How much redundancy: Some cost considerations, including examples for spacecraft systems

How much redundancy should be built into a subsystem such as a space power subsystem. How does a reliability or design engineer choose between a power subsystem with 0.990 reliability and a more costly subsystem with 0.995 reliability. How does the engineer designing a power subsystem for a satellite decide between one power subsystem and a more reliable but heavier power subsystem. High reliability is not necessarily an end in itself. High reliability may be desirable in order to reduce the statistically expected loss due to a subsystem failure. However, this may not be the wisest use of funds since the expected loss due to subsystem failure is not the only cost involved. The subsystem itself may be very costly. The cost of the subsystem or the expected loss due to subsystem failure may not be considered separately. Therefore, the total of the two costs is minimized, i.e., the total of the cost of the subsystem plus the expected loss due to subsystem failure. A specific type of redundant system is considered, called a k-out-of-n: G subsystem. Such a subsystem has n modules, of which k are required to be good for the subsystem to be good. Five models are discussed which can be applied in the design of a power subsystem to select the unique redundancy method which will minimize the total of the cost of the power subsystem plus the expected loss due to the power subsystem failure. A BASIC computer program is available.