Asymptotic reliability functions of some nonhomogeneous series-parallel and parallel-series systems

Abstract

In the reliability investigation 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 the system components tends to infinity and finding the limit reliability function. In this paper three-element classes of limit reliability functions for series-parallel and parallel-series systems with different components are presented. The series-parallel system is such that the number of its series components is of greater order than the logarithm of the number of its parallel components. The parallel-series system is such that the number of its parallel components is of greater order than the logarithm of the number of its series components. The fixed classes are different from the known three-element classes of asymptotic distributions of maximin and minimax statistics of independent random variables with a common distribution function. All results are obtained under the assumption that lifetimes of the particular components are independent random variables. Moreover, an example of the considered systems and its limit reliability function is given. The results may be useful in the reliability evaluation of large systems with unalike components.