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Risk based decision tool for space exploration missions

This paper presents an approach and corresponding tool to assess and analyze the risks involved in a mission during the pre-phase A design process. This approach is based on creating a risk template for each subsystem expert involved in the mission design process and defining appropriate interactions between the templates.

space exploration proposals↗

Human Reliability Assessments: Using the Past (Shuttle) to Predict the Future (ORION)

NASA uses two HRA assessment methodologies. The first is a simplified method which is based on how much time is available to complete the action, with consideration included for environmental and personal factors that could influence the human's reliability. This method is expected to provide a conservative value or placeholder as a preliminary estimate. This preliminary estimate is used to determine which placeholder needs a more detailed assessment. The second methodology is used to develop a more detailed human reliability assessment on the performance of critical human actions. This assessment needs to consider more than the time available, this would include factors such as: the importance of the action, the context, environmental factors, potential human stresses, previous experience, training, physical design interfaces, available procedures/checklists and internal human stresses. The more detailed assessment is still expected to be more realistic than that based primarily on time available. When performing an HRA on a system or process that has an operational history, we have information specific to the task based on this history and experience. In the case of a PRA model that is based on a new design and has no operational history, providing a "reasonable" assessment of potential crew actions becomes more problematic. In order to determine what is expected of future operational parameters, the experience from individuals who had relevant experience and were familiar with the system and process previously implemented by NASA was used to provide the "best" available data. Personnel from Flight Operations, Flight Directors, Launch Test Directors, Control Room Console Operators and Astronauts were all interviewed to provide a comprehensive picture of previous NASA operations. Verification of the assumptions and expectations expressed in the assessments will be needed when the procedures, flight rules and operational requirements are developed and then finalized.

DeMott, Diana L.↗

A systems approach to computer-based training

This paper describes the hardware and software systems approach used in the Automated Recertification Training System (ARTS), a Phase 2 Small Business Innovation Research (SBIR) project for NASA Kennedy Space Center (KSC). The goal of this project is to optimize recertification training of technicians who process the Space Shuttle before launch by providing computer-based training courseware. The objectives of ARTS are to implement more effective CBT applications identified through a need assessment process and to provide an ehanced courseware production system. The system's capabilities are demonstrated by using five different pilot applications to convert existing classroom courses into interactive courseware. When the system is fully implemented at NASA/KSC, trainee job performance will improve and the cost of courseware development will be lower. Commercialization of the technology developed as part of this SBIR project is planned for Phase 3. Anticipated spin-off products include custom courseware for technical skills training and courseware production software for use by corporate training organizations of aerospace and other industrial companies.

Drape, Gaylen W.↗

Aliasing as noise - A quantitative and qualitative assessment

We present a model-based argument that, for the purposes of system design and digital image processing, aliasing should be treated as signal-dependent additive noise. By using a computational simulation based on this model, we process (high resolution images of) natural scenes in a way which enables the 'aliased component' of the reconstructed image to be isolated unambiguously. We demonstrate that our model-based argument leads naturally to system design metrics which quantify the extent of aliasing. And, by illustrating several aliased component images, we provide a qualitative assessment of aliasing as noise.

