On a class of limit reliability functions for series-parallel and parallel-series systems

Abstract

In the reliability investigation of large-scale systems, the problem of the complexity of their reliability functions arises. This problem may be approximately solved by the assuming that the number of system components tends to infinity and finding the limit reliability function. This paper presents the solution of this problem and some applications. The classes of asymptotic reliability functions for series-parallel and parallel-series systems with identical and unlike components are presented. They are ten-element and more extensive than the known three-element classes of asymptotic distributions of maximum and minimum statistics of independent random variables with a common distribution function. The results may be useful in the reliability evaluation of large scale systems.