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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. 

Topological Data Analysis (TDA) studies the “shape” of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukherjee, and Boyer showed that one can reconstruct a simplicial complex embedded in R^3 using persistence diagrams generated from all possible height filtrations (an uncountably infinite number of directions). In this paper, we present an algorithm for reconstructing plane graphs K = (V, E) in R^2, i.e., a planar graph with vertices in general position and a straight-line embedding, from a quadratic number height filtrations and their respective persistence diagrams.