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NASA's New Approach for Evaluating Risk Reduction Due to Space Shuttle Upgrades

As part of NASA's intensive effort to incorporate quantitative risk assessment (QRA) tools in the Agency's decision-making process concerning Space Shuttle risk, NASA has developed a powerful risk assessment tool called the Quantitative Risk Assessment System (QRAS). The QRAS is a tool designed to estimate Space Shuttle risk and evaluate Space Shuttle upgrades. This paper presents an overview of the QRAS with focus on its application for evaluating the risk reduction due to proposed Space Shuttle upgrades. The application includes a case study from the Space Shuttle main engine (SSME). The QRAS overview section of the paper includes the QRAS development process, the technical approach to model development, the QRA quantification methods and techniques, and observations concerning the complex modeling involved in QRAS. The application section of the paper describes a practical case study using QRAS models for evaluating critical Space Shuttle Program upgrades, specifically a proposed SSME nozzle upgrade. This paper presents the method for evaluating the proposed upgrade by comparing the current nozzle (old design with well-established probabilistic models) to the channel wall nozzle (new design at the preliminary design level).

Safie, Fayssal M.↗

A System-Level Cost Modeling Framework for Design for Remanufacturing: A Case Study of an Agricultural Machine Transmission

Remanufacturing offers significant environmental and economic benefits by restoring end-of-life products to as-new conditions. Although extensive research has been conducted on the topic, the adoption of remanufacturing practices remains limited across various industries. A primary barrier to broader implementation is the substantial upfront investment required, which necessitates reliable cost modeling to justify potential future savings. Most existing models treat components independently and ignore inter-component dependencies. We develop a probabilistic, system-level cost modeling framework that integrates reliability, reusability, and a dependency matrix to capture cascading effects across components over multiple life cycles. Our model identifies those critical components that maximize remanufacturing benefits across a product's many lives. A toy example and an industry case study (John Deere PowrQuad transmission subassembly) illustrate how design alternatives affect cumulative cost. Using a Monte Carlo simulation (MCS) to perform life cycle cost analysis on the system with different design changes, we show the normalized average cost savings after three remanufacturing cycles. Accounting for dependencies meaningfully alters cost projections and ignoring them underestimates accumulated cost by up to 20% in our examples. Furthermore, the results of our study confirm that accounting for component interdependencies is necessary to produce cost estimates that meet industry standards.

Life Cycle Analysis and Design↗

flat10MIP: an emissions-driven experiment to diagnose the climate response to positive, zero and negative CO2 emissions

Abstract. The proportionality between global mean temperature and cumulative emissions of CO2 predicted in Earth system models (ESMs) is the foundation of carbon budgeting frameworks. Deviations from this behavior could impact estimates of required net-zero timings and negative emissions requirements to meet the Paris Agreement climate targets. However, existing ESM diagnostic experiments do not allow for direct estimation of these deviations as a function of defined emissions pathways. Here, we perform a set of climate model diagnostic experiments for the assessment of transient climate response to cumulative CO2 emissions (TCRE), the Zero Emissions Commitment (ZEC), and climate reversibility metrics in an emissions-driven framework. The emissions-driven experiments provide consistent independent variables simplifying simulation, analysis and interpretation, with emissions rates more comparable to recent levels than existing protocols using model-specific compatible emissions from the CMIP DECK 1pctCO2 experiment, where emissions rates tend to increase during the experiment, such that at the time of CO2 doubling in year 70, emissions are much greater than present-day values. A base experiment, “esm-flat10”, has constant emissions of CO2 of 10 GtC per year (near-present-day values), and initial results show that the TCRE estimated in this experiment is about 0.1 K less than that obtained using 1pctCO2. A subset of ESMs exhibit land carbon sinks that saturate during this experiment. A branch experiment, esm-flat10-zec, illustrates that both positive and negative ZEC effects are less pronounced under esm-flat10 than under 1pctCO2 – the magnitude of ZEC50 in ESMs is, on average, reduced by 30 % compared with 1pctCO2 branch experiments. A final experiment, esm-flat10-cdr, assesses climate reversibility under negative emissions, where we find that peak warming may occur before or after net zero and that the asymmetry in temperature at a given level of cumulative emissions between the positive and negative emissions phases is well described by ZEC in most models. Further, we find that existing probabilistic simple climate model (SCM) ensembles tend to overestimate temperature reversibility compared with ESMs, highlighting the need for additional constraints. We propose a set of climate diagnostic indicators to quantify various aspects of climate reversibility. These experiments were suggested as potential candidates in CMIP7 and have since been adopted as “fast track” simulations.