Park, Stephen K.↗

CO2 Insulation for Thermal Control of the Mars Science Laboratory

The National Aeronautics and Space Administration (NASA) is sending a large (>850 kg) rover as part of the Mars Science Laboratory (MSL) mission to Mars in 2011. The rover's primary power source is a Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) that generates roughly 2000 W of heat, which is converted to approximately 110 W of electrical power for use by the rover electronics, science instruments, and mechanism-actuators. The large rover size and extreme thermal environments (cold and hot) for which the rover is designed for led to a sophisticated thermal control system to keep it within allowable temperature limits. The pre-existing Martian atmosphere of low thermal conductivity CO2 gas (8 Torr) is used to thermally protect the rover and its components from the extremely cold Martian environment (temperatures as low as -130 deg C). Conventional vacuum based insulation like Multi Layer Insulation (MLI) is not effective in a gaseous atmosphere, so engineered gaps between the warm rover internal components and the cold rover external structure were employed to implement this thermal isolation. Large gaps would lead to more thermal isolation, but would also require more of the precious volume available within the rover. Therefore, a balance of the degree of thermal isolation achieved vs. the volume of rover utilized is required to reach an acceptable design. The temperature differences between the controlled components and the rover structure vary from location to location so each gap has to be evaluated on a case-by-case basis to arrive at an optimal thickness. For every configuration and temperature difference, there is a critical thickness below which the heat transfer mechanism is dominated by simple gaseous thermal conduction. For larger gaps, the mechanism is dominated by natural convection. In general, convection leads to a poorer level of thermal isolation as compared to conduction. All these considerations play important roles in the optimization process. A three-step process was utilized to design this insulation. The first step is to come up with a simple, textbook based, closed-form equation assessment of gap thickness vs. resultant thermal isolation achieved. The second step is a more sophisticated numerical assessment using Computational Fluid Dynamics (CFD) software to investigate the effect of complicated geometries and temperature contours along them to arrive at the effective thermal isolation in a CO2 atmosphere. The third step is to test samples of representative geometries in a CO2 filled chamber to measure the thermal isolation achieved. The results of these assessments along with the consistency checks across these methods leads to the formulation of design-guidelines for gap implementation within the rover geometry. Finally, based on the geometric and functional constraints within the real rover system, a detailed design that accommodates all these factors is arrived at. This paper will describe in detail this entire process, the results of these assessments and the final design that was implemented.

CO2↗

An Intelligent Computer-aided Training System (CAT) for Diagnosing Adult Illiterates: Integrating NASA Technology into Workplace Literacy

An important part of NASA's mission involves the secondary application of its technologies in the public and private sectors. One current application being developed is The Adult Literacy Evaluator, a simulation-based diagnostic tool designed to assess the operant literacy abilities of adults having difficulties in learning to read and write. Using Intelligent Computer-Aided Training (ICAT) system technology in addition to speech recognition, closed-captioned television (CCTV), live video and other state-of-the-art graphics and storage capabilities, this project attempts to overcome the negative effects of adult literacy assessment by allowing the client to interact with an intelligent computer system which simulates real-life literacy activities and materials and which measures literacy performance in the actual context of its use. The specific objectives of the project are as follows: (1) to develop a simulation-based diagnostic tool to assess adults' prior knowledge about reading and writing processes in actual contexts of application; (2) to provide a profile of readers' strengths and weaknesses; and (3) to suggest instructional strategies and materials which can be used as a beginning point for remediation. In the first and development phase of the project, descriptions of literacy events and environments are being written and functional literacy documents analyzed for their components. From these descriptions, scripts are being generated which define the interaction between the student, an on-screen guide and the simulated literacy environment.

Yaden, David B., Jr.↗

The adult literacy evaluator: An intelligent computer-aided training system for diagnosing adult illiterates

An important part of NASA's mission involves the secondary application of its technologies in the public and private sectors. One current application being developed is The Adult Literacy Evaluator, a simulation-based diagnostic tool designed to assess the operant literacy abilities of adults having difficulties in learning to read and write. Using ICAT system technology in addition to speech recognition, closed-captioned television (CCTV), live video and other state-of-the art graphics and storage capabilities, this project attempts to overcome the negative effects of adult literacy assessment by allowing the client to interact with an intelligent computer system which simulates real-life literacy activities and materials and which measures literacy performance in the actual context of its use. The specific objectives of the project are as follows: (1) To develop a simulation-based diagnostic tool to assess adults' prior knowledge about reading and writing processes in actual contexts of application; (2) to provide a profile of readers' strengths and weaknesses; and (3) to suggest instructional strategies and materials which can be used as a beginning point for remediation. In the first and developmental phase of the project, descriptions of literacy events and environments are being written and functional literacy documents analyzed for their components. Examples of literacy events and situations being considered included interactions with environmental print (e.g., billboards, street signs, commercial marquees, storefront logos, etc.), functional literacy materials (e.g., newspapers, magazines, telephone books, bills, receipts, etc.) and employment related communication (i.e., job descriptions, application forms, technical manuals, memorandums, newsletters, etc.). Each of these situations and materials is being analyzed for its literacy requirements in terms of written display (i.e., knowledge of printed forms and conventions), meaning demands (i.e., comprehension and word knowledge) and social situation. From these descriptions, scripts are being generated which define the interaction between the student, an on-screen guide and the simulated literacy environment. The proposed outcome of the Evaluator is a diagnostic profile which will present broad classifications of literacy behaviors across the major areas of metacognitive abilities, word recognition, vocabulary knowledge, comprehension and writing. From these classifications, suggestions for materials and strategies for instruction with which to begin corrective action will be made. The focus of the Literacy Evaluator will be essentially to provide an expert diagnosis and an interpretation of that assessment which then can be used by a human tutor to further design and individualize a remedial program as needed through the use of an authoring system.

