Reliability analysis of communication network system with redundant relay station under partial and complete failure

The purpose of this paper is to study the performance of a communication network system consisting of a transmitter, two relay stations and a receiver arranged in series parallel. Through the transition diagram, the partial differential equations are derived, and Laplace transforms are then taken on these equations to derive system reliability, availability, the mean time to system failure (MTTF) and cost function. It is assumed that failure rates are constant and follows exponential distribution, repair rates of partial failure state are assumed to follow general distribution and complete failure states are repaired through Gumbel-Hougaard family copula. The system is analyzed through supplementary variable technique and Laplace transform. Different measures of testing system effectiveness which include reliability, availability, mean time to failure (MTTF) and profit function have been calculated for particular values of time, failure and repair rates. From the study, it is clear that time and failure rates of both transmitter, relay stations and receiver influence the reliability, availability, MTTF and profit function. Mathematical models developed in this paper can aid plant management for proper maintenance and system safety, avoiding incorrect reliability, availability and profit assessment and leading to inadequate maintenance decision making, which may result in unnecessary expenditures and reduction of safety standards.