A new approach in the mean residual lifetime evaluation of a multi-state system

Abstract

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.