Chapter 5 - Reliability of Large Multi-State Systems

Abstract

This chapter analyzes auxiliary theorems on limit reliability functions of multistate systems, which are necessary for their approximate reliability evaluation. The classes of limit reliability functions are fixed for homogeneous and nonhomogeneous series, such as parallel, series-parallel, and parallel-series multi-state systems, and for a homogeneous multi-state "m out of n'" system. Practical applications of the multistate asymptotic approach to reliability evaluation of real technical systems are presented. On the basis of auxiliary theorems, some corollaries are formulated and proved and then applied to approximate reliability and risk characteristics determination of real technical multistate systems that have parallel, "m out of n,” series-parallel, and parallel-series reliability structures. The chapter evaluates multistate reliability functions, mean sojourn times in state subsets and their standard deviations, mean lifetimes in states, risk functions, and exceeding moments of a permitted risk level for selected real systems. The homogeneous series-piping transportation system, the model, homogeneous series-telecommunication network, the homogeneous series bus transportation system, the nonhomogeneous series-piping transportation system, the homogeneous parallel system of an electrical cable, the nonhomogeneous parallel rope system, the "10 out of 36" homogeneous steel rope system, the model homogeneous series-parallel system, the homogeneous and nonhomogeneous series-parallel pipeline systems, and the homogeneous parallel-series electrical energy distribution system are analyzed and their reliability characteristics are also evaluated in the chapter.