Risk Severity Index (RSI) Insights

• RSI is a scalar risk summary that combines event frequency and severity, with definitions and metrics that vary by domain such as telematics and LLM safety.
• Methodological approaches include inverse-probability weighting, Bayesian updating, and calibrated expert assessments to quantify risk impacts in diverse applications.
• RSI serves as a practical governance tool to prioritize alerts and guide data-driven decision-making in fields ranging from cyber-security to structural reliability.

Risk Severity Index (RSI) denotes a family of domain-specific risk measures rather than a single standardized statistic. Across recent literature, the label is used for a portfolio-anchored telematics index combining abnormal-event frequency with tail-rarity severity, an adversarial-prompt safety score for LLMs, a severity term in cyber-induced relay risk modeling, and closely related normalized severity constructs in medical-device security, component-based software, structural reliability, and machine-condition monitoring (Lee et al., 16 Mar 2026, Akiri et al., 12 Sep 2025, Yang et al., 2018, Mahler et al., 2020, Gupta et al., 2012, Leblouba et al., 16 Aug 2025, Jeon et al., 4 Apr 2025).

1. Terminological scope and conceptual variants

The literature suggests that RSI is best understood as a recurrent naming pattern for scalar risk summaries that combine at least two ingredients: an estimate of how often adverse behavior occurs, and a measure of how serious that behavior is once observed. What changes across fields is the operational meaning of “severity.” In actuarial telematics, severity is tail rarity in a portfolio distribution; in LLM safety evaluation, it is harmful compliance net of refusal; in power-system security, it is outage impact conditioned on power-flow behavior; in structural reliability, it is the conditional depth of failure; and in medical-device and software-risk settings, it is a weighted or directly elicited consequence score.

Domain	RSI meaning	Representative definition
Telematics ratemaking	Joint frequency–severity trip and driver index	Severity-weighted posterior rate from MLTC and Poisson–Gamma updating
LLM safety	Bounded risk score under adversarial prompts	$$\text{RSI} = \frac{1 + \text{Defect Rate} - \text{Refusal Rate}}{2}$$
Substation relay security	Severity term within relay risk	$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$
Medical-device cyber risk	Continuous attack-priority score	$R_j = L_j \times S_j$
COTS/RUP risk management	Normalized overall project risk burden	$\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$
Structural reliability	Severity-aware reliability index	$\beta_s = F^{-1}(E_f^\ast)$
Mechanical fault monitoring	Continuous exceedance-based severity profile	$S_{t,m} = \mu_t + m\sigma_t$

A common misconception is that RSI values are directly comparable across these domains. They are not. Some RSIs are bounded in $[0,1]$, some are dimensionless but unbounded by construction, some are posterior means, and some are only meaningful relative to a domain-specific benchmark or classification scheme.

2. Portfolio-anchored RSI in telematics and actuarial ratemaking

In "A Portfolio-Anchored Frequency-Severity Risk Index for Trip and Driver Assessment Using Telematics Signals" (Lee et al., 16 Mar 2026), RSI is defined as a joint frequency–severity trip-level risk index anchored to a portfolio-level baseline distribution of driving behavior. The telematics input is longitudinal acceleration at 10 Hz, measured in G, and the signal is represented with the maximal overlap discrete wavelet transform (MODWT), which preserves localized multi-scale patterns. Coefficients are aggregated across selected levels to form a time series $C_{i,t}$, then thinned to reduce serial dependence; exposure $E_i$ is the number of retained coefficients.

Severity is not interpreted as claim size. Instead, it is modeled as tail rarity relative to the portfolio distribution. The portfolio distribution is fitted by a Gaussian–Uniform layered mixture in which Gaussian components capture typical driving behavior and ordered Uniform tail intervals define increasing extremeness. Layer probabilities induce inverse-probability severity weights,

$$w_m(\gamma) = \frac{\pi_m^{-\gamma}}{\sum_{\ell=1}^{M} \pi_\ell^{-\gamma}}, \qquad \gamma \ge 0.$$

Trip behavior is summarized by multi-layer tail counts,

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$0

which are modeled as Poisson counts with Gamma priors. Conjugacy yields the trip-level RSI

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$1

and sequential updating yields the driver-level index

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$2

with

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$3

The methodological significance of this formulation is that frequency and severity are estimated from telematics signals alone, without claim outcomes or demographic covariates. The UAH-DriveSet study used 40 trips from 6 drivers under normal, aggressive, and drowsy states. On the secondary-road set, trip-level RSI ranked all risky trips above all normal trips, and severity weighting improved classification performance from 72.6% to 75.0% to 88.2% under stratified K-fold CV and from 76.0% to 76.0% to 91.3% under leave-one-driver-out CV when moving from total frequency to unweighted multi-layer to severity-weighted multi-layer models. The paper also argues that a purely behavior-driven index may mitigate fairness concerns associated with traditional ratemaking covariates.

