Geodesic
Reliability Estimation of a Complex Renewable System with an Unbounded Number of Repair Units
Teoriâ veroâtnostej i ee primeneniâ, Tome 37 (1992) no. 1, pp. 91-94

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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\} $. 
@article{TVP_1992_37_1_a13,
     author = {A. D. Solov'ev and D. G. Konstantinidis},
     title = {Reliability {Estimation} of a {Complex} {Renewable} {System} with an {Unbounded} {Number} of {Repair} {Units}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {91--94},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1992_37_1_a13/}
}
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A. D. Solov'ev; D. G. Konstantinidis. Reliability Estimation of a Complex Renewable System with an Unbounded Number of Repair Units. Teoriâ veroâtnostej i ee primeneniâ, Tome 37 (1992) no. 1, pp. 91-94. http://geodesic.mathdoc.fr/item/TVP_1992_37_1_a13/