In this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, \(i=0,\ldots ,n-k,\) failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

在本文中，我们研究了一个相干系统中失效组件的数量。我们考虑组件寿命是离散随机变量的情况，这些离散随机变量可能是相关的且分布不相同。首先，我们计算出在时间为t的情况下，第k个out-of- n系统中完全存在i，\（i = 0，\ ldots，nk，\）个故障的概率。接下来，我们将此结果扩展到其他相干系统。另外，我们表明，在独立和相同分布的组件寿命的最流行的模型中，获得的概率对应于连续情况下得出并存在于文献中的相应概率。