Reliability analysis of 1-for-2 shared protection systems with general repair-time distributions

In this paper, we investigate the reliability of a type of 1-for-2 shared protection systems. The 1-for-2 shared protection system is the most basic fault-tolerant configuration with shared backup units. We assume that there are two working units each serving a single user and one shared protection (spare) unit in the system. We also assume that the times to failure and to repair are subject to exponential and general distributions respectively. Under these assumptions, we derive the Laplace transform of the survival function (the cdf that the system will survive beyond a given time) for each user as well as the user-perceived Mean Time to First Failure (MTTFF) by combining the state transition analysis and the supplementary variable method. We also show the effect of the repair-time distribution, the failure rates and the repair rates of the units through the case study of small-sized two enterprises that share one spare device for backup purpose. The analysis reveals what is important and what should be done in order to improve the user-perceived reliability of shared protection systems.