Availability, MTTF and Cost analysis of complex system under Preemptive resume repair policy using copula distribution

In the present paper authors have focused  on the study of complex system consisting two subsystems, in series configuration and handling by a human operator. The subsystem (1) has three units at super priority, priority and ordinary & the subsystem (2) has one unit in series configuration with the subsystem-1. The whole system is operated by a human operator and human failure can also appear at different state where system is in operational mode. Initially super priority unit starts function and failure during  of super priority unit the priority unit start functioning and super priority unit goes under repair. The primitive resume repair policy is employed for repair of subsystem-1. The all failure rates are assumed to constants and follow exponential distribution but repair follow general and Gumbel-Hougaard family copula distribution. The system is studied by supplementary variable technique and Laplace transform. Various measure of reliability such as availability, state transition probabilities, mean time to system failure(M.T.T.F) and profit function has been discussed for available maintenance  cost for all time and profit incurred by unit time for given interval. Some particular cases have been discussed for different values of different rates .