AFARS—an algorithm for analyzing the reliability of systems

Abstract

In this paper, the authors use the AFARS (Algorithm For Analyzing the Reliability of Systems) to solve the mathematical model of a reliability block diagram of a generalized complex system. The block diagram is typical for maintained and non-maintained equipments found in aerospace, nuclear power, rapid-transit, facility-security systems and myriads of industrial systems. The solutions obtained are in the form of computer tabulations which may be used for plotting the characteristic curves of the dynamic parameters of interest, namely, the predicted operational readiness A(t), interval availability A(t 1, t 2 ), reliability or mission success ( R(t)), and maintainability ( M(t). For the unique “stationary-case” when all times-to-failure and all times-to-repair obey the Exponential probability law, the printout includes the predicted equilibrium availabilty A, the mean-time-to-first sytem-failure MITTFSF, mean-time-between-failure MTBF, and the mean-time-to-repair MTTR of the system being analyzed. AFARS is an analytical algorithm using Markovian state-transition diagrams and is capable of solving reliability mathematical models of complex systems at least one magnitude of CPU processing time quicker than by simulation algorithms such as GERT by Pritsker and Whitehouse. AFARS is written in ANSI FORTRAN and is totally interactive. Furthermore, the user need not know FORTRAN or have any programming skills. In using AFARS, the user does no programming, writes no equations and does not need to know probability theory. The algorithm is designed to run on mini and large-frame computers. The AFARS program is now restricted to solving reliability models; it may be used to solve queueing models and any stochastic model that can be described as a birth-and-death process.