Mission Reliability, Cost and Time for Cold Standby Computing Systems with Periodic Backup

Abstract

Life critical applications like space missions and flight controls require their computing systems to be equipped with some fault-tolerance mechanism to meet stringent reliability requirements by performing the intended function even in the case of element failures. Such benefit, however, cannot come without extra time as well as extra overhead and capital costs. This paper for the first time considers the modeling and evaluation of mission reliability, expected mission time and cost simultaneously for 1-out-of- <inline-formula><tex-math>$N$</tex-math></inline-formula> : G non-repairable cold standby computing systems subject to periodic backup actions. Based on the suggested numerical evaluation method, the optimal backup frequency problems are formulated and solved, providing the optimal number of backup operations during the mission to maximize the system reliability or to minimize the mission cost or time. In the case of non-identical system elements, the optimal standby element sequencing problem arises as the order in which the system elements are initiated can impact the system reliability and mission cost and time greatly; such problems are formulated and solved for the 1-out-of- <inline-formula><tex-math>$N$</tex-math></inline-formula> : G cold standby computing systems with periodic backups. Furthermore, a combined optimization problem is considered, where a combination of the element initiation sequence and backup frequency providing the best combination of mission reliability, cost, and time is found. The proposed methodology can facilitate a reliability-cost-time tradeoff study in the practical design of cold standby systems, thus assist in making the optimal decision on the system's standby and backup policy. Examples are provided for illustrating the considered problems and suggested solution methodology.