Belief Availability for Repairable Systems Based on Uncertain Alternating Renewal Process

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.