Sanderson, Benjamin M↗

Towards a Probabilistic Preliminary Design Criterion for Buckling Critical Composite Shells

A probability-based analysis method for predicting buckling loads of compression-loaded laminated-composite shells is presented, and its potential as a basis for a new shell-stability design criterion is demonstrated and discussed. In particular, a database containing information about specimen geometry, material properties, and measured initial geometric imperfections for a selected group of laminated-composite cylindrical shells is used to calculate new buckling-load "knockdown factors". These knockdown factors are shown to be substantially improved, and hence much less conservative than the corresponding deterministic knockdown factors that are presently used by industry. The probability integral associated with the analysis is evaluated by using two methods; that is, by using the exact Monte Carlo method and by using an approximate First-Order Second- Moment method. A comparison of the results from these two methods indicates that the First-Order Second-Moment method yields results that are conservative for the shells considered. Furthermore, the results show that the improved, reliability-based knockdown factor presented always yields a safe estimate of the buckling load for the shells examined.

Arbocz, Johann↗

A New Approach to Extreme Value Estimation Applicable to a Wide Variety of Random Variables

Designing reliable structures requires an estimate of the maximum and minimum values (i.e., strength and load) that may be encountered in service. Yet designs based on very extreme values (to insure safety) can result in extra material usage and hence, uneconomic systems. In aerospace applications, severe over-design cannot be tolerated making it almost mandatory to design closer to the assumed limits of the design random variables. The issue then is predicting extreme values that are practical, i.e. neither too conservative or non-conservative. Obtaining design values by employing safety factors is well known to often result in overly conservative designs and. Safety factor values have historically been selected rather arbitrarily, often lacking a sound rational basis. To answer the question of how safe a design needs to be has lead design theorists to probabilistic and statistical methods. The so-called three-sigma approach is one such method and has been described as the first step in utilizing information about the data dispersion. However, this method is based on the assumption that the random variable is dispersed symmetrically about the mean and is essentially limited to normally distributed random variables. Use of this method can therefore result in unsafe or overly conservative design allowables if the common assumption of normality is incorrect.

Holland, Frederic A., Jr.↗

CV4Quantum: Reducing the Sampling Overhead in Probabilistic Error Cancellation Using Control Variates

Quasiprobabilistic decompositions (QPDs) play a key role in maximizing the utility of near-term quantum hardware. For example, Probabilistic Error Cancellation (PEC) (an error mitigation technique) and circuit cutting (which enables large quantum computations to be performed on quantum hardware with a limited number of qubits) both involve QPDs. Computations based on QPDs typically incur large sampling overheads that grow exponentially with the number of error-terms mitigated or number of circuit-cuts employed, limiting their practical feasibility. In this work, we adapt the control variates variance reduction technique from the statistics literature in order to reduce the sampling overhead in QPD-based computations. We demonstrate our method using simulation experiments that mimic a realistic PEC scenario. In our experiments, we observed a more than 50% reduction in the number of samples needed to achieve a given precision, in more than 50% of the PEC-based estimations performed in the study when using our approach. We discuss how future research on constructing good control variates can lead to even stronger sampling overhead reduction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Enhanced Severe Transient Analysis for Prevention Technical Program Plan

