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.
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Harvey J. Greenberg (1970) studied this question.