ABSTRACT

A general consecutive-type system, called $m$-consecutive-$k$,$\mathrm{\ell }$-out-of-$n$:F system, is considered. Such a system consists of $n$ linearly or circularly ordered components and fails if and only if there are at least $m$ $\mathrm{\ell }$-overlapping runs of $k$ consecutive failed components. For systems with statistically independent components, the system reliability is obtained via recursive schemes and simulation. Reliability importance measures for system components are calculated and analyzed as well. Illustrative analytic and numerical examples demonstrate further the theoretical results.

中文翻译：

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一般连续型系统的可靠性和重要性措施

摘要

一般的连续型系统，称为 $米$-连续-$ķ$，$\mathrm{\ell }$-在......之外-$ñ$：F系统，被考虑。这样的系统包括$ñ$ 线性或圆形排序的组件，并且仅当至少存在 $米$ $\mathrm{\ell }$-的重叠运行 $ķ$连续失败的组件。对于具有统计独立组件的系统，系统可靠性是通过递归方案和仿真获得的。还计算和分析了系统组件的可靠性重要性度量。说明性的分析和数值示例进一步说明了理论结果。