3. RSI as an adversarial safety metric for LLMs

In "Safety and Security Analysis of LLMs: Risk Profile and Harm Potential" (Akiri et al., 12 Sep 2025), RSI is a composite metric for quantifying LLM safety risk under adversarial prompting. It combines two rates: Refusal Rate, defined as the percentage of occurrences in which a model refuses to interact with a user given a potentially harmful prompt, and Defect Rate, defined as the percentage of occurrences in which a model generates a response that exceeds the harm threshold of a specific category. The exact formula is

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$4

With rates expressed as percentages, the operational form is

$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$5

The score is bounded on $$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$6 and interpreted through discrete tiers: No Harm Observed at $$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$7, Negligible for $$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$8–$$\mathbf{R}_{i,k} = \mathbf{Pr}_{i,k}\cdot\mathbf{Sr}_{i,k}$$9, Minor for $R_j = L_j \times S_j$0–$R_j = L_j \times S_j$1, Moderate for $R_j = L_j \times S_j$2–$R_j = L_j \times S_j$3, Significant for $R_j = L_j \times S_j$4–$R_j = L_j \times S_j$5, Severe for $R_j = L_j \times S_j$6–$R_j = L_j \times S_j$7, and Maximal Harm Observed at $R_j = L_j \times S_j$8. RSI is computed per harm topic by averaging refusal and defect rates across categories within that topic and then applying the formula; no category weights are used.

The empirical study evaluated nine LLMs on 24 categories grouped into seven harm topics using 120 single-turn adversarial prompts. Responses were manually labeled as refused, blocked, redirected, or defective. The reported results show strong between-model variation. For advancing violent or terroristic behavior, Gemini 2.5 Flash had RSI $R_j = L_j \times S_j$9, GPT-4o $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$0, and Claude Opus 4 $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$1, whereas DeepSeek V3 Online reached $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$2 and Mistral 7B $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$3. For advancing societal harm, GPT-4o had $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$4, while Grok 3 had $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$5 and DeepSeek V3 Online $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$6. The study uses these scores for risk profiling, governance, deployment gating, and ongoing monitoring.

This RSI is distinctive because it treats safety risk as the net balance between harmful compliance and robust refusal. It is therefore not a direct severity-of-output score; rather, it is a bounded deployment-oriented index of adversarial safety posture.

4. Cyber-physical, medical-device, and software-lifecycle formulations

In substation cybersecurity, "Cyber-Induced Risk Modeling for Microprocessor-Based Relays in Substations" defines RSI as the severity component $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$7 of an overall relay risk model (Yang et al., 2018). Overall risk is

$\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$8

and the severity term is piecewise. If the post-outage power flow converges, severity is the fraction of the substation’s total injected power controlled by relay $\mathrm{RF} = \frac{\mathrm{TRVS}}{\mathrm{ITRVS}}$9,

$\beta_s = F^{-1}(E_f^\ast)$0

If the power flow diverges, the numerator becomes total system injection. In the simulations, diverged-case risks were set to $\beta_s = F^{-1}(E_f^\ast)$1 to flag worst scenarios. This RSI is therefore a topology- and power-flow-conditioned impact ratio, not a probabilistic severity estimate.

In medical-device security, the TLDR methodology uses a continuous product-form risk score that functions as an RSI for attack prioritization (Mahler et al., 2020). Likelihood is derived by mapping attacks to CAPEC patterns, eliciting CAPEC likelihoods from four senior healthcare information security experts, normalizing to $\beta_s = F^{-1}(E_f^\ast)$2, and applying a calibration shift $\beta_s = F^{-1}(E_f^\ast)$3. Severity was elicited directly from four senior radiologists on a $\beta_s = F^{-1}(E_f^\ast)$4–$\beta_s = F^{-1}(E_f^\ast)$5 scale. The final score is

$\beta_s = F^{-1}(E_f^\ast)$6

The study covered 23 attacks across generic medical imaging devices, CT, MRI, and ultrasound. Ransomware on the generic MID had the highest reported risk, $\beta_s = F^{-1}(E_f^\ast)$7, followed by disruption of patient-to-image linkage and alteration of imaging exam results. The paper states that a fuller severity decomposition into weighted aspects is part of the broader TLDR framework but was replaced in this study by a single overall severity judgment.

A closely related normalized severity construct appears in the COTS/RUP literature, although the paper does not explicitly use the term RSI (Gupta et al., 2012). Its "Risk Factor" is

$\beta_s = F^{-1}(E_f^\ast)$8

where TRVS is the total risk value of the software and ITRVS is the ideal total risk value when all risks attain rank $\beta_s = F^{-1}(E_f^\ast)$9 by Users and Risk Managers. RF is then classified as Negligible for $S_{t,m} = \mu_t + m\sigma_t$0–$S_{t,m} = \mu_t + m\sigma_t$1, Low for $S_{t,m} = \mu_t + m\sigma_t$2–$S_{t,m} = \mu_t + m\sigma_t$3, Moderate for $S_{t,m} = \mu_t + m\sigma_t$4–$S_{t,m} = \mu_t + m\sigma_t$5, and High for $S_{t,m} = \mu_t + m\sigma_t$6–$S_{t,m} = \mu_t + m\sigma_t$7. This suggests an RSI-like normalization of aggregated survey-assessed project risk. The same paper also defines

$S_{t,m} = \mu_t + m\sigma_t$8

and labels

$S_{t,m} = \mu_t + m\sigma_t$9

which the paper itself treats as a cost-derived quantity rather than a statistical probability.