Yaden, David B., Jr.↗

Helioseismic Holography and a Study of the Process of Magnetic Flux Disappearance in Canceling Bipoles

Project 1: We have developed and applied a technique of helioseismic holography along the lines of originally set out in our proposal. The result of the application of this diagnostic technique to solar activity and the quiet Sun has produced a number of important discoveries: (1) acoustic moats surrounding sunspots; (2) acoustic glories surround large active regions; (3) acoustic condensations beneath active regions; and (4) temporally-resolve acoustic images of a solar flare. These results have been published in a series of papers in the Astrophysical Journal. We think that helioseismic holography is now established as the most powerful and discriminating diagnostic in local helioseismology. Project 2: We conducted a collaborative observational program to define the physical character and magnetic geometry of canceling magnetic bipoles aimed at determining if the cancellation process is the result of submergence of magnetic fields. This assessment is based on ground-based observations combining photospheric and chromospheric magnetograms from NSO/KP, BBSO, and SOHO-MDI, and EUV and X-ray images from SOHO EIT/CDS, Yohkoh/SXT, and TRACE. Our study involves the analysis of data taken during three observing campaigns to define the height structure of canceling bipoles inferred from magnetic field and intensity images, and how this varies with time. We find that some canceling bipoles can be explained by the submerge of their magnetic flux. A paper on the results of this analysis will be presented at an upcoming scientific meeting and be written up for publication.

Lindsey, Charles↗

Ames Hybrid Combustion Facility

The report summarizes the design, fabrication, safety features, environmental impact, and operation of the Ames Hybrid-Fuel Combustion Facility (HCF). The facility is used in conducting research into the scalability and combustion processes of advanced paraffin-based hybrid fuels for the purpose of assessing their applicability to practical rocket systems. The facility was designed to deliver gaseous oxygen at rates between 0.5 and 16.0 kg/sec to a combustion chamber operating at pressures ranging from 300 to 900. The required run times were of the order of 10 to 20 sec. The facility proved to be robust and reliable and has been used to generate a database of regression-rate measurements of paraffin at oxygen mass flux levels comparable to those of moderate-sized hybrid rocket motors.

Zilliac, Greg↗

Monitoring Water-Related Ecosystems with Earth Observation Data in Support of Sustainable Development Goal (SDG) 6 Reporting

Lack of national data on water-related ecosystems is a major challenge to achieving the Sustainable Development Goal (SDG) 6 targets by 2030. Monitoring surface water extent, wetlands, and water quality from space can be an important asset for many countries in support of SDG 6 reporting. We demonstrate the potential for Earth observation (EO) data to support country reporting for SDG Indicator 6.6.1, ‘Change in the extent of water-related ecosystems over time’ and identify important considerations for countries using these data for SDG reporting. The spatial extent of water-related ecosystems, and the partial quality of water within these ecosystems is investigated for seven countries. Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat 5, 7, and 8 with Shuttle Radar Topography Mission (SRTM) are used to measure surface water extent at 250 m and 30 m spatial resolution, respectively, in Cambodia, Jamaica, Peru, the Philippines, Senegal, Uganda, and Zambia. The extent of mangroves is mapped at 30 m spatial resolution using Landsat 8 Operational Land Imager (OLI), Sentinel-1, and SRTM data for Jamaica, Peru, and Senegal. Using Landsat 8 and Sentinel 2A imagery, total suspended solids and chlorophyll-a are mapped over time for a select number of large surface water bodies in Peru, Senegal, and Zambia. All of the EO datasets used are of global coverage and publicly available at no cost. The temporal consistency and long time-series of many of the datasets enable replicability over time, making reporting of change from baseline values consistent and systematic. We find that statistical comparisons between different surface water data products can help provide some degree of confidence for countries during their validation process and highlight the need for accuracy assessments when using EO-based land change data for SDG reporting. We also raise concern that EO data in the context of SDG Indicator 6.6.1 reporting may be more challenging for some countries, such as small island nations, than others to use in assessing the extent of water-related ecosystems due to scale limitations and climate variability. Country-driven validation of the EO data products remains a priority to ensure successful data integration in support of SDG Indicator 6.6.1 reporting. Multi-country studies such as this one can be valuable tools for helping to guide the evolution of SDG monitoring methodologies and provide a useful resource for countries reporting on water-related ecosystems. The EO data analyses and statistical methods used in this study can be easily replicated for country-driven validation of EO data products in the future.

