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Performing general prognostics and health management (PHM), especially in electronic systems, continues to present significant challenges. The low availability of failure data makes learning generalized models difficult and constructing generalized models during the design phase often requires a level of understanding of the failure mechanisms that elude the designers. In this paper, we present a generalized approach to PHM based on two types of probabilistic models, Bayesian Networks (BNs) and Continuous-Time Bayesian Networks (CTBNs), and we pose the PHM problem from the perspective of risk mitigation rather than failure prediction. This paper also constitutes an extension of previous work where we proposed this framework initially [1]. In this extended version, we also provide a comparison of exact and approximate sample-based inference for CTBNs to provide practical guidance on conducting inference using the proposed framework. 

Since its introduction in the mid-1990s, DBSCAN has become one of the most widely used clustering algorithms. However, one of the steps in DBSCAN is to perform a range query, a task that is difficult in many spaces, including the space of persistence diagrams. In this paper, we introduce a spanner into the DBSCAN algorithm to facilitate range queries in such spaces. We provide a proof-of-concept implementation, and study time and clustering performance for two data sets of persistence diagrams.