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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRSDate not supplied

A Prognostics Framework for Battery Health Monitoring Integrated with Thermal Modeling

Urban Air Mobility (UAM) promises to revolutionize transportation in major cities, offering passenger travel, cargo delivery, and emergency medical services through a network of electric vertical takeoff and landing (eVTOL) aircraft. However, the limited range of current eVTOLs, due to the low specific energy of lithium-ion batteries along with a possibility of thermal runaway conditions poses significant safety concerns, leading to potentially compromising operational safety. To address this critical challenge, researchers are actively evaluating the impact of flight and environmental conditions on onboard lithium-ion battery health. This involves carefully assessing the performance of battery packs under laboratory and operational conditions for developing models to estimate future health using prognostics framework. This study examines the effectiveness of evaluating battery degradation leading to catastrophic failures under varying operational conditions in laboratory. These are captured using physics based models of underlying phenomenons and integrated into the prognostics framework. A fully charged battery undergoes controlled discharge cycles at varying C-rates based on the simulated power draw profile, with current and voltage, temperature data recorded throughout the experiment. The observed data provides valuable insights into how different operating conditions and mission profiles affect battery performance. This information is crucial for developing strategies to optimize battery systems, enhance range, and ultimately ensure the safe and reliable operation of UAM vehicles.

Thermal Modeling↗
NASA NTRS2002

Mesoscale Convective Systems During SCSMEX: Simulations with a Regional Climate Model and a Cloud-Resolving Model

The South China Sea Monsoon Experiment (SCSMEX) was conducted in May-June 1998. One of its major objectives is to better understand the key physical processes for the onset and evolution of the summer monsoon over Southeast Asia and southern China. Multiple observation platforms (e.g., upper-air soundings, Doppler radar, ships, wind profilers, radiometers, etc.) during SCSMEX provided a first attempt at investigating the detailed characteristics of convection and circulation changes associated with monsoons over the South China Sea region. SCSMEX also provided precipitation derived from atmospheric budgets and comparison to those obtained from the Tropical Rainfall Measuring Mission (TRMM). In this paper, a regional scale model (with grid size of 20 km) and Goddard Cumulus Ensemble (GCE) model (with 1 km grid size) are used to perform multi-day integration to understand the precipitation processes associated with the summer monsoon over Southeast Asia and southern China. The regional climate model is used to understand the soil-precipitation interaction and feedback associated with a flood event that occurred in and around China's Yantz River during SCSMEX Sensitivity tests on various land surface models, sea surface temperature (SST) variations, and cloud processes are performed to understand the precipitation processes associated with the onset of the monsoon over the S. China Sea during SCSMEX. These tests have indicated that the land surface model has a major impact on the circulation over the S. China Sea. Cloud processes can effect the precipitation pattern while SST variation can effect the precipitation amounts over both land and ocean. The exact location (region) of the flooding can be effected by the soil-rainfall feedback. The GCE-model results captured many observed precipitation characteristics because it used a fine grid size. For example, the model simulated rainfall temporal variation compared quite well to the sounding-estimated rainfall. The results show there are more latent heat fluxes prior to the onset of the monsoon. However, more rainfall was simulated after the onset of the monsoon. This modeling study indicates the latent heat fluxes (or evaporation) have more of an impact on precipitation processes and rainfall in the regional climate model simulations than in the cloud-resolving model simulations. Research is underway to determine if the difference in the grid sizes or the moist processes used in these two models is responsible for the differing influence of surface fluxes an precipitation processes.

Tao, W.-K.↗
NASA NTRSDate not supplied

Evaluating Subgrid-Scale Properties of Low Clouds over the Beaufort Sea in Arctic System Reanalysis using ARISE Airborne In Situ Observations

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. To better understand the magnitude and possible causes of this problem, we analyze the disagreements between the Arctic System Reanalysis version 2 (ASR) and data taken during the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign conducted over the Beaufort Sea. Previous analysis of grid scale-averaged meteorological variables revealed a lack of cloud water produced in ASR, related to warm/dry biases, a failure to produce sufficient cloud water in conditions that are observed to be favorable for large cloud water values, and sampling issues with the ARISE flight paths. However, ARISE collected meteorological observations at one second intervals, offering spatial data resolution comparable to the subgrid scale of ASR. Subgrid scale properties and processes must be parameterized in conventional atmospheric models and reanalyses such as ASR, and often rely on assumed distributions of meteorological variables about the grid box mean state. To enable an examination of the realism of ASR’s subgrid scale properties, we use high resolution data from ARISE determine the “subgrid scale” distributions of cloud water and thermodynamic variables in the real atmosphere. Preliminary results show that the subgrid scale distribution of thermodynamic variables about the grid scale mean resembles the triangular distribution assumed in many bulk microphysical parameterization schemes, but also with tails resembling Gaussian distributions. The main goal is to understand the partitioning of the total available atmospheric water into water vapor and cloud water. Models typically covert some percentage of total water in a grid box to cloud water based on the estimated amount of supersaturation from the assumed vapor distribution. The ARISE measurements can reveal the relationship between subgrid scale supersaturation and the partition between cloud water and water vapor.

Jason Brant Dodson↗
NASA NTRS1990

A comparison of cloud radiation fields obtained by in-situ aircraft measurements and a numerical simulation of a tropical mesoscale convective system

The radiation budget of a tropical mesoscale convective system (MCS) is investigated by comparing in situ aircraft measurements obtained in a tropical MCS during the Equatorial Mesoscale Experiment (EMEX), and coordinated aircraft radiation measurements, with radiation profiles calculated using cloud properties obtained from a cloud model simulation of a tropical MCS. Preliminary results indicate that the stratiform region of the tropical System B simulation represents the gross properties of the observed stratiform system between 4.5 to 15 km. The flux profiles predicted by the model are consistent with observed fluxes.

Wong, Takmeng↗
NASA NTRS1999

A Study of the December 1992 Westerly Wind Burst Event during TOGA COARE

Using the Penn State/NCAR MM5 mesoscale model, a westerly wind burst (WWB) that occurred during the period from 19 to 30 December 1992 over the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) has been simulated and compared with observation. This event is characterized by the presence of super cloud clusters and the occurrence of a major WWB that extended over the western and central Pacific Ocean. Although several of the observed convective systems were not precisely simulated by MM5, the model did capture many other observed characteristics, such as the explosive development of convection, the cyclonic circulation and the WWB. The WWB resulted from the coalescence of three types of tropical disturbances. The first type was a low-level westerly jet (LWJ) that developed at the equator and may be associated with the eastward propagation of an ISO (Intraseasonal Oscillation). The second type featured an easterly wave-like disturbance that originated in the south central Pacific Ocean and propagated westward. Finally, the third type involved a cross-equatorial flow that deflected Northern Hemispheric easterlies into the Southern Hemisphere and may be caused by inertial instability. These disturbances worked in concert, resulting in intense convection over the TOGA COARE region. Once intense convection developed, a large-scale circulation was produced over the western Pacific warm pool, propagated eastward, and initiated a WWB.

Chen, Chaing↗
NASA NTRS2007

Use of Combined A-Train Observations to Validate GEOS Model Simulated Dust Distributions During NAMMA

During August 2006, the NASA African Multidisciplinary Analyses Mission (NAMMA) field experiment was conducted to characterize the structure of African Easