Reliability properties associated with the classic models of systems with age replacement have been a usual topic of research. Most previous works have checked the aging properties of the lifetime of the working units using stochastic comparisons among the systems with age replacement at different times. However, from a practical point of view, it would also be interesting to deduce to which aging classes the lifetime of the system belongs, making use of the aging properties of the lifetime of its working units. The first part of this article deals with this problem. Further along, stochastic orderings are established between the systems with replacement at the same time using several stochastic comparisons among the lifetimes of their working units. In addition, the lifetimes of two systems with age replacement are compared as well. This is performed assuming stochastic orderings between the number of replacement until failure, and the lifetimes of their working units conditioned to be less or equal than the replacement time. Similar comparisons are accomplished considering two systems with age replacement where the replacements occur at a random time. Illustrative examples are presented throughout the paper.

与具有年龄替换的经典系统模型相关的可靠性属性一直是一个常见的研究主题。以前的大多数工作都使用在不同时间进行老化更换的系统之间的随机比较来检查工作单元寿命的老化特性。然而，从实际的角度来看，利用其工作单元寿命的老化特性来推断系统的寿命属于哪些老化等级也是很有趣的。本文的第一部分处理了这个问题。更进一步，使用它们工作单元的生命周期之间的几个随机比较，同时在具有替换的系统之间建立随机排序。此外，还比较了具有年龄替换的两个系统的寿命。这是假设在故障之前的更换次数与其工作单元的寿命小于或等于更换时间之间的随机排序来执行的。考虑到两个具有年龄替换的系统，其中替换发生在随机时间，可以完成类似的比较。整篇论文都提供了说明性示例。