Safety of some homogeneous series-„k out of n” systems

In the reliability investigation of large-scale systems, the problem of the complexity of their safety functions arises. This problem may be approximately solved by assuming that the number of system components tends to infinity and finding the limit safety function of the system. The problem of finding the limit reliability function of large-scale systems is well known for basic two-state systems (Gnedenko for series and parallel systems [1], Smirnov for “k out of n” systems [8]). The problem of possible limit reliability functions for series-parallel and parallel-series is also well recognized [3]. The solution for two-state series-“k out of n” systems, while k/n→0 and also while k/n→1 can be found in [5] and [6]. The paper is concerned with mathematical methods in multistate asymptotic approach to series-“k out of n” systems safety and shows the methods of establishing its possible limit safety functions, while k/n→ λ, 0˂ λ˂ 1.