This document outlines the development of a high fidelity, best estimate nuclear power plant severe transient simulation capability that will complement or enhance the integral system codes historically used for licensing and analysis of severe accidents. As with other tools in the Risk Informed Safety Margin Characterization (RISMC) Toolkit, the ultimate user of Enhanced Severe Transient Analysis and Prevention (ESTAP) capability is the plant decision-maker; the deliverable to that customer is a modern, simulation-based safety analysis capability, applicable to a much broader class of safety issues than is traditional Light Water Reactor (LWR) licensing analysis. Currently, the RISMC pathway’s major emphasis is placed on developing RELAP-7, a next-generation safety analysis code, and on showing how to use RELAP-7 to analyze margin from a modern point of view: that is, by characterizing margin in terms of the probabilistic spectra of the “loads” applied to systems, structures, and components (SSCs), and the “capacity” of those SSCs to resist those loads without failing. The first objective of the ESTAP task, and the focus of one task of this effort, is to augment RELAP-7 analyses with user-selected multi-dimensional, multi-phase models of specific plant components to simulate complex phenomena that may lead to, or exacerbate, severe transients and core damage. Such phenomena include: coolant crossflow between PWR assemblies during a severe reactivity transient, stratified single or two-phase coolant flow in primary coolant piping, inhomogeneous mixing of emergency coolant water or boric acid with hot primary coolant, and water hammer. These are well-documented phenomena associated with plant transients but that are generally not captured in system codes. They are, however, generally limited to specific components, structures, and operating conditions. The second ESTAP task is to similarly augment a severe (post-core damage) accident integral analyses code with high fidelity simulations that would allow investigation of multi-dimensional, multi-phase containment phenomena that are only treated approximately in established codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Hydrogen Plus Other Alternative Fuels Risk Assessment Models (HyRAM+) Version 4.1 Technical Reference Manual

The HyRAM+ software toolkit provides a basis for conducting quantitative risk assessment and consequence modeling for hydrogen, methane, and propane systems. HyRAM+ is designed to facilitate the use of state-of-the-art models to conduct robust, repeatable assessments of safety, hazards, and risk. HyRAM+ integrates deterministic and probabilistic models for quantifying accident scenarios, predicting physical effects, characterizing hazards (thermal effects from jet fires, overpressure effects from delayed ignition), and assessing impacts on people. HyRAM+ is developed at Sandia National Laboratories to support the development and revision of national and international codes and standards, and to provide developed models in a publicly-accessible toolkit usable by all stakeholders. This document provides a description of the methodology and models contained in HyRAM+ version 4.1. The two most significant changes for HyRAM+ version 4.1 from HyRAM+ version 4.0 are direct incorporation of unconfined overpressure into the QRA calculations and modification of the models for cryogenic liquid flow through an orifice. In QRA mode, the user no longer needs to input peak overpressure and impulse values that were calculated separately; rather, the unconfined overpressure is estimated for the given system inputs, leak size, and occupant location. The orifice flow model now solves for the maximum mass flux through the orifice at constant entropy while conserving energy, which does not require a direct speed of sound calculation. This does not affect the mass flow for all-gaseous releases; the method results in the same speed of sound for choked flow. However, this method does result in a higher (and more realistic) mass flow rate for a given leak size for liquid releases than was previously calculated.

08 HYDROGEN↗

Transfer learning for probabilistic localization of hidden cracks in concrete structures

Abstract The utility of discriminative supervised learning models built using multiple training-data sources is investigated for hidden crack localization in concrete. Feed-forward neural network (FFNN) is chosen as the model architecture, and transfer learning is used to assimilate the information obtained from different sources (computational physics simulations and laboratory experiments). The labeled training data consists of values of a damage index and the known locations of hidden cracks. The classification models need to learn how the presence of damage (hidden cracks) affects the damage index at different sensors for different test conditions. To this end, diagnostic FFNN models are built by sequentially adding and training new hidden layers to assimilate labeled information from computer models (different model geometries, test conditions, crack lengths, crack locations) and laboratory experiments on a plain cement slab. These transfer learning-based models are then used to localize damage in concrete specimens that reflect real-world conditions (i.e., specimens with steel reinforcement and randomly distributed aggregate). The actual damage state in these specimens is determined by extracting cores and performing petrographic studies on the extracted cores. The damage probability estimated by transfer learning-based models is compared with the petrographic damage rating index (DRI) to identify the most suitable approach to train the diagnostic models. The transfer learning-based diagnostic methodology shows promise and could be used in various structural health monitoring applications, where sufficient labeled data are typically not available from a single data source.