5. Severity beyond frequency: structural reliability and machine diagnostics

In structural engineering, "A Severity-Aware Reliability Index for Risk-Informed Structural Design" introduces a quantity that the secondary explanation denotes as RSI but the paper names the Severity-Aware Reliability Index (Leblouba et al., 16 Aug 2025). The framework starts from the failure event $[0,1]$0 and the Expected Failure Deficit

$[0,1]$1

For Gaussian systems, the benchmark mapping is

$[0,1]$2

and the severity-aware index is defined implicitly by

$[0,1]$3

The inverse exists only when

$[0,1]$4

If $[0,1]$5, $[0,1]$6 is not computable, which the paper interprets as a signal of excessive tail severity relative to the Gaussian benchmark. The proposed five-level classification ranges from Level I (Mild) for $[0,1]$7 to Level V (Extreme) when $[0,1]$8 is incomputable. This RSI differs sharply from frequency-based reliability indices because it is explicitly designed to expose hidden severity in rare but catastrophic tails.

In machine-condition monitoring, "A Robust Method for Fault Detection and Severity Estimation in Mechanical Vibration Data" introduces a continuous severity index built from anomaly-score exceedances and then describes how it can be adapted into an RSI (Jeon et al., 4 Apr 2025). A T-GCN forecaster produces one-step-ahead residuals and anomaly scores

$[0,1]$9

With threshold $C_{i,t}$0 set to the maximum training prediction error, exceedances are

$C_{i,t}$1

The online mean and standard deviation of exceedances define

$C_{i,t}$2

The paper then proposes a risk-ready adaptation

$C_{i,t}$3

or, in a minimalist proxy, $C_{i,t}$4. Here severity is a smoothed summary of persistence and variability in anomalous behavior, intended to reduce the instability of raw threshold crossings in predictive-maintenance settings.

6. Comparative interpretation, limitations, and acronym collisions

Across these literatures, three recurrent design choices appear. First, severity is frequently decoupled from raw event frequency: telematics RSI uses inverse-probability tail rarity rather than claim size, structural reliability uses conditional failure deficit rather than failure probability, and machine diagnostics uses exceedance magnitude and variability rather than binary alarms (Lee et al., 16 Mar 2026, Leblouba et al., 16 Aug 2025, Jeon et al., 4 Apr 2025). Second, aggregation is central: Bayesian conjugacy in telematics, unweighted topic averages in LLM safety, CAPEC-based ontology averaging in TLDR, and survey normalization in COTS all compress heterogeneous evidence into a scalar ranking index (Akiri et al., 12 Sep 2025, Mahler et al., 2020, Gupta et al., 2012). Third, several papers position RSI as a governance or prioritization tool rather than a causal model of harm.

The limitations are equally heterogeneous. The LLM-safety study does not report confidence intervals, significance tests, or bootstrapped uncertainty for RSI comparisons (Akiri et al., 12 Sep 2025). The telematics framework assumes Gaussianity for typical behavior, independence after thinning, and a layered Uniform tail structure, while noting possible violations from persistent serial dependence, regime shifts, or non-Gaussian bulk (Lee et al., 16 Mar 2026). TLDR relies on small expert panels and equal weighting across mapped CAPECs, and the full multi-aspect severity decomposition is deferred (Mahler et al., 2020). The COTS survey method does not report reliability coefficients or a fully specified FRVR aggregation rule, and its “Risk Probability” is explicitly unconventional as a probability notion (Gupta et al., 2012). The structural index becomes undefined when normalized failure deficit exceeds the Gaussian-equivalence domain, which is diagnostically useful but also marks the limit of that benchmark (Leblouba et al., 16 Aug 2025).

A further source of confusion is acronym collision. "Accelerated Gradient Methods with Biased Gradient Estimates: Risk Sensitivity, High-Probability Guarantees, and Large Deviation Bounds" uses RSI to mean "Risk-Sensitive Index," defined as an exponential-moment functional of cumulative suboptimality,

$C_{i,t}$5

rather than a risk-severity score (Gürbüzbalaban et al., 17 Sep 2025). This use belongs to robust control and stochastic optimization, not to severity indexing in the actuarial, safety, or engineering senses discussed above.

Taken together, the literature indicates that RSI is a flexible naming convention for scalar risk summaries whose semantics are entirely domain-dependent. In some settings it is a posterior risk rate, in others a bounded compliance score, a severity subindex, a normalized survey burden, or an inverse image of a tail benchmark. The shared