Redundancy allocation for k-out-of-n: G systems with mixed spare types

This paper considers the redundancy allocation problem pertaining to k-out-of-n: G heterogeneous series-parallel systems. Different from existing approaches that consider either hot or cold standby redundancy for a parallel subsystem, our approach considers a mix of cold and hot standby redundancies within one subsystem to achieve a balance between fast recovery and power conservation in the optimal system design. Given the available versions of hot and cold standby units and minimum number of operating components (k) for the system to function, the objective of the optimal design is to select versions of components and hot and cold standby redundancy levels within the subsystem to minimize system unreliability while satisfying system-level constraint on cost. To formulate the objective function, an analytical method has been proposed for the reliability analysis of a k-out-of-n: G subsystem with both hot and cold standby units. The method has no limitation on the type of time-to-failure distributions for the system components. An optimization solution methodology based on genetic algorithm is presented for obtaining the optimal design configuration. The proposed methodology is tested on several example data sets.