Miele, S.↗

Validating induced seismicity forecast models—Induced Seismicity Test Bench

Abstract Induced earthquakes often accompany fluid injection, and the seismic hazard they pose threatens various underground engineering projects. Models to monitor and control induced seismic hazard with traffic light systems should be probabilistic, forward‐looking, and updated as new data arrive. In this study, we propose an Induced Seismicity Test Bench to test and rank such models; this test bench can be used for model development, model selection, and ensemble model building. We apply the test bench to data from the Basel 2006 and Soultz‐sous‐Forêts 2004 geothermal stimulation projects, and we assess forecasts from two models: Shapiro and Smoothed Seismicity (SaSS) and Hydraulics and Seismics (HySei). These models incorporate a different mix of physics‐based elements and stochastic representation of the induced sequences. Our results show that neither model is fully superior to the other. Generally, HySei forecasts the seismicity rate better after shut‐in but is only mediocre at forecasting the spatial distribution. On the other hand, SaSS forecasts the spatial distribution better and gives better seismicity rate estimates before shut‐in. The shut‐in phase is a difficult moment for both models in both reservoirs: the models tend to underpredict the seismicity rate around, and shortly after, shut‐in.

Király‐Proag, Eszter↗

Installation Quality Framework: Investment Return Approach for Energy Savings on Building Product Installation

A case study was conducted on 44 residential homes using both traditional house wrap and ZIP System systems to measure the overall airtightness and compare estimated energy usages. The labor, material, and overhead and profit (O&P) costs were analyzed and used to determine the optimal choice for long-term benefits in terms of cost and performance. The impact of insulation installation is considered a key factor in improving the strategy of reducing energy consumption. Improved installation practices can affect the airtightness of common wall assemblies to reduce the building energy performance gaps and provide insight on how to allocate resources better. A framework was developed to analyze operational costs and building energy performance to address how installation quality is a factor in the return of investment in building construction for heating and cooling systems within the thermal envelope. With this methodology, aggressive energy performance goals will be met while balancing the tradeoff between installation techniques and building systems efficiency based on the introduced probabilistic investment return (PIR) metric.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Probabilisitc Geobiological Classification Using Elemental Abundance Distributions and Lossless Image Compression in Recent and Modern Organisms

Last year we presented techniques for the detection of fossils during robotic missions to Mars using both structural and chemical signatures[Storrie-Lombardi and Hoover, 2004]. Analyses included lossless compression of photographic images to estimate the relative complexity of a putative fossil compared to the rock matrix [Corsetti and Storrie-Lombardi, 2003] and elemental abundance distributions to provide mineralogical classification of the rock matrix [Storrie-Lombardi and Fisk, 2004]. We presented a classification strategy employing two exploratory classification algorithms (Principal Component Analysis and Hierarchical Cluster Analysis) and non-linear stochastic neural network to produce a Bayesian estimate of classification accuracy. We now present an extension of our previous experiments exploring putative fossil forms morphologically resembling cyanobacteria discovered in the Orgueil meteorite. Elemental abundances (C6, N7, O8, Na11, Mg12, Ai13, Si14, P15, S16, Cl17, K19, Ca20, Fe26) obtained for both extant cyanobacteria and fossil trilobites produce signatures readily distinguishing them from meteorite targets. When compared to elemental abundance signatures for extant cyanobacteria Orgueil structures exhibit decreased abundances for C6, N7, Na11, All3, P15, Cl17, K19, Ca20 and increases in Mg12, S16, Fe26. Diatoms and silicified portions of cyanobacterial sheaths exhibiting high levels of silicon and correspondingly low levels of carbon cluster more closely with terrestrial fossils than with extant cyanobacteria. Compression indices verify that variations in random and redundant textural patterns between perceived forms and the background matrix contribute significantly to morphological visual identification. The results provide a quantitative probabilistic methodology for discriminating putatitive fossils from the surrounding rock matrix and &om extant organisms using both structural and chemical information. The techniques described appear applicable to the geobiological analysis of meteoritic samples or in situ exploration of the Mars regolith. Keywords: cyanobacteria, microfossils, Mars, elemental abundances, complexity analysis, multifactor analysis, principal component analysis, hierarchical cluster analysis, artificial neural networks, paleo-biosignatures

