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Reliability and Probabilistic Risk Assessment - How They Play Together

PRA methodology is one of the probabilistic analysis methods that NASA brought from the nuclear industry to assess the risk of LOM, LOV and LOC for launch vehicles. PRA is a system scenario based risk assessment that uses a combination of fault trees, event trees, event sequence diagrams, and probability and statistical data to analyze the risk of a system, a process, or an activity. It is a process designed to answer three basic questions: What can go wrong? How likely is it? What is the severity of the degradation? Since 1986, NASA, along with industry partners, has conducted a number of PRA studies to predict the overall launch vehicles risks. Planning Research Corporation conducted the first of these studies in 1988. In 1995, Science Applications International Corporation (SAIC) conducted a comprehensive PRA study. In July 1996, NASA conducted a two-year study (October 1996 - September 1998) to develop a model that provided the overall Space Shuttle risk and estimates of risk changes due to proposed Space Shuttle upgrades. After the Columbia accident, NASA conducted a PRA on the Shuttle External Tank (ET) foam. This study was the most focused and extensive risk assessment that NASA has conducted in recent years. It used a dynamic, physics-based, integrated system analysis approach to understand the integrated system risk due to ET foam loss in flight. Most recently, a PRA for Ares I launch vehicle has been performed in support of the Constellation program. Reliability, on the other hand, addresses the loss of functions. In a broader sense, reliability engineering is a discipline that involves the application of engineering principles to the design and processing of products, both hardware and software, for meeting product reliability requirements or goals. It is a very broad design-support discipline. It has important interfaces with many other engineering disciplines. Reliability as a figure of merit (i.e. the metric) is the probability that an item will perform its intended function(s) for a specified mission profile. In general, the reliability metric can be calculated through the analyses using reliability demonstration and reliability prediction methodologies. Reliability analysis is very critical for understanding component failure mechanisms and in identifying reliability critical design and process drivers. The following sections discuss the PRA process and reliability engineering in detail and provide an application where reliability analysis and PRA were jointly used in a complementary manner to support a Space Shuttle flight risk assessment.

Safie, Fayssal M.

The calculation of radial dose from heavy ions: predictions of biological action cross sections

The track structure model of heavy ion cross sections was developed by Katz and co-workers in the 1960s. In this model the action cross section is evaluated by mapping the dose-response of a detector to gamma rays (modeled from biological target theory) onto the radial dose distribution from delta rays about the path of the ion. This is taken to yield the radial distribution of probability for a "hit" (an interaction leading to an observable end-point). Radial integration of the probability yields the cross section. When different response from ions of different Z having the same stopping power is observed this model may be indicated. Since the 1960s there have been several developments in the computation of the radial dose distribution, in the measurement of these distributions, and in new radiobiological data against which to test the model. The earliest model, by Butts and Katz made use of simplified delta ray distribution functions, of simplified electron range-energy relations, and neglected angular distributions. Nevertheless it made possible the calculation of cross sections for the inactivation of enzymes and viruses, and allowed extension to tracks in nuclear emulsions and other detectors and to biological cells. It set the pattern for models of observable effects in the matter through which the ion passed. Here we outline subsequent calculations of radial dose which make use of improved knowledge of the electron emission spectrum, the electron range-energy relation, the angular distribution, and some considerations of molecular excitation, of particular interest both close to the path of the ion and the outer limits of electron penetration. These are applied to the modeling of action cross sections for the inactivation of several strains of E-coli and B. subtilis spores where extensive measurements in the "thin-down" region have been made with heavy ion beams. Such calculations serve to test the radial dose calculations at the outer limit of electron penetration. We lack data from which to test these calculations in regions close to the path of the ion aside from our earliest work on latent tracks in plastics, though it appears that the criterion then suggested for the threshold of track formation, of a minimal dose at a minimal distance (of about 20 angstroms, in plastics), remains valid.

NASA Discipline Radiation Health

A comparative analysis of YOLOv8 and U-Net image segmentation approaches for transmission electron micrographs of polycrystalline thin films

Metallic thin films offer a platform to experimentally study the dynamics of microstructural evolution, but the required transmission electron microscopy (TEM)-based imaging generates complex images that are challenging to segment and quantify. This work provides a comparative analysis of a new YOLOv8 model and an established U-Net model for bright-field TEM images of polycrystals, employing a framework leveraging physical observables to evaluate performance against two hand-traced benchmark datasets. This methodology obviates the comparison of large, diversely structured, and manually labeled datasets that are required to assess performance on a per-image/per-pixel basis. It is found that the YOLOv8 model, adapted for real-time instance segmentation, has up to 43× faster inferencing (NVIDIA GeForce RTX 4090) compared to U-Net and reconstructs hand-traced grain size distributions (GSDs) with excellent fidelity, finding mean diameter within 3% for grains near an optimal magnification; for grains that deviate from the optimal pixel-diameter, the size of small- (large)-diameter grains is systematically over- (under)-estimated. This is partially mitigated by including scale-aware augmentations during training. Moreover, when the bias is corrected post-inference by a rigid shift in distribution, the YOLOv8 model reproduces ground truth GSDs with exceptional fidelity, with statistical tests indicating <5% probability that the distributions are distinct. Based on ground truth data, calibration curves pertaining to this shift can be constructed for a given model. This issue is not present in the U-Net model’s results, indicating that for quantitative measurements where the true size of objects is of interest, special procedures must be implemented for YOLO-based models.

36 MATERIALS SCIENCE

A Framework for the Optimization of Water Treatment Processes Under Uncertainty Assessed through Process Operability

Conference presentation conveying work conducted on developing a framework for the optimization of water treatment processes after applying robust optimization and process operability tools. The objective of this framework is to optimize treatment processes under the uncertainty of source water conditions. This work contributes to robust optimization and process operability methodologies, allowing for the extension of probability from statistical models to operability calculations.

Barber, Hunter

Probabilistic Error Bounds for Low-Rank Tensor Decompositions Used in Large-Scale Data Analysis Applications (LDRD Final Report)

This report documents a research project on analyzing low-rank tensor models for data analysis that took place at Sandia National Laboratories from October 2023–September 2025. The focus of this work was to extend theoretical frameworks from statistics and probability theory for use with models for scalar, vector, and matrix data to models with tensor, or general multi-dimensional array, data. Through this work, we have provided a new set of tools for bounding errors on low-rank tensor models of both complete and sampled data. The remainder of this report is organized as follows. In Section 1, we describe the proposed work at the start of the project. Section 2 describes the research advances made as part of the project. Other research contributions in the form of conference presentations and software development is provided in Section 3. Workforce development at Sandia and Florida Atlantic University (via a subcontract on this project) is provided in Section 4.

97 MATHEMATICS AND COMPUTING