Reliability Estimation of a Complex Renewable System with an Unbounded Number of Repair Units

In this study an asymptotical analysis of the reliability of a complex renewable system with an unbounded number of repair units is provided. The system state is given through a binary vector $e(t)=[e_1(t),\cdots,e_n (t)]$, $e_i(t)=0(1)$, if at the moment $t$ the $i$th element is failure-free (failed). We assume, that at the state $e$ the $i$th element has failure intensity $\lambda_i (e)$. At the instant of failure of every element the renewal work begins and the renewal time has distribution function $G_i (t)$. Let $E_-$ be the set of failed system states. The goal of this study is the asymptotic estimation of the distribution of the time until the first system failure $\tau=\inf\{t:e(t)\in E_-|e(0)=\bar0\} $.