Prognostics-Based Identification of the Top- $k$ Units in a Fleet

This paper considers a fleet of identical units where each unit consists of the same critical components. The degradation state of each critical component is assumed to be monitored by an on-board sensor. The paper presents a methodology for identifying the top-k (the k most reliable) units in a fleet using sensor-based prognostic information. Specifically, we develop a prognostics-based ranking (PBR) algorithm that combines stochastic degradation models with computer science database ranking algorithms. The stochastic degradation modeling framework is used to compute and update, in real-time, residual life distributions (RLDs) of the critical components of each unit. Using a base case exponential degradation model, we identify conditions necessary to establish stochastic ordering among the RLDs of similar components. A preference relationship, consistent with the stochastic ordering results, is then used to sort the units of the fleet based on the RLDs of their respective components. A database ranking algorithm, known as the threshold algorithm (TA), is then used to identify the top-k units without necessarily computing all the RLDs. The paper concludes with an illustrative example.