Risk-Based Prognostics Overview

• Risk-based prognostics is an approach that couples predictions of remaining useful life with risk analysis and decision-making criteria to inform maintenance strategies.
• It employs probabilistic hazard models, Bayesian networks, and machine learning techniques to quantify uncertainty and provide actionable insights.
• Researchers integrate sensor data, failure probabilities, and cost metrics within this framework to optimize maintenance planning and enhance system reliability.

Searching arXiv for recent and foundational papers on risk-based prognostics, uncertainty, and PHM. Risk-based prognostics is a prognostic paradigm in which predictions of remaining useful life, future condition, or probability of reliable operation are coupled explicitly to risk, uncertainty, and decision consequences rather than being treated as isolated forecasting outputs. In the engineering PHM literature, this coupling appears in several forms: probabilistic estimation of failure likelihood and hazard propagation, RUL prediction with predictive distributions or credible intervals, cost- and utility-aware maintenance optimization, and structured integration of failure semantics, diagnostics, and prognostics into a unified decision model (Taheri et al., 2019). More recent work further tightens this coupling by representing faults, tests, hazards, and decisions in a single probabilistic framework, for example with continuous-time Bayesian networks, so that prognostics and risk assessment become jointly queryable rather than sequentially stitched together (Sheppard, 14 Aug 2025).

1. Definitions and conceptual scope

In the surveyed PHM literature, prognostics is described as the prediction of the remaining useful life, future condition, or probability of reliable operation of equipment using condition monitoring data (Taheri et al., 2019). A risk-based interpretation extends this notion by treating the prognostic output as an input to maintenance, logistics, or operational decisions under uncertainty, typically through failure probabilities, reliability functions, hazard rates, confidence or credible intervals, or expected utility formulations (Taheri et al., 2019).

A recurrent distinction in recent reviews is between regression-based prognostics and classification-based prognostics. Regression-based methods estimate RUL as a continuous quantity, whereas classification-based methods forecast the probability of failure across defined time intervals (Jamshidi et al., 25 Jun 2025). This distinction is not merely methodological. It implies different representations of risk: continuous time-to-failure estimates support long-horizon planning, while interval-wise failure probabilities map more directly to operational risk thresholds and trigger logic (Jamshidi et al., 25 Jun 2025). The ISO 13381-1:2004 definition cited in the predictive maintenance review is especially consequential here, because it frames prognostics as “the estimated time to failure and the risk of existence or subsequent appearance of one or more failure modes” (Jamshidi et al., 25 Jun 2025).

The literature also emphasizes that risk-based prognostics is not identical to RUL prediction alone. Several contributions argue that classical PHM pipelines often separate diagnostics, prognostics, and risk evaluation, requiring manual transfer of information between stages. The risk-based PHM chapter instead proposes an integrated view in which faults, effects, tests, and decision scenarios are modeled jointly in a Continuous Time Bayesian Network (CTBN), thereby allowing inference over current and future risk directly from observed evidence (Sheppard, 14 Aug 2025). This suggests that, within mature formulations, risk is not a post-processing layer added to prognostic outputs, but part of the state representation itself.

2. Mathematical representations of risk, reliability, and uncertainty

Risk-based prognostics relies on explicit probabilistic objects. In the survey literature, these include the reliability function $R(t) = P(T > t)$, hazard models such as the proportional hazards model

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$

and predictive distributions over failure time or RUL rather than point forecasts alone (Taheri et al., 2019). One reviewed formulation expresses conditional expected failure time as

$$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$

which makes the decision-theoretic role of uncertainty explicit (Taheri et al., 2019).

Reliability-oriented formulations are also central in survival-based prognostics. The comparative review of predictive maintenance methods summarizes the Weibull reliability function

$$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$

and the corresponding failure probability over a time window,

$$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$

as standard tools for translating degradation estimates into risk over actionable horizons (Jamshidi et al., 25 Jun 2025). The bifurcated turbofan framework applies related ideas in a state-aware way: in the healthy regime it uses Conditional Weibull Survival Analysis and Mean Residual Life, while in the degraded regime it relies on a probabilistic neural model, then fuses the two using a continuous state probability (Belaunzaran et al., 29 May 2026).

