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At least 199 records · Page 11

Convection equation modeling: A non-iterative direct matrix solution algorithm for use with SINDA

The determination of the boundary conditions for a component-level analysis, applying discrete finite element and finite difference modeling techniques often requires an analysis of complex coupled phenomenon that cannot be described algebraically. For example, an analysis of the temperature field of a coldplate surface with an integral fluid loop requires a solution to the parabolic heat equation and also requires the boundary conditions that describe the local fluid temperature. However, the local fluid temperature is described by a convection equation that can only be solved with the knowledge of the locally-coupled coldplate temperatures. Generally speaking, it is not computationally efficient, and sometimes, not even possible to perform a direct, coupled phenomenon analysis of the component-level and boundary condition models within a single analysis code. An alternative is to perform a disjoint analysis, but transmit the necessary information between models during the simulation to provide an indirect coupling. For this approach to be effective, the component-level model retains full detail while the boundary condition model is simplified to provide a fast, first-order prediction of the phenomenon in question. Specifically for the present study, the coldplate structure is analyzed with a discrete, numerical model (SINDA) while the fluid loop convection equation is analyzed with a discrete, analytical model (direct matrix solution). This indirect coupling allows a satisfactory prediction of the boundary condition, while not subjugating the overall computational efficiency of the component-level analysis. In the present study a discussion of the complete analysis of the derivation and direct matrix solution algorithm of the convection equation is presented. Discretization is analyzed and discussed to extend of solution accuracy, stability and computation speed. Case studies considering a pulsed and harmonic inlet disturbance to the fluid loop are analyzed to assist in the discussion of numerical dissipation and accuracy. In addition, the issues of code melding or integration with standard class solvers such as SINDA are discussed to advise the user of the potential problems to be encountered.

Schrage, Dean S.↗

Future Improvements to Impact for Long Duration Exploration Spaceflight

BACKGROUND: While NASA currently uses the Integrated Medical Model (IMM) to model spaceflight medical risk for Low Earth Orbit missions, IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) was created to improve the fidelity of medical risk analysis for exploration missions involving the Lunar surface and beyond. OVERVIEW: While completion work continues on the initial version of the IMPACT tool, work has already begun to investigate ways to further enhance the fidelity of the model and its utility to stakeholders. DISCUSSION: Future additions leveraging the more robust and flexible IMPACT architecture include analyzing mission segments to account for segment-specific environments (ie. Lunar surface or microgravity), clinically tracible outcomes based on partial treatment of conditions, the ability to model mission outcomes based on provider Knowledge, Skills, and Abilities (KSAs), and the ability to affect the incidence of conditions based on the occurrence of related conditions (e.g. UTI progressing to sepsis). IMPACT also enables the addition of new conditions to its database as required to meet future risk assessment needs. Ultimately, the desire is to broaden IMPACT from a tool that models/trades medical risk to one that does so for all crew health and performance relevant systems (e.g., food, exercise, etc.).

E Stratton↗

Complexity Management Using Metrics for Trajectory Flexibility Preservation and Constraint Minimization

The growing demand for air travel is increasing the need for mitigating air traffic congestion and complexity problems, which are already at high levels. At the same time new surveillance, navigation, and communication technologies are enabling major transformations in the air traffic management system, including net-based information sharing and collaboration, performance-based access to airspace resources, and trajectory-based rather than clearance-based operations. The new system will feature different schemes for allocating tasks and responsibilities between the ground and airborne agents and between the human and automation, with potential capacity and cost benefits. Therefore, complexity management requires new metrics and methods that can support these new schemes. This paper presents metrics and methods for preserving trajectory flexibility that have been proposed to support a trajectory-based approach for complexity management by airborne or ground-based systems. It presents extensions to these metrics as well as to the initial research conducted to investigate the hypothesis that using these metrics to guide user and service provider actions will naturally mitigate traffic complexity. The analysis showed promising results in that: (1) Trajectory flexibility preservation mitigated traffic complexity as indicated by inducing self-organization in the traffic patterns and lowering traffic complexity indicators such as dynamic density and traffic entropy. (2)Trajectory flexibility preservation reduced the potential for secondary conflicts in separation assurance. (3) Trajectory flexibility metrics showed potential application to support user and service provider negotiations for minimizing the constraints imposed on trajectories without jeopardizing their objectives.

