Dynamic reliability measures are important characteristics for understanding the lifetime behaviour of multi-state systems. This study aims to analyze the mean residual lifetime (MRL) function for a one-unit three-state system.The system considered has just three states such as “0, 1, 2”. State “2” and “1” signify the perfect functioning and partially working states, respectively while state “0” is the failure state. We let $T^1$ and $T^2$ be the lifetimes of the system spent at state “1” and “2,” respectively. We assess a particular performance characteristic, MRL, of this three-state system via conditional survival functions, when $T^1$ and $T^2$ are both independent and dependent. In case of independency, MRL functions are obtained and the results are discussed with reference to a case study. The effect of different distributions on the MRLs are also investigated in this case study. In case of dependency, on the other hand, the effect of dependency on MRL functions is especially underlined given that the system is at state “j” ($j=1,2$) for $\forall t$. To understand the time dependent behaviour of the related MRL functions, certain graphical illustrations are also presented.

动态可靠性度量是了解多状态系统生命周期行为的重要特征。本研究旨在分析一单元三态系统的平均剩余寿命（MRL）函数。所考虑的系统只有三个状态，例如“ 0、1、2”。状态“ 2”和“ 1”分别表示正常运行状态和部分工作状态，而状态“ 0”表示故障状态。我们让${Ť}^{\mathrm{1个}}$ 和 ${Ť}^{\mathrm{2个}}$分别是系统在状态“ 1”和“ 2”花费的生命周期。我们通过条件生存函数评估该三态系统的特定性能特征MRL，当${Ť}^{\mathrm{1个}}$ 和 ${Ť}^{\mathrm{2个}}$既独立又依赖。在独立的情况下，将获得MRL函数，并参考案例研究对结果进行讨论。在本案例研究中，还研究了不同分布对最大残留限量的影响。另一方面，在依赖的情况下，特别要强调依赖于MRL函数的影响，因为系统处于状态“ j ”（$Ĵ=\mathrm{1个}，\mathrm{2个}$） 为了 $\forall Ť$。为了了解相关MRL功能的时间依赖性行为，还提供了某些图形说明。