Mathematical and Simulation Model for Reliability Analysis of a Heterogeneous Redundant Data Transmission System

Abstract

In the actual study, we carried out a reliability analysis of a repairable redundant data transmission system with the use of the elaborated mathematical and simulation model of a closed heterogeneous cold standby system. The system consists of one repair unit and two different data sources with an exponential cumulative distribution function (CDF) of their uptime and a general independent CDF of their repair time. We consider five special cases of the general independent CDF; including Gamma, Weibull-Gnedenko, Exponential, Lognormal and Pareto. We study the system-level reliability, defined as the steady-state probability (SSP) of failure-free system operation. The proposed analytical methodology made it possible to assess the reliability of the whole system in the event of failure of its components. Specific analytic expressions and asymptotic valuations are obtained for the steady-state probabilities of the system and the SSP of failure-free system operation. A simulation model of the system in cases where it is not workable to obtain expressions for the steady-state probabilities of the system in an explicit analytical form was considered, in particular for constructing the empirical system reliability function. The issue of sensitivity analysis of reliability characteristics of the considered system to the types of repair time distributions was also studied. The simulation modeling was done with the R statistics package.

Keywords

• reliability of redundant systems
• stochastic modeling
• simulation
• steady-state probability distribution
• generally distributed repair times