Idris, Husni↗

Brace For Impact – It’s Coming, Do You Know What to Do With It?

Long-duration human exploration spaceflight missions to the Moon and Mars present unprecedented challenges for providing in-mission medical care. Compared with the International Space Station, the greater distance from Earth will mean increased mission durations, communication delays, limited to no resupply opportunities, and significant limitations on the evacuation of ill or injured crew. Spacecraft mass, volume, and power will be curtailed while higher demands will be placed on the crew’s knowledge, skills, and abilities. In this higher risk environment, it is important to define and quantitatively estimate human system risk attributable to medical conditions. IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a probabilistic risk assessment (PRA) and medical trade space analysis tool being developed by NASA to advance medical system design for exploration missions. IMPACT has made a number of enhancements on the Integrated Medical Model, the PRA tool currently used by NASA. These updates include a novel medical evidence base baselined to a long duration, deep space exploration environment; an expanded medical condition list; and a trade space analysis capability (e.g. comparing risk profiles and mass/volume constraints for medical capabilities and resources). IMPACT core functionality includes quantification of a medical capability set and assisting with identification of specific medical resources/hardware for exploration missions. In addition, IMPACT provides sophisticated trade space capabilities to estimate how human system risk varies with changes to the mission architecture or medical capability set. This presentation will provide a brief overview of the IMPACT tool, discuss representative use cases, and show example results.

Benjamin Easter↗

Selection of Next Priority IMPACT Medical Conditions Based on Available Terrestrial and Spaceflight Data

BACKGROUND: As the era of exploration class missions begins, identification of medical conditions that may occur and require management becomes essential for the modeling of medical risk. To this end, NASA has developed IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces), a suite of tools to assist in assessment of medical risk analysis. It has incorporated an initial list of the 120 conditions of highest concern, labeled the IMPACT condition list 1.0 (ICL 1.0). This abstract describes a method for prioritizing the 92 conditions included on the Proposed Future Conditions List (PFCL) for inclusion in future iterations of the ICL. OVERVIEW: To construct the Prioritized Proposed Future Conditions List (P-PFCL), each condition on the PFCL was scored as “low,” “medium,” or “high” on each of four variables: incidence, likelihood of significant task impairment, diagnostic and treatment complexity, and treatment futility. Qualitative assessment using clinical judgement was utilized to score complexity, futility, and likelihood of impairment. Incidence was assessed quantitatively using spaceflight data and/or analog populations where available then assigned a score using established cutoffs. Logarithmic numerical values were assigned to each category label. A Prioritization Score was generated for each condition by taking the product of incidence and likelihood of task impairment (risk) divided by the product of complexity and futility (difficulty of care), with higher values corresponding to higher priority for future inclusion in the ICL. DISCUSSION: The described methods allow for the generation of a ranked P-PFCL to act as a decision support tool for selection of the next generation of modeled medical conditions. Some of the conditions ranked highly on the P-PFCL include EVA-related upper and lower extremity sprain/strain, iron deficiency, delirium, and hypertension, among others. While this effort does not attempt to quantify the absolute risk associated with each condition, it does attempt to semi-quantitatively estimate the risk of each condition relative to the other possible conditions. This tool in concert with subject matter expert opinion could optimize the future use of limited resources thereby producing a more accurate medical risk model, which will be essential to the upcoming exploration class missions.

