On a class of limit reliability functions of some regular homogeneous series-parallel systems

In the investigation of large-scale systems the problem of the complexity of their reliability functions arises. This problem may be solved approximately by assuming that the number of system components tends to infinity and finding the limit reliability function. In this paper a four-element class of limit reliability functions for a regular homogeneous series-parallel system is presented. The number of series components of the system has the order of the logarithm of the number of its parallel components. The result is obtained under the assumption that the lifetimes of the particular components are independent and identically distributed random variables. The class presented is different from the known class of limit distributions of minimax statistics of independent random variables with the same distribution. Moreover, some examples of the systems considered and their limit reliability functions are given. The results can be useful in the investigation of the reliability of large systems.