Limit reliability functions of some 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 the assumption that the number of the system components tends to infinity and by finding the limit reliability function of this system. In this paper, some three-element closed classes of limit reliability functions for series-parallel and parallel-series systems with identical components are fixed. 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. 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 identical components and may be the origin in the reliability investigation of large systems with different components.