要更精确的系统任务可靠性评估结果，因此必须考虑这种冗余。本文提出了一种组合方法来模拟具有此类相位备份的 PMS 的任务可靠性。构建仅包含失败分支的压缩事件树，每个分支将任务失败原因描述为一组相关阶段任务的执行序列。每个阶段任务由一种阶段配置支持，其故障原因由说明组件故障逻辑关系的故障树建模。基于二元决策图的方法应用于该组合模型来计算任务失败概率，并且始终比其他替代解决方案具有更好的性能。分析示例以进行说明，结果显示了所提出方法的有效性。基于二元决策图的方法应用于该组合模型来计算任务失败概率，并且始终比其他替代解决方案具有更好的性能。分析示例以进行说明，结果显示了所提出方法的有效性。基于二元决策图的方法应用于该组合模型来计算任务失败概率，并且始终比其他替代解决方案具有更好的性能。分析示例以进行说明，结果显示了所提出方法的有效性。