On asymptotic reliability functions of series-parallel and parallel-series systems with identical components

Abstract

Abstract In the investigations of large scale systems the problem of the complexity of their reliability functions appears. This problem may be approximately solved by assuming that the number of system components tend to infinity and finding the limit reliability function of this system. In this paper 10-element closed classes of limit reliability functions for regular homogeneous series-parallel and parallel-series systems are fixed. These systems are such that at least the number of their series components or the number of their parallel components tends to infinity. The result is obtained under the assumption that lifetimes of the particular components are independent, identically distributed random variables. The fixed classes are more extensive than classes hitherto known of limit distributions of minimax and maximin statistics of independent random variables with the same distributions. The results can be useful in the reliability evaluation of large regular homogeneous systems and may originate reliability investigations of large nonregular nonhomogeneous systems.