Recent uncertainty-aware work makes an additional distinction between epistemic and aleatoric uncertainty. The uncertainty quantification tutorial for engineering design and health prognostics treats this distinction as fundamental for sound risk assessment, noting that predictive uncertainty can guide both conservative intervention and data collection strategies (Nemani et al., 2023). In the Bayesian PINN framework for insulation ageing, total predictive uncertainty is decomposed as

$$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$

thereby supporting “risk-aware decision-making” with full predictive posteriors rather than deterministic forecasts (Ramirez et al., 7 Jan 2026). A related theme appears in the hierarchical Bayesian framework for model-based prognostics, where historical run-to-failure data from similar systems are used to construct priors and produce predictive RUL distributions that tighten as operational data accumulate (Jia et al., 22 Jan 2026).

3. Modeling frameworks

Several model classes recur across the literature, but they differ in how tightly they embed risk.

A broad taxonomy from the condition-based maintenance survey distinguishes data-driven, model-based, hybrid, and knowledge-based prognostic approaches (Taheri et al., 2019). Data-driven methods learn from sensor or degradation data without requiring detailed physical models; model-based methods use physical or stochastic degradation models; hybrid approaches combine the two; knowledge-based methods incorporate expert systems or fuzzy logic (Taheri et al., 2019). This classification remains useful because different risk formulations map naturally onto different classes. For example, proportional hazards models and survival analysis sit comfortably in data-driven statistical prognostics, while Kalman and particle filtering support probabilistic state updating in model-based settings (Taheri et al., 2019).

State-space and latent-state models are especially important when degradation is only indirectly observable. The Higher Order Hidden Semi-Markov Model (HOHSMM) was proposed for systems with unobservable health states and complex transition dynamics, allowing hidden states to depend on more distant history and state durations to follow general distributions (Liao et al., 2020). In the NASA turbofan case study, the learned state sequence was governed by a second-order Markov chain, and RUL was then obtained by simulating future state trajectories until a designated failure state was reached (Liao et al., 2020). This is a risk-relevant formulation because it propagates uncertainty through latent health-state transitions rather than relying only on direct regression to RUL.

Another latent-state formulation is the joint dynamic threshold approach based on Quantized Kernel Recursive Least Squares (QKRLS). It predicts continuous degradation signals and discrete health states simultaneously, with the codebook regions defining dynamic thresholds and the final region corresponding to failure (Bao et al., 2018). The RUL is then

$t_{RUL} = t_f - t_c,$

where $t_f$ is the first predicted time at which the signals enter the final region (Bao et al., 2018). The paper positions this as a response to the inadequacy of fixed thresholds under uncertainty and dynamic operating conditions, which is directly relevant to risk because threshold mis-specification can induce both false alarms and missed failures (Bao et al., 2018).

The most explicit unification of prognostics and risk appears in the CTBN-based framework for risk-based PHM. There, each variable evolves in continuous time, and faults, hazards, tests, and decisions are represented in one graphical model using Conditional Intensity Matrices (CIMs) (Sheppard, 14 Aug 2025). For a binary fault node,

$$Q = \begin{bmatrix} -\lambda & \lambda \ \mu & -\mu \end{bmatrix},$$

with $\lambda = 1/\text{MTBF}$ and $$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$0 (Sheppard, 14 Aug 2025). The stated advantage is that observed evidence can be used to infer both future faults and the hazards those faults may induce, which supports decision support and performance-based logistics in a single inferential substrate (Sheppard, 14 Aug 2025).

4. Decision-theoretic integration and risk optimization

The defining feature of risk-based prognostics is that predictions are evaluated with respect to consequences. A particularly explicit formulation is DeepFMEA, which structures domain expertise in a standardized FMEA-inspired data model including SystemElement, Asset, Signal, Measurement, VirtualSensor, FailureMode, DetectionMethod, FailureIncident, Intervention, and risk attributes such as failure frequency, cost of incident, and impact severity (Netsch et al., 2024). The framework uses quantitative risk expressions including

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$1

and

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$2

then refines this after PHM deployment to

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$3

with risk reduction computed as

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$4

(Netsch et al., 2024). In this formulation, model evaluation is inseparable from intervention cost, false alarms, and missed detections.