Michael Pohlen↗

Automated Desalting Apparatus

Because salt and metals can mask the signature of a variety of organic molecules (like amino acids) in any given sample, an automated system to purify complex field samples has been created for the analytical techniques of electrospray ionization/ mass spectroscopy (ESI/MS), capillary electrophoresis (CE), and biological assays where unique identification requires at least some processing of complex samples. This development allows for automated sample preparation in the laboratory and analysis of complex samples in the field with multiple types of analytical instruments. Rather than using tedious, exacting protocols for desalting samples by hand, this innovation, called the Automated Sample Processing System (ASPS), takes analytes that have been extracted through high-temperature solvent extraction and introduces them into the desalting column. After 20 minutes, the eluent is produced. This clear liquid can then be directly analyzed by the techniques listed above. The current apparatus including the computer and power supplies is sturdy, has an approximate mass of 10 kg, and a volume of about 20 20 20 cm, and is undergoing further miniaturization. This system currently targets amino acids. For these molecules, a slurry of 1 g cation exchange resin in deionized water is packed into a column of the apparatus. Initial generation of the resin is done by flowing sequentially 2.3 bed volumes of 2N NaOH and 2N HCl (1 mL each) to rinse the resin, followed by .5 mL of deionized water. This makes the pH of the resin near neutral, and eliminates cross sample contamination. Afterward, 2.3 mL of extracted sample is then loaded into the column onto the top of the resin bed. Because the column is packed tightly, the sample can be applied without disturbing the resin bed. This is a vital step needed to ensure that the analytes adhere to the resin. After the sample is drained, oxalic acid (1 mL, pH 1.6-1.8, adjusted with NH4OH) is pumped into the column. Oxalic acid works as a chelating reagent to bring out metal ions, such as calcium and iron, which would otherwise interfere with amino acid analysis. After oxalic acid, 1 mL 0.01 N HCl and 1 mL deionized water is used to sequentially rinse the resin. Finally, the amino acids attached to the resin, and the analytes are eluted using 2.5 M NH4OH (1 mL), and the NH4OH eluent is collected in a vial for analysis.

Spencer, Maegan K.↗

Stress analysis of gas turbine engine structures using the boundary element method

The theory of the boundary element method is briefly reviewed with particular reference to the feasibility of elastic and inelastic three-dimensional stress analysis of complex structures characteristic of gas turbine engine components. Particular requirements of gas turbine analysis are defined, and examples of the use of a boundary element code designed for the three-dimensional stress analysis of turbine components are presented. It is shown that the general-purpose boundary element code can accurately and efficiently analyze many of the gas turbine engine structures.

Wilson, R. B.↗

The Strengths and Weaknesses of Logic Formalisms to Support Mishap Analysis

The increasing complexity of many safety critical systems poses new problems for mishap analysis. Techniques developed in the sixties and seventies cannot easily scale-up to analyze incidents involving tightly integrated software and hardware components. Similarly, the realization that many failures have systemic causes has widened the scope of many mishap investigations. Organizations, including NASA and the NTSB, have responded by starting research and training initiatives to ensure that their personnel are well equipped to meet these challenges. One strand of research has identified a range of mathematically based techniques that can be used to reason about the causes of complex, adverse events. The proponents of these techniques have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. Mathematical proofs can reduce the bias that is often perceived to effect the interpretation of adverse events. Others have opposed the introduction of these techniques by identifying social and political aspects to incident investigation that cannot easily be reconciled with a logic-based approach. Traditional theorem proving mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators routinely use in their analysis of adverse events. This paper summarizes some of the benefits that logics provide, describes their weaknesses, and proposes a number of directions for future research.

Johnson, C. W.↗

Model verification of mixed dynamic systems

A parameter-estimation method is described for verifying the mathematical model of mixed (combined interactive components from various engineering fields) dynamic systems against pertinent experimental data. The model verification problem is divided into two separate parts: defining a proper model and evaluating the parameters of that model. The main idea is to use differences between measured and predicted behavior (response) to adjust automatically the key parameters of a model so as to minimize response differences. To achieve the goal of modeling flexibility, the method combines the convenience of automated matrix generation with the generality of direct matrix input. The equations of motion are treated in first-order form, allowing for nonsymmetric matrices, modeling of general networks, and complex-mode analysis. The effectiveness of the method is demonstrated for an example problem involving a complex hydraulic-mechanical system.

Chrostowski, J. D.↗

Transportation Network Topologies

The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.