water-related ecosystems; surface water extent; ma↗

Monitoring Water-Related Ecosystems with Earth Observation Data in Support of Sustainable Development Goal (SDG) 6 Reporting

Lack of national data on water-related ecosystems is a major challenge to achieving the Sustainable Development Goal (SDG) 6 targets by 2030. Monitoring surface water extent, wetlands, and water quality from space can be an important asset for many countries in support of SDG 6reporting. We demonstrate the potential for Earth observation (EO) data to support country reporting for SDG Indicator 6.6.1, ‘Change in the extent of water-related ecosystems over time’ and identify important considerations for countries using these data for SDG reporting. The spatial extent of water-related ecosystems, and the partial quality of water within these ecosystems is investigated for seven countries. Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat 5, 7, and 8 with Shuttle Radar Topography Mission (SRTM) are used to measure surface water extent at 250 m and 30 m spatial resolution, respectively, in Cambodia, Jamaica, Peru, the Philippines, Senegal, Uganda, and Zambia. The extent of mangroves is mapped at 30 m spatial resolution using Landsat 8 Operational Land Imager (OLI), Sentinel-1, and SRTM data for Jamaica, Peru, and Senegal. Using Landsat 8 and Sentinel 2A imagery, total suspended solids and chlorophyll-a are mapped overtime for a select number of large surface water bodies in Peru, Senegal, and Zambia. All of the EO datasets used are of global coverage and publicly available at no cost. The temporal consistency and long time-series of many of the datasets enable replicability over time, making reporting of change from baseline values consistent and systematic. We find that statistical comparisons between different surface water data products can help provide some degree of confidence for countries during their validation process and highlight the need for accuracy assessments when using EO-based land change data for SDG reporting. We also raise concern that EO data in the context of SDG Indicator 6.6.1reporting may be more challenging for some countries, such as small island nations, than others to use in assessing the extent of water-related ecosystems due to scale limitations and climate variability. Country-driven validation of the EO data products remains a priority to ensure successful data integration in support of SDG Indicator 6.6.1 reporting. Multi-country studies such as this one can be valuable tools for helping to guide the evolution of SDG monitoring methodologies and provide a useful resource for countries reporting on water-related ecosystems. The EO data analyses and statistical methods used in this study can be easily replicated for country-driven validation of EO data products in the future.

Raha Hakimdavar↗

Dimensions of Credibility in Models and Simulations

Based on the National Aeronautics and Space Administration's (NASA's) work in developing a standard for models and simulations (M&S), the subject of credibility in M&S became a distinct focus. This is an indirect result from the Space Shuttle Columbia Accident Investigation Board (CAIB), which eventually resulted in an action, among others, to improve the rigor in NASA's M&S practices. The focus of this action came to mean a standardized method for assessing and reporting results from any type of M&S. As is typical in the standards development process, this necessarily developed into defming a common terminology base, common documentation requirements (especially for M&S used in critical decision making), and a method for assessing the credibility of M&S results. What surfaced in the development of the NASA Standard was the various dimensions credibility to consider when accepting the results from any model or simulation analysis. The eight generally relevant factors of credibility chosen in the NASA Standard proved only one aspect in the dimensionality of M&S credibility. At the next level of detail, the full comprehension of some of the factors requires an understanding along a couple of dimensions as well. Included in this discussion are the prerequisites for the appropriate use of a given M&S, the choice of factors in credibility assessment with their inherent dimensionality, and minimum requirements for fully reporting M&S results.

Steele, Martin J.↗

Evaluating Primary Dendrite Trunk Diameters in Directionally Solidified Al-Si Alloys

The primary dendrite trunk diameters of Al-Si alloys that were directionally solidified over a range of processing conditions have been measured. These data are analyzed with a model based primarily on an assessment of secondary dendrite arm dissolution in the mushy zone. Good fit with the experimental data is seen and it is suggested that the primary dendrite trunk diameter is a useful metric that correlates well with the actual solidification processing parameters. These results are placed in context with the limited results from the aluminium - 7 wt. % silicon samples directionally solidified aboard the International Space Station as part of the MICAST project.

