Limit reliability functions of some homogeneous regular series–parallel and parallel–series systems of higher order

摘要

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. It is well known that there exist only three possible nondegenerate limit reliability functions for regular, homogeneous, series and parallel systems [1]. The same three-element classes of limit reliability functions for series–parallel and parallel–series systems of order 1 has been fixed by Chernoff and Teicher [2]. These classes have been extended to ten-element classes of limit reliability functions by Kołowrocki [3–6]. This paper presents the generalization of the results given in [6].