In this paper, we study reliability properties of a $k$-out-of-$n$ system with a single cold standby unit. We mainly focus on the case when the system operates in discrete time. In order to describe its aging behavior we consider three different mean residual life functions. By using some properties of order statistics we present several monotonicity results associated with these reliability characteristics. Since the calculation of the described quantities requires finding sums of infinite series, we provide a procedure to approximate them with an error not greater than a desired value. As an illustration we consider three special cases when the component lifetimes have geometric, negative binomial and discrete Weibull distributions.

在本文中，我们研究了 $ķ$-在......之外-$ñ$系统具有一个冷备用单元。我们主要关注系统在离散时间内运行的情况。为了描述其老化行为，我们考虑三种不同的平均剩余寿命函数。通过使用阶跃统计的一些属性，我们提出了与这些可靠性特征相关的几个单调性结果。由于描述数量的计算需要找到无限序列的和，因此我们提供了一种以不大于期望值的误差近似它们的过程。作为说明，我们考虑三种特殊情况，其中组件寿命具有几何分布，负二项式分布和离散威布尔分布。