Grugel, R. N.↗

Construction of Polarimetric Radar-Based Reference Rain Maps for the Iowa Flood Studies Campaign

The Global Precipitation Measurement (GPM) Mission Iowa Flood Studies (IFloodS) campaign was conducted in central and northeastern Iowa during the months of April-June, 2013. Specific science objectives for IFloodS included quantification of uncertainties in satellite and ground-based estimates of precipitation, 4-D characterization of precipitation physical processes and associated parameters (e.g., size distributions, water contents, types, structure etc.), assessment of the impact of precipitation estimation uncertainty and physical processes on hydrologic predictive skill, and refinement of field observations and data analysis approaches as they pertain to future GPM integrated hydrologic validation and related field studies. In addition to field campaign archival of raw and processed satellite data (including precipitation products), key ground-based platforms such as the NASA NPOL S-band and D3R Ka/Ku-band dual-polarimetric radars, University of Iowa X-band dual-polarimetric radars, a large network of paired rain gauge platforms, and a large network of 2D Video and Parsivel disdrometers were deployed. In something of a canonical approach, the radar (NPOL in particular), gauge and disdrometer observational assets were deployed to create a consistent high-quality distributed (time and space sampling) radar-based ground "reference" rainfall dataset, with known uncertainties, that could be used for assessing the satellite-based precipitation products at a range of space/time scales. Subsequently, the impact of uncertainties in the satellite products could be evaluated relative to the ground-benchmark in coupled weather, land-surface and distributed hydrologic modeling frameworks as related to flood prediction. Relative to establishing the ground-based "benchmark", numerous avenues were pursued in the making and verification of IFloodS "reference" dual-polarimetric radar-based rain maps, and this study documents the process and results as they pertain specifically to efforts using the NPOL radar dataset. The initial portions of the "process" involved dual-polarimetric quality control procedures which employed standard phase and correlation-based approaches to removal of clutter and non-meteorological echo. Calculation of a scale-adaptive KDP was accomplished using the method of Wang and Chandrasekar (2009; J. Atmos. Oceanic Tech.). A dual-polarimetric blockage algorithm based on Lang et al. (2009; J. Atmos. Oceanic Tech.) was then implemented to correct radar reflectivity and differential reflectivity at low elevation angles. Next, hydrometeor identification algorithms were run to identify liquid and ice hydrometeors. After the quality control and data preparation steps were completed several different dual-polarimetric rain estimation algorithms were employed to estimate rainfall rates using rainfall scans collected approximately every two to three minutes throughout the campaign. These algorithms included a polarimetrically-tuned Z-R algorithm that adjusts for drop oscillations (via Bringi et al., 2004, J. Atmos. Oceanic Tech.), and several different hybrid polarimetric variable approaches, including one that made use of parameters tuned to IFloodS 2D Video Disdrometer measurements. Finally, a hybrid scan algorithm was designed to merge the rain rate estimates from multiple low level elevation angle scans (where blockages could not be appropriately corrected) in order to create individual low-level rain maps. Individual rain maps at each time step were subsequently accumulated over multiple time scales for comparison to gauge network data. The comparison results and overall error character depended strongly on rain event type, polarimetric estimator applied, and range from the radar. We will present the outcome of these comparisons and their impact on constructing composited "reference" rainfall maps at select time and space scales.

Radar↗

Applying Generative-AI to NASA Documentation and Processes

This research and development project leverages generative-AI to assist in the generation of software process documentation based on NASA standards. By utilizing fine-tuned AI models, the proposed system will analyze NASA's software guidelines, helping to translate them into well-structured, compliant process documents. This assistance can reduce the manual effort required to produce such documentation, enhance consistency, and assure alignment with NASA's stringent software development and operational requirements. In addition to assisting in the generation of software process documentation, the project explores how generative-AI can help create audit checklists as well as assess the compliance of NASA provider documentation against applicable NASA standards. This approach would support the compliance auditing process, providing real-time insights and assessments. The intended result will be a streamlined process, potentially including a Python-based tool and database, that improves audit efficiency, reduces human error, lowers manpower costs and required manhours, and assures continuous compliance with NASA and industry evolving standards for safety-critical software development. Future task might be to investigate the software industry approach and standards for potential collaboration.

