In this paper, we propose a shock model for an m-consecutive-k, l-out-of-n: F system. This paper presents a reliability analysis of an m-consecutive-k, l-out-of-n: F system subjected to shocks that destroy a random number of components. One of the main random variables is the number of components affected by successive shocks. Phase-type distributions have been used to model the intervals between successive shocks. The main objective of this study is to show how phase-type distributions can be used to determine the reliability of m-consecutive-k, l-out-of-n: F systems subjected to shocks, which destroy a random number of components. Consideration is given to the optimal replacement time problem, which addresses the minimization of the total long-run average cost per unit time.

在本文中，我们提出了一个m -consecutive- k, l -out-of- n: F系统的冲击模型。本文介绍了一个m -consecutive- k, l -out-of- n: F系统受到破坏随机数量组件的冲击的可靠性分析。主要随机变量之一是受连续冲击影响的成分数量。相位型分布已被用于模拟连续冲击之间的间隔。本研究的主要目的是展示如何使用相类型分布来确定m -consecutive- k, l -out-of- n的可靠性：F系统受到冲击，这会破坏随机数量的组件。考虑了最佳更换时间问题，该问题解决了单位时间总长期平均成本的最小化问题。