A closely related decision-theoretic structure appears in structural health monitoring. The probabilistic risk-based SHM framework models failure modes as Bayesian network representations of fault trees, assigns utilities to failure events and decisions, and uses influence diagrams to select actions that maximize expected utility (Hughes et al., 2021). The decision rule is written as

$$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$5

and the truss demonstration reports decision “accuracy” greater than $$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$6 relative to a ground-truth policy with perfect health knowledge (Hughes et al., 2021). The relevance to prognostics is broader than the structural setting: it shows how marginal damage probabilities from probabilistic classifiers can be pushed through failure logic and utility nodes to produce maintenance decisions rather than only condition estimates (Hughes et al., 2021).

The CTBN-based risk-based PHM framework generalizes this logic to runtime and design-time settings. Decision vertices represent choices such as performing maintenance, changing control mode, or selecting among subsystem designs; performance functions define mission value, cost, or risk; and inference yields trade-offs or Pareto-optimal alternatives (Sheppard, 14 Aug 2025). This goes beyond static maintenance triggering and places prognostics inside performance-based logistics, where the same model can support pre-deployment design selection and in-service health management (Sheppard, 14 Aug 2025).

A more conventional but still risk-aware route is to use probabilistic prognostic outputs in policy optimization. The survey literature notes dynamic programming and Q-learning as examples of methods that can schedule actions to minimize expected cost or risk using probabilistic prognostic outputs (Taheri et al., 2019). This suggests that risk-based prognostics is as much about downstream decision interfaces as about upstream prediction.

5. Data-driven, hybrid, and interpretable implementations

Risk-based prognostics increasingly relies on machine learning, but the literature repeatedly stresses that predictive accuracy alone is insufficient in safety-critical settings. One response is hybridization with physical knowledge. The framework for fusing physics-based and deep learning models calibrates a thermodynamic performance model to infer unobservable health parameters $$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$7 using an Unscented Kalman Filter, then augments sensor data with $$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$8, virtual sensors $$h(t \mid \mathbf{x}) = h_0(t)\exp(\beta^T\mathbf{x}),$$9, and $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$0 before feeding them to a neural network (Chao et al., 2020). The resulting input vector is

$$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$1

and the case study reports RMSE reductions of $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$2–$$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$3, NASA $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$4-metric improvements of $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$5–$$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$6, and an average prediction horizon extension of $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$7 relative to purely data-driven models (Chao et al., 2020). The paper also reports that when the training dataset is halved, the data-driven RMSE increases by $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$8 while the hybrid approach degrades by only $$E[T_{fail}\mid \text{CM data}] = \int_{t_{cur}}^{\infty} t \cdot f_{RUL}(t\mid \text{data})\,dt,$$9 (Chao et al., 2020). This suggests a practical route for risk-based deployment under data scarcity and operational shift.

Real-time aerospace PHM offers a complementary implementation. The aircraft actuation framework combines physical models of different fidelity with machine-learning surrogates for nearly real-time Fault Detection and Identification and RUL estimation (Berri et al., 2020). Proper Orthogonal Decomposition, Gappy POD, an MLP for fault vector estimation, an ODE-based damage propagation model, and an SVM surrogate for the failure criterion are integrated into an onboard-capable pipeline (Berri et al., 2020). Reported results include mean fault-identification errors of approximately $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$0 per parameter, binary healthy/faulty SVM accuracy greater than $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$1, and online execution in milliseconds, “four orders of magnitude faster” than full physics-based simulation (Berri et al., 2020). Since the method generates RUL distributions with $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$2, $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$3, and $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$4 quantiles, it directly supports risk-aware mission reconfiguration and maintenance planning (Berri et al., 2020).

