Reliability analysis of repairable network system of three computer labs connected with a server under 2- out- of- 3 G configuration

This paper presents the study of reliability measures of a complex system consisting of three computer labs connecting to a server in the parallel configuration under 2-out-of-3: G operation policy. The system is assumed to work if at least two labs are in good operative condition. The server failure brings the system to a complete failed state. The failure rates of all labs are different and assumed to follow an exponential distribution, but their repair supports two types of distribution, namely general distribution and Gumbel–Hougaard family copula distribution. The system of three labs with the server studied using the supplementary variable technique, laplace transform, expressions of reliability measures such as system availability, system reliability, MTTF, and cost analysis as incurred profit by operations have been computed. The numerical results for relevant measures like availability, reliability, MTTF, and profit function are also obtained by taking particular values of various failure and repair rate as stated. Tables and figures demonstrate the computed results.