Alexandrov, Natalia↗

Comparison of Artemis 2 and Artemis 5 Model Outcomes Using the Impact Probabilistic Risk Assessment Tool

BACKGROUND The Artemis campaign is a Moon exploration program with a series of six planned missions, five of which will be crewed. These five crewed missions will contain a single mission segment (space flight), or multiple mission segments involving space flight (Orion), lunar landing (LTV) and/or space habitat (Gateway). Each crewed segment faces the risk of unique medical conditions, necessitating medical sets/kits tailored to those specificities. To support and enable a data-driven and evidence-based decision-making process through out a mission’s life cycle, a software tool called IMPACT was developed. Using probabilistic risk assessment (PRA) methodologies, IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a novel tool built for analyzing the possibility of encountering complex medical risks during space flight, and for identifying the medical resources and capabilities needed to treat those potential at-risk medical conditions. This presentation will seek to compare IMPACT’s computational results upon potential complex space medical conditions (e.g., sprain/strain back or sleep disturbance) using IMPACT’s risk metrics and the associated optimized medical sets/kits between two Artemis missions: single segment Artemis 2 and multi-segmented Artemis 5. OVERVIEW By identifying potential medical conditions in space using input criteria such as crew quantity and composition, certain crew physical characteristics, mission duration and mission activities, IMPACT can produce analyses on the type of medical resources and capabilities needed to produce an optimized medical set/kit to address those medical conditions. IMPACT achieves this by performing hundreds of thousands of Monte Carlo simulations of missions to build aggregate pictures of medical risk. IMPACT’s risk metrics include loss of crew life (LOCL) – a measure of crew mortality due to medical conditions in space, return to definitive care (RTDC) – the need to perform crew evacuation, and task time lost (TTL) – a measure of the inability to perform activities due to crew disability. These risk metrics are applied to every medical condition identified by IMPACT’s computation analyses for every segment of the mission. Medical sets/kits are optimized to address these medical conditions but must fit within the stated Artemis Design Reference Mission (DRM) request for mass and volume physical size constraints. ANTICIPATED ANALYSIS AND CONCLUSION Using two Artemis missions, Artemis 2 and Artemis 5, IMPACT will provide the analyses for comparison of medical set/kit contents based upon mass and/or volume requirements and identify the at-risk medical conditions within both missions. This paper serves as an initial exploration of probabilistic risk assessment (PRA) medical risk calculations between two crewed Artemis missions and is not intended to be deemed the official medical response for the Artemis campaign.

probabilistic risk assessment↗

Global Droughts Connected By Linkages Between Drought Hubs

Quantifying the spatial and interconnected structure of regional to continental scale droughts is one of the unsolved global hydrology problems, which is important for understanding the looming risk of mega-scale droughts and the resulting water and food scarcity and their cascading impact on the worldwide economy. Using a Complex Network analysis, this study explores the topological characteristics of global drought events based on the self-calibrated Palmer Drought Severity Index. Event Synchronization is used to measure the strength of association between the onset of droughts at different spatial locations within the time lag of 1-3 months. The network coefficients derived from the synchronization network indicate a highly heterogeneous connectivity structure underlying global drought events. Drought hotspot regions such as Southern Europe, Northeast Brazil, Australia, and Northwest USA behave as drought hubs that synchronize regionally and with other hubs at inter-continental or even inter-hemispheric scale. This observed affinity among drought hubs is equivalent to the ‘rich-club phenomenon’ in Network Theory, where ‘rich’ nodes (here, drought hubs) are tightly interconnected to form a club, implicating the possibility of simultaneous large-scale droughts over multiple continents.

