Chapter 4 - Reliability of Large Two-State Systems

Abstract

This chapter formulates auxiliary theorems on limit reliability functions of large two-state systems, which are necessary for their approximate reliability evaluation. The classes of limit reliability functions for homogeneous and nonhomogeneous series, parallel, series-parallel, and parallel-series systems, as well as for a homogeneous "m out of n" system, are fixed. Applications of the asymptotic approach to reliability evaluations of model systems are presented. Six corollaries are formulated and proved on the basis of auxiliary theorems and are applied to find the limit-reliability functions of considered systems and approximate evaluations of their reliability functions, lifetime mean values, and lifetime standard deviations. Further, a reliability evaluation is done for systems such as the model nonhomogeneous series system, the homogeneous parallel system of an energetic cable, the "16 out of 35" lighting system, the homogeneous regular series-parallel gas distribution system, the nonhomogeneous regular series-parallel water supply system, and the model homogeneous regular parallel-series system. The reliability data of components are assumed either to be arbitrary or to come from experts. These reliability evaluations of the considered systems' characteristics are an illustration of the possibility of applying the asymptotic approach in system reliability analysis of large and real technical systems.