Reliability evaluation and optimization of series–parallel systems with k-out-of-n: G subsystems and mixed redundancy types

This article 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 energy conservation in the optimal system design. Given the available versions of hot and cold standby units and minimum number of operating components ( k ) for each subsystem 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 the system unreliability while satisfying a system-level constraint on cost. To formulate the objective function, an analytical method is 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. The proposed analytical method is demonstrated using several examples and verified using a Markov-based method. An optimization solution methodology based on the penalty-guided genetic algorithm is presented for obtaining the optimal design configuration. The proposed system reliability optimization methodology is tested on several example data sets.