Interpretability is another recurrent implementation theme. Concept Bottleneck Models (CBMs) have been proposed for RUL prediction by using degradation modes as intermediate concepts rather than relying on post-hoc input attribution (Forest et al., 2024). The abstract states that case studies on the N-CMAPSS dataset show that CBM performance can be “on par or superior to black-box models,” while remaining more interpretable, and that verified concept activations can be intervened upon at test time by domain experts (Forest et al., 2024). Because the provided body is unavailable, only these abstract-level claims are secure. Still, they indicate a line of work in which risk-based prognostics is linked to expert oversight through manipulable intermediate concepts rather than only through uncertainty bars.

Interpretable functional modeling appears in multivariate FDA as well. The MFPCA-based health prognostics method models multi-sensor trajectories as functions, uses nearest-neighbor similarity in MFPC space for RUL estimation, and identifies alarm points by analyzing derivatives of predicted trajectories (Yildirim et al., 10 Mar 2025). On C-MAPSS FD001, it reports RMSE $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$5 for MFPCA compared with $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$6 for FPCA and $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$7 for an exponential model, with prediction errors confined to $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$8 cycles (Yildirim et al., 10 Mar 2025). The paper further reports that $$R(t) = \exp\left(-\left(\frac{t}{\eta}\right)^{\beta}\right)$$9 of engines have alarms before actual failure and that $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$0 of alarms occur in the last $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$1 of engine lifetime (Yildirim et al., 10 Mar 2025). This is a particularly clear example of a prognostic model being designed not only to output RUL but also to support risk communication through projected sensor trajectories and alarm statistics (Yildirim et al., 10 Mar 2025).

6. Robustness, security, and open technical issues

Risk-based prognostics must account not only for stochastic degradation but also for adversarial, distributional, and data-quality threats. The adversarial attack study on deep-learning prognostics demonstrates that LSTM-, GRU-, and CNN-based RUL estimators are highly vulnerable to FGSM and BIM perturbations on NASA’s turbofan engine dataset (Mode et al., 2020). On clean data, RMSEs are $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$2 for GRU, $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$3 for LSTM, and $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$4 for CNN; under FGSM with $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$5, RMSE rises to $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$6, $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$7, and $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$8, and under BIM with $$P_{\text{fail}}(t,\Delta t) = 1 - R(t+\Delta t \mid t),$$9, $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$0, $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$1, it rises to $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$2, $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$3, and $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$4 respectively (Mode et al., 2020). The reported RMSE increases are $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$5–$$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$6 for FGSM and $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$7–$$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$8 for BIM (Mode et al., 2020). For risk-based deployment, the significance is immediate: deceptive sensor perturbations can induce both premature maintenance and hazardous overestimation of RUL.

Robust statistical inference is therefore relevant beyond conventional accuracy benchmarks. In one-shot device reliability prognosis under a cumulative risk model, a robust Bayesian approach replaces the conventional likelihood with a robustified posterior based on density power divergence, uses Hamiltonian Monte Carlo for posterior computation, and examines influence functions for both estimators and Bayes factors (Baghel et al., 2024). The stated motivation is that likelihood-based Bayesian estimation can fail in the presence of outliers, and the paper reports that robust estimators outperform non-robust ones under contamination in simulation studies (Baghel et al., 2024). Although this work concerns nondestructive one-shot devices under SSALT, it shows a general pattern: in risk-based settings, the credibility of the inferred uncertainty is itself a modeling problem.

Uncertainty calibration remains a major concern. The UQ tutorial compares Gaussian process regression, Bayesian neural networks, neural network ensembles, MC Dropout, and SNGP in health prognostics, emphasizing not only predictive accuracy but also calibration, out-of-distribution detection, and decomposition of uncertainty (Nemani et al., 2023). In the case studies summarized there, neural network ensembles show strong calibration and robust RUL uncertainty, whereas MC Dropout tends to be overconfident and SNGP can also be overconfident in some turbofan settings (Nemani et al., 2023). The recent Bayesian PINN work makes a similar point from the physics-informed side, reporting that heteroscedastic B-PINN yields better-calibrated uncertainty estimates than deterministic PINN, dropout-based PINN, and alternative B-PINN variants, with a Total RMSE of $$\sigma^2(u\mid x) = \underbrace{\sigma_\theta^2\!\left[E_{u\mid x,\theta}(u\mid x,\theta)\right]}_{\text{epistemic uncertainty}} + \underbrace{E_\theta\!\left[\sigma_{u\mid x,\theta}^2(u\mid x,\theta)\right]}_{\text{aleatoric uncertainty}},$$9 and a $t_{RUL} = t_f - t_c,$0 reduction versus vanilla PINN (Ramirez et al., 7 Jan 2026).

