An Application of a Lagrangian Penalty Function to Obtain Optimal Redundancy

A system is defined whereby there are N p subsystems in passive redundancy, and each subsystem has N A components in active redundancy. The mean time to failure is derived under the assumption of independent failure time, and this is used as a measure of system effectiveness. A budget constraint limits the number of components and switches which may be used to construct a system. This paper finds the maximum mean time to failure for different values of the budget parameters.