Stochastic analysis of a three unit complex system with active and passive redundancies and correlated failures and repair times

Abstract

The paper deals with the cost-benefit and reliability analysis of a system model consisting of three non-identical units- A, B and C. The system functions satisfactorily if at least one unit is operative but if at least two units are good then they work in parallel. The priority in operation is being given to unit-A and unit-B over unit-C. So that initially unit A and B work in parallel and unit-C is kept into cold standby. A single repairman is always available to repair a failed unit and priority in repair is being given to unit-A and B over unit-C. However, the repair discipline is FCFS for unit-A and unit-B. The failure and repair times of each unit are correlated having their joint distribution as Bivariate Exponentials. By using regenerative point technique various important measures of system effectiveness have been obtained.