Drought↗

Astrodynamics Convention and Modeling Reference for Lunar, Cislunar, and Libration Point Orbits

The purpose and direction of this document is to provide U.S. government agencies, specifically National Aeronautics and Space Administration (NASA) and Department of Defense (DoD) space related centers, with a foundational summary of astrodynamics concepts for trajectory design, navigation, and operations in the cislunar, lunar, and libration point regions. This document is provided in response to an Interagency Agreement (IAA) between NASA and the National Geospatial-Intelligence Agency (NGA). With applications to these regions of the Earth-Moon system, this document summarizes: the definitions of standard and unique coordinate systems for Positioning, Navigation, Timing and targeting (PNT), transformations between those coordinate frames, definitions of common time systems, a description of numerical integration, description of a widely-used and approximate dynamical model of a three-body system for preliminary analysis and nomenclature definition, description of higher-fidelity models of cislunar space, and the application of these concepts to sample scenarios with a focus on common steps in trajectory and maneuver design for a spacecraft in cislunar space. This information is critical to mission design and navigation far above the geosynchronous orbit region, where lunar perturbations are required to be modeled accurately and consistently but render trajectory design and analysis a complex procedure. Software tools such as the Goddard Space Flight Center (GSFC) open source General Mission Analysis Tool (GMAT) is used as a reference, along with a wide variety of resources constructed by NASA and other government agencies, academia, and industry, for mathematical specifications and practical considerations. This document has been prepared by and under the auspices of NASA. The GSFC Mission Engineering and Systems Analysis (MESA) Division (Code 590) and the Navigation and Mission Design Branch (Code 595) are part of NASA. Their engineers and scientists have expertise in lunar, cislunar, and libration point region trajectory guidance and navigation and timing. NASA GSFC has supported many successful lunar and cislunar missions over the past several decades. These missions include the Lunar Reconnaissance Orbiter (LRO), the two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) spacecraft, Transiting Exoplanet Survey Satellite (TESS), Lunar Prospector, Lunar Crater Observation and Sensing Satellite (LCROSS), Clementine, and several Sun-Earth libration point missions such as WIND and Deep Space Climate Observatory (DSCOVR), dating back four decades. NASA GSFC also supports the upcoming Gateway lunar mission, the Artemis Lunar Program and Human Landing Systems, and leads both the Lunar IceCube low thrust mission and concept design for the Lunar Communication Relay and Navigation System (LCRNS).

Lunar, CisLunar, Libration, trajectory dynamics, p↗

Artificial Intelligence (AI) Methods for Automating the Impact Tool Evidence Library

INTRODUCTION: The development of the Evidence Library for use with the IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) probability risk assessment tool involved a multilayered, time intensive process of data collection and analysis by subject matter experts from the Exploration Medical Capability (ExMC) Element Clinical and Science Team to produce clinical findings forms (CliFFs) for 120 medical conditions. Artificial Intelligence Large Language Models (LLMs) can be leveraged to facilitate this process, thus reducing labor and time. TOPIC: CliFFs contain information about medical conditions as they pertain to spaceflight. This includes condition definitions, incidence data, crew task impairment estimates caused by conditions, treatment protocols and references to literature used for gathering condition evidence. Guided by the Evidence Library Methods document and the CliFF development instructions, a team has leveraged Microsoft Azure AI services and open-source documentation to construct an AI-assisted automated pipeline for CliFF development. This process is designed to search, retrieve, and evaluate the applicable data, and ultimately generate a completed CliFF. The LLM evaluates the relevance of each of the source materials to spaceflight, either as direct evidence or as an analog. The model extracts keywords and generates brief summaries to enhance search and retrieval in later stages of CliFF development. For instance, it can calculate epidemiological statistical data, such as incidence rates and the likelihood of best or worst-case scenarios. APPLICATION: Large Language Models (LLMs) can efficiently summarize large amounts of text. Leveraging this technology will automate data retrieval and evidence gathering for medical databases, like the IMPACT tool, by aiding in the labor-intensive process of analyzing large bodies of literature and organizing it into a formatted document like a CliFF. This added efficiency will enable expeditious expansion of the Evidence Library with additional medical conditions and update previous CLiFFs as new technology becomes available.

