Epistemic uncertainty exists in system availability evaluation due to the lack of data and information. To address it, this article proposes a series of definitions of the uncertainty theory-based availability, called belief availability, expanding the scope of belief reliability by introducing uncertainty-measured logistics and maintenance into belief reliability. Based on an uncertain alternating renewal process, we construct a belief availability model for repairable systems subject to the epistemic uncertainty. From the model, we derive formulas of several belief availability metrics, including belief availability (inherent, achieved, and operational), delay time ratio, maintenance time ratio, and belief failure frequency. We find an interesting property that the states order or the initial state in the model will not influence these metrics. A case study about the oxygen generation system (OGS) on the international space station was conducted to analyze the impact of its working, logistics, and maintenance time on the OGS belief operational availability. The results show a potential application in belief availability tradeoff between the OGS's availability-related parameters. In addition, we compared the proposed availability with probability one based on the time distributions of the OGS states, illustrating our method can effectively reduce the deviation of availability evaluation with insufficient data.

For the edge computing network, whether the end-to-end delay satisfies the delay constraint of the task is critical, especially for delay-sensitive tasks. Virtual machine (VM) migration improves the robustness of the network, whereas it also causes service downtime and increases the end-to-end delay. To study the influence of failure, migration, and recovery of VMs, we define three states for the VMs in an edge server and build a continuous-time Markov chain (CTMC). Then, we develop a matrix-geometric method and a first passage time method to obtain the VMs timely reliability (VTR) and the end-to-end timely reliability (ETR). The numerical results are verified by simulation based on OMNeT++. Results show that VTR is a monotonic function of the migration rate and the number of VMs. However, in some cases, the increase in task VMs (TVMs) may conversely decrease VTR, since more TVMs also brings about more failures in a given time. Moreover, we find that there is a trade-off between TVMs and backup VMs (BVMs) when the total number of VMs is limited. Our findings may shed light on understanding the impact of VM migration on end-to-end delay and designing a more reliable edge computing network for delay-sensitive applications.

The train braking system with redundant components has an essential effect on driver safety. In this paper, we consider the failure of K-out-of-N brake motors during operation and the redundant recovery by preventive maintenance. Two Continuous Time Markov Chains (CTMC) are used to model the working process and the preventive maintenance process of the braking system corresponding to the real situation of the train. Considering the maintenance effect of intermittent daily and cyclical overhaul with nested relationships, a new operation risk assessment model of the K-out-of-N system is developed to evaluate the effectiveness of the preventive maintenance of the train. Some safety parameters are solved based on the two coupled preventive maintenance periods, which conveniently design the safety of the train braking system. Finally, a case study illustrates the effectiveness of the safety evaluation method. The results show that we can trade off the effects of the multiple PM intervals on train safety considering the redundancy structure of the braking system by the proposed model.