Storrie-Lombardi, Michael C.↗

Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. Here, we explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quan- tified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Reduced carbon use efficiency and increased microbial turnover with soil warming

Global soil carbon (C) stocks are expected to decline with warming, and changes in microbial processes are key to this projection. However, warming responses of critical microbial parameters such as carbon use efficiency (CUE) and biomass turnover (rB) are not well understood. Here, we determine these parameters using a probabilistic inversion approach that integrates a microbial-enzyme model with 22 years of carbon cycling measurements at Harvard Forest. We find that increasing temperature reduces CUE but increases rB, and that two decades of soil warming increases the temperature sensitivities of CUE and rB. These temperature sensitivities, which are derived from decades-long field observations, contrast with values obtained from short-term laboratory experiments. We also show that long-term soil C flux and pool changes in response to warming are more dependent on the temperature sensitivity of CUE than that of rB. Using the inversion-derived parameters, we project that chronic soil warming at Harvard Forest over six decades will result in soil C gain of <1.0% on average (1 st and 3 rd quartiles: 3.0% loss and 10.5% gain) in the surface mineral horizon. Our results demonstrate that estimates of temperature sensitivity of microbial CUE and rB can be obtained and evaluated rigorously by integrating multidecadal datasets. This approach can potentially be applied in broader spatiotemporal scales to improve long-term projections of soil C feedbacks to climate warming.

54 ENVIRONMENTAL SCIENCES↗

A Computational Approach for Probabilistic Analysis of LS-DYNA Water Impact Simulations

NASA s development of new concepts for the Crew Exploration Vehicle Orion presents many similar challenges to those worked in the sixties during the Apollo program. However, with improved modeling capabilities, new challenges arise. For example, the use of the commercial code LS-DYNA, although widely used and accepted in the technical community, often involves high-dimensional, time consuming, and computationally intensive simulations. Because of the computational cost, these tools are often used to evaluate specific conditions and rarely used for statistical analysis. The challenge is to capture what is learned from a limited number of LS-DYNA simulations to develop models that allow users to conduct interpolation of solutions at a fraction of the computational time. For this problem, response surface models are used to predict the system time responses to a water landing as a function of capsule speed, direction, attitude, water speed, and water direction. Furthermore, these models can also be used to ascertain the adequacy of the design in terms of probability measures. This paper presents a description of the LS-DYNA model, a brief summary of the response surface techniques, the analysis of variance approach used in the sensitivity studies, equations used to estimate impact parameters, results showing conditions that might cause injuries, and concluding remarks.

Horta, Lucas G.↗

NASA's GMAO Atmospheric Motion Vectors Simulator: Description and Application to the MISTiC Winds Concept

An atmospheric wind vectors (AMVs) simulator was developed by NASA's GMAO to simulate observations from future satellite constellation concepts. The synthetic AMVs can then be used in OSSEs to estimate and quantify the potential added value of new observations to the present Earth observing system and, ultimately, the expected impact on the current weather forecasting skill. The GMAO AMV simulator is a tunable and flexible computer code that is able to simulate AMVs expected to be derived from different instruments and satellite orbit configurations. As a case study and example of the usefulness of this tool, the GMAO AMV simulator was used to simulate AMVs envisioned to be provided by the MISTiC Winds, a NASA mission concept consisting of a constellation of satellites equipped with infrared spectral midwave spectrometers, expected to provide high spatial and temporal resolution temperature and humidity soundings of the troposphere that can be used to derive AMVs from the tracking of clouds and water vapor features. The GMAO AMV simulator identifies trackable clouds and water vapor features in the G5NR and employs a probabilistic function to draw a subset of the identified trackable features. Before the simulator is applied to the MISTiC Winds concept, the simulator was calibrated to yield realistic observations counts and spatial distributions and validated considering as a proxy instrument to the MISTiC Winds the Himawari-8 Advanced Imager (AHI). The simulated AHI AMVs showed a close match with the real AHI AMVs in terms of observation counts and spatial distributions, showing that the GMAO AMVs simulator synthesizes AMVs observations with enough quality and realism to produce a response from the DAS equivalent to the one produced with real observations. When applied to the MISTiC Winds scanning points, it can be expected that the MISTiC Winds will be able to collect approximately 60,000 wind observations every 6 hours, if considering a constellation composed of 12 satellites (4 orbital planes). In addition, one of the main expected impacts of the MISTiC Winds concept is the ability to derive water vapor feature tracking AMVs below 500-400 hPa, an unique feature among the water vapor AMVs derived from the current Earth observing system.

