Performance Analysis of Complex System in Series Configuration Under Different Failure and Repair Discipline Using Copula

Abstract

This paper deal with the study of reliability of a complex system consists of three subsystems, (subsystem-1, subsystem-2 and subsystem-3) connected in series configuration. The subsystem-1 has three units and working under the policy 2-out-of-3: F policy, subsystem-2 has two units in parallel configuration and is working under 1-out-of-2: G policy and subsystem-3 is connected with subsystem-2. All three subsystems are connected in series configuration. The system has two types of failure, partial failure and completely failure. It is assumed that the partial failure bring the system to degraded state, while the complete failure stop functioning in the system. All failure rates are constant and assumed to follow exponential time distribution, but the repair follow two types of distribution, i.e., general distribution and exponential distribution. It is assumed that the system in partially failed/degraded states are repaired by employing general time distribution but the completely failed states are repaired by Gumbel–Hougaard family copula distribution. The system is analyzed by supplementary variable technique. Some crucial measures of reliability such as Availability, mean-time-to-failure (MTTF) and profit analysis have been discussed. Some computations are taken as special case by evaluating Availability, MTTF and profit by taking different failure rates.