Abstract: In practical engineering, it is significant to estimate the lifetime and residual life of a system. The research is limited for how to obtain the lifetime and residual life of a system efficiently by using the lifetime and reliability of components. Motivated by this problem, relationship between reliability, lifetime and residual life is analyzed in this paper. Further, on the assumption that the components are identically and independently Weibull distributed, the closedforms for lifetime and residual life of series, parallel and r/n(G) systems are derived based on lifetime and reliability function of components, respectively. And the calculation method is presented accordingly. Next, for the lifetime and residual life of the cold standby system, the closed-form is obtained when the components lifetime are identically exponentially distributed and numerical method is proposed when components follow Weibull distributions. The numerical examples prove the proposed method is accurate and efficient. Finally, a r/n(G) system composed by momentum wheels is taken as an example and the results shows that this method is worth learning in engineering practice.

Key words: typical system, lifetime of system, residual life of system, Weibull distribution, closed-form