NASA Standards↗

Georgia resource assessment project: Institutionalizing LANDSAT and geographic data base techniques

Digital data from LANDSAT for each 1.1-acre cell in Georgia were processed and the land cover conditions were categorized. Several test cases were completed and an operational hardware and software processing capability was established at the Georgia Institute of Technology. The operational capability was developed to process the entire state (60,000 sq. miles and 14 LANDSAT scenes) in a cooperative project between eleven divisions and agencies at the regional, state, and federal levels. Products were developed for State agencies such as in both mapped and statistical formats. A computerized geographical data base was developed for management programs. To a large extent the applications of the data base evolved as users of LANDSAT information requested that other data (i.e., soils, slope, land use, etc.) be made compatible with LANDSAT for management programs. To date, geographic data bases incorporating LANDSAT and other spatial data deal with elements of the municipal solid waste management program, and reservoir management for the Corps of Engineers. LANDSAT data are also being used for applications in wetland, wildlife, and forestry management.

Pierce, R. R.↗

The Utility and Validity of Kinematic GPS Positioning for the Geosar Airborne Terrain Mapping Radar System

GeoSAR is an airborne, interferometric Synthetic Aperture Radar (IFSAR) system for terrain mapping, currently under development by a consortium including NASA's Jet Propulsion Laboratory (JPL), Calgis, Inc., a California mapping sciences company, and the California Department of Conservation (CaIDOC), with funding provided by the U.S. Army Corps of Engineers Topographic Engineering Center (TEC) and the U.S. Defense Advanced Research Projects Agency (DARPA). IFSAR data processing requires high-accuracy platform position and attitude knowledge. On 9 GeoSAR, these are provided by one or two Honeywell Embedded GPS Inertial Navigation Units (EGI) and an Ashtech Z12 GPS receiver. The EGIs provide real-time high-accuracy attitude and moderate-accuracy position data, while the Ashtech data, post-processed differentially with data from a nearby ground station using Ashtech PNAV software, provide high-accuracy differential GPS positions. These data are optimally combined using a Kalman filter within the GeoSAR motion measurement software, and the resultant position and orientation information are used to process the dual frequency (X-band and P-band) radar data to generate high-accuracy, high -resolution terrain imagery and digital elevation models (DEMs). GeoSAR requirements specify sub-meter level planimetric and vertical accuracies for the resultant DEMS. To achieve this, platform positioning errors well below one meter are needed. The goal of GeoSAR is to obtain 25 cm or better 3-D positions from the GPS systems on board the aircraft. By imaging a set of known point target corner-cube reflectors, the GeoSAR system can be calibrated. This calibration process yields the true position of the aircraft with an uncertainty of 20- 50 cm. This process thus allows an independent assessment of the accuracy of our GPS-based positioning systems. We will present an overview of the GeoSAR motion measurement system, focusing on the use of GPS and the blending of position data from the various systems. We will present the results of our calibration studies that relate to the accuracy the GPS positioning. We will discuss the effects these positioning, errors have on the resultant DEM products and imagery.

Freedman, Adam↗

Life Qualification of Hall Thrusters By Analysis and Test

High power Hall thrusters under development for deep space robotic and human exploration missions have demanding lifetime and operational requirements that make thruster life qualification challenging. The required burn times make it infeasible to conduct multiple tests with durations exceeding the life requirement, and complex wearout phenomena and the need for power throttling during missions complicate analyses and testing. The traditional qualification approach, a single life test that typically demonstrates 50 to 100% margin on the required lifetime, does not provide enough information to demonstrate low failure risk. It is a weak source of statistical information about the location of the peak in the failure probability distribution and provides no information on the width of the distribution. Testing does provide information that can be used to validate physics-based models of failure processes, however, and the combination can be used to assess mission risk. Validated, conservative, deterministic analysis can be used to demonstrate that most failure processes have such large margins that more detailed analysis is unnecessary. For a subset of the failure modes a more detailed probabilistic analysis is required. Pole erosion in a 12.5 kW Hall thruster is used as a detailed example of this qualification process.

Brophy, John R.↗