On Limit Reliability Functions of Large Systems. Part I

Abstract

In the reliability investigation of large systems the problem of the complexity of their reliability functions appears. This problem may be approximately solved by the assuming that the number of the system components tends to infinity and finding the limit reliability function of the system. It is closely related to the limit theorems in the extreme value theory discussed in many publications. The solution for simple series and parallel systems is well known and given for instance in Barlow and Proschan (1975). The limit reliability functions of more complex series-parallel and parallel-series systems with identical components are discussed in Kolowrocki (1993). The results on limit reliability functions of series-parallel and parallel- series systems with different components are given in Kolowrocki (1994). In the paper the classes of limit reliability functions of any homogeneous and nonhomogeneous large series, parallel, series-parallel and parallel-series system are presented. Moreover, practically useful lemmas and their applications are given. Systems with multistate components are more general and play an important role in the reliability practice. Therefore in the paper limit reliability functions of large homogeneous multi-state series, parallel, series-parallel and parallel-series systems are given. As a summary of this part of the paper a hypothesis on the class of possible limit reliability functions of considered multi-state systems is stated.Keywords and phrasesLarge scale systemsasymptotic reliabilitymultistate systems