Carvalho, David↗

NASA's GMAO Atmospheric Motion Vectors Simulator: Description and Application to the MISTiC Winds Concept

An atmospheric wind vectors (AMVs) simulator was developed by NASA's GMAO to simulate observations from future satellite constellation concepts. The synthetic AMVs can then be used in OSSEs to estimate and quantify the potential added value of new observations to the present Earth observing system and, ultimately, the expected impact on the current weather forecasting skill. The GMAO AMV simulator is a tunable and flexible computer code that is able to simulate AMVs expected to be derived from different instruments and satellite orbit configurations. As a case study and example of the usefulness of this tool, the GMAO AMV simulator was used to simulate AMVs envisioned to be provided by the MISTiC Winds, a NASA mission concept consisting of a constellation of satellites equipped with infrared spectral midwave spectrometers, expected to provide high spatial and temporal resolution temperature and humidity soundings of the troposphere that can be used to derive AMVs from the tracking of clouds and water vapor features. The GMAO AMV simulator identifies trackable clouds and water vapor features in the G5NR and employs a probabilistic function to draw a subset of the identified trackable features. Before the simulator is applied to the MISTiC Winds concept, the simulator was calibrated to yield realistic observations counts and spatial distributions and validated considering as a proxy instrument to the MISTiC Winds the Himawari-8 Advanced Imager (AHI). The simulated AHI AMVs showed a close match with the real AHI AMVs in terms of observation counts and spatial distributions, showing that the GMAO AMVs simulator synthesizes AMVs observations with enough quality and realism to produce a response from the DAS equivalent to the one produced with real observations. When applied to the MISTiC Winds scanning points, it can be expected that the MISTiC Winds will be able to collect approximately 60,000 wind observations every 6 hours, if considering a constellation composed of 12 satellites (4 orbital planes). In addition, one of the main expected impacts of the MISTiC Winds concept is the ability to derive water vapor feature tracking AMVs below 500-400 hPa, an unique feature among the water vapor AMVs derived from the current Earth observing system.

Carvalho, David↗

A Mechanistic Reliability Assessment of RVACS and Metal Fuel Inherent Reactivity Feedbacks

GE Hitachi Nuclear Energy (GEH) and Argonne National Laboratory (Argonne) participated in a two year collaboration to modernize and update the probabilistic risk assessment (PRA) for the PRISM sodium fast reactor. At a high level, the primary outcome of the project was the development of a next-generation PRA that is intended to enable risk-informed prioritization of safety- and reliability-focused research and development. A central Argonne task during this project was a reliability assessment of passive safety systems, which included the Reactor Vessel Auxiliary Cooling System (RVACS) and the inherent reactivity feedbacks of the metal fuel core. Both systems were examined utilizing a methodology derived from the Reliability Method for Passive Safety Functions (RMPS), with an emphasis on developing success criteria based on mechanistic system modeling while also maintaining consistency with the Fuel Damage Categories (FDCs) of the mechanistic source term assessment. This paper provides an overview of the reliability analyses of both systems, including highlights of the FMEAs, the construction of best-estimate models, uncertain parameter screening and propagation, and the quantification of system failure probability. In particular, special focus is given to the methodologies to perform the analysis of uncertainty propagation and the determination of the likelihood of violating FDC limits. Additionally, important lessons learned are also reviewed, such as optimal sampling methodologies for the discovery of low likelihood failure events and strategies for the combined treatment of aleatory and epistemic uncertainties.

Grabaskas, David↗