Chapter 8 - Related and Open Problems

Abstract

This chapter provides an introduction to the attractive domains of the limit reliability functions of two-state systems. They are accepted with the condition that the reliability functions of the particular components of a system have to satisfy that the system limit reliability function comes from the limit reliability functions, which, in turn, come from the previously fixed classes of this system. The chapter presents exemplary theorems related to the attractive domains of limit reliability functions of homogeneous series systems. An important problem related to accuracy of the asymptotic approach to large-system reliability evaluation concerned with the speed of convergence of system reliability sequence is also discussed. This problem is illustrated by analyzing the speed at which the homogeneous series-parallel system reliability sequences are converged to their limit reliability functions. "M out of n"-series systems and "mout of n"-series systems are defined and exemplary theorems on their limit reliability functions are presented and applied to the reliability evaluation of an illumination system and a rope elevator. Hierarchical series-parallel and parallel-series systems of any order are defined, their reliability functions are determined and limit theorems on their reliability functions are applied to reliability evaluation of exemplary hierarchical systems of second order. Applications of the asymptotic approach in large-series-system-reliability improvements are also analyzed in the chapter.