Optimization of predetermined standby mode transfers in 1-out-of-N: G systems

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Warm standby redundancy is an important fault-tolerant design technique for improving the reliability of many systems used in life-critical or mission-critical applications. Traditional warm standby models aim to reduce the operational cost and failure rate of the standby elements by keeping them partially powered and partially exposed to operational stresses. However, depending on the level of readiness of a standby element, significant restoration delays and replacement costs can be incurred when the standby element is needed to replace the failed online element. To achieve a balance between the operation cost of standby elements and the replacement costs, this paper proposes a new warm standby model with scheduled (or time-based) standby mode transfer of standby elements. In particular, each standby element can be transferred from warm standby mode to hot standby mode (a mode in which the standby element is ready to take over at any time) at a fixed/predetermined time instants after the mission starts. To facilitate the optimal design and implementation of the proposed model, this paper first suggests a new algorithm for evaluating the reliability and expected mission cost of 1-out-of-N: G system with standby elements subject to the time-based standby mode transfer. The algorithm is based on a discrete approximation of time-to-failure distributions of the elements and can work with any type of distributions. Based on the suggested algorithm the problem of optimizing transfer times of standby elements to the hot standby mode and optimal sequencing of their transfer to the operation mode is formulated and solved. In this problem the expected mission cost associated with elements’ standby and operation expenses and mode transfer expenses is minimized subject to system reliability constraint. Illustrative examples are provided.