Ali Al↗

Specialists Meeting on Rotorcraft Dynamics, Moffett Field, Calif., February 13-15, 1974, Proceedings

Analysis of specific problems in rotorcraft dynamics. Topics include hingeless rotor theory, dynamic stall modelling, periodic systems identification, analysis of complex systems with phasing matrices, flapping stability, flap-lag dynamics at high advance ratios, finite element analysis and fuselage free-vibration characteristics, coupled rotor/frame vibration methods, gust response characteristics with unsteady stall effects, antiresonance theory, cyclic feathering motions and dynamic loads, control load envelope shaping, rotor aeroelasticity, use of Floquet theory, theory of proprotors and tilt-rotors, two-bladed teetering rotors, stability of air and ground resonance, vertical-plane pendulum absorbers, multicyclic jet-flap control, engine/frame interface dynamics, and others. The minutes of the question and answer periods following the presentations are presented in the supplement. Individual items are announced in this issue.

Source record↗

Impact Real World System Validation

Introduction NASA has developed a new evidence-based data-driven probabilistic risk assessment and tradespace analysis tool as a successor to the Integrated Medical Model. This updated decision support tool is known as IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces). IMPACT estimates the frequency and consequences of medical conditions that might arise during exploration missions. A validation analysis of IMPACT was performed with respect to a set of International Space Station (ISS) and Shuttle Transportation System (STS) real world system (RWS) referent data due to the limited referent data available from exploration missions. Methods Observed mission and crew characteristics from STS and ISS missions were used as model inputs within MEDPRAT (Medical Extensible Dynamic Probabilistic Risk Assessment Tool). For each mission, two hundred thousand simulations were generated. For each mission, model outputs included occurrence counts for each condition, total medical events (TME), and the probability of loss of crew life (LOCL). These simulated model outputs were compared to the RWS referent data. Results The predicted number of total medical events exceeded the total RWS medical events for ISS missions and combined ISS and STS missions and fell within the 90% confidence interval for STS missions. For the 32 ISS missions simulated by IMPACT, the number of total medical events was overpredicted for 19 missions and fell within the 90% confidence interval for 13 missions. For the 21 STS missions, the total number of medical events was overpredicted for 3 missions, fell within the 90% confidence interval for 16 missions, and was underpredicted for 2 missions. Combined, 29 missions were in range, 22 were overpredicted, and 2 were underpredicted. The predicted LOCL probability for the 32 ISS missions, the 21 STS missions, and the combined ISS and STS missions was consistent with the zero LOCL events observed in the RWS referent data. The validation analysis included a comparison of the number of medical events predicted by IMPACT and the number of medical events observed in the RWS data on a condition-by-condition basis. For ISS missions, 50 conditions were in range, 52 conditions were statistically underpowered (not enough observed sample to draw any conclusions on precision), 8 conditions were overpredicted, and 9 conditions were underpredicted. Overall, only 14% (17/119) of conditions were out of range for STS missions, 40 conditions were in range, 59 conditions were statistically underpowered, 10 conditions were overpredicted, and 10 conditions were underpredicted. Overall, only 17% (20/119) of conditions were out of range. For combined ISS and STS missions, 11 conditions were overpredicted, and 11 conditions were underpredicted. Overall, only 18% (22/119) of conditions were out of range. For combined ISS and STS missions, 49 conditions were in range, 46 conditions were statistically underpowered, 18 conditions were overpredicted, and 8 conditions were underpredicted. Overall, 21% (26/121) of conditions were out of range. Conclusion The results of this validation analysis should not be interpreted as a pass/fail test of the validity of IMPACT. Instead, this validation analysis should be used to assess some of the IMPACT outcomes in terms of consistencies and inconsistencies with the ISS and STS RWS referent data.

L. Boley↗

SMART: A Propositional Logic-Based Trade Analysis and Risk Assessment Tool for a Complex Mission

This paper introduces a new trade analysis software called the Space Mission Architecture and Risk Analysis Tool (SMART). This tool supports a high-level system trade study on a complex mission, such as a potential Mars Sample Return (MSR) mission, in an intuitive and quantitative manner. In a complex mission, a common approach to increase the probability of success is to have redundancy and prepare backups. Quantitatively evaluating the utility of adding redundancy to a system is important but not straightforward, particularly when the failure of parallel subsystems are correlated.

Ono, Masahiro↗