A common misconception is that more complex predictive models automatically imply better risk awareness. The surveyed literature suggests the opposite: without explicit uncertainty quantification, calibrated probabilities, or consequence models, more accurate point predictions may still be unsuitable for maintenance decisions (Taheri et al., 2019, Nemani et al., 2023). A second misconception is that risk-based prognostics requires only failure probability estimation. The classification-versus-regression review makes clear that both continuous RUL distributions and interval-wise risk forecasts can serve risk-based decision making, depending on the maintenance and logistics problem (Jamshidi et al., 25 Jun 2025).

7. Applications and research directions

Aviation is the dominant application domain across the cited work. Turbofan engines appear in studies of hybrid physics-informed deep learning (Chao et al., 2020), dynamic-state prognostics (Bao et al., 2018), HOHSMM-based latent-state prognosis (Liao et al., 2020), MFPCA-based multi-sensor modeling (Yildirim et al., 10 Mar 2025), adversarial vulnerability (Mode et al., 2020), and uncertainty-aware bifurcated RUL prediction (Belaunzaran et al., 29 May 2026). Aircraft actuation systems provide a separate aerospace application in which onboard computational constraints are central (Berri et al., 2020). This concentration is unsurprising because safety, reliability, logistics, and asymmetric failure costs make aviation a natural testbed for risk-based PHM.

Other domains broaden the methodological picture. Transformer insulation ageing motivates Bayesian PINNs with disentangled uncertainty (Ramirez et al., 7 Jan 2026). Crack growth and lithium battery degradation motivate hierarchical Bayesian model-based prognostics that leverage historical fleets as priors (Jia et al., 22 Jan 2026). Structural systems motivate Bayesian-network and influence-diagram decision frameworks (Hughes et al., 2021). Quantum machine learning has also been proposed for diagnostics and prognostics on ball bearing data as a hybrid quantum-classical framework, presented as the first attempt to apply such methods to PHM problems in “areas of risk and reliability” (Martín et al., 2021). A plausible implication is that risk-based prognostics is increasingly serving as an umbrella under which heterogeneous computational paradigms are evaluated, provided they can produce uncertainty-aware or probability-based outputs.

Several technical trends are explicit in papers and reviews. One is the increasing use of full predictive posteriors rather than point forecasts, especially via Bayesian deep learning, ensembles, or hierarchical models (Nemani et al., 2023, Jia et al., 22 Jan 2026, Ramirez et al., 7 Jan 2026). Another is regime awareness: the bifurcated framework argues that early-life and degraded-life prognostics should use different models, with uncertainty widening honestly in healthy regimes and narrowing near end-of-life (Belaunzaran et al., 29 May 2026). A third is the formalization of expert knowledge in machine-readable structures, as seen in DeepFMEA and concept-based interpretability (Netsch et al., 2024, Forest et al., 2024). A fourth is the explicit fusion of hazard modeling and diagnostics in continuous-time graphical models for decision support and logistics (Sheppard, 14 Aug 2025).

The survey literature also identifies persistent open problems: data scarcity and quality, incomplete or noisy condition monitoring data, poor transferability, multiple and interacting failure modes, and the difficulty of integrating probabilistic outputs into business processes (Taheri et al., 2019). The predictive maintenance review adds data imbalance and high-dimensional feature spaces as practical obstacles, especially for classification-based failure forecasting (Jamshidi et al., 25 Jun 2025). These issues indicate that the future of risk-based prognostics is likely to depend as much on calibrated uncertainty, semantic data structures, and decision integration as on further reductions in RMSE alone (Taheri et al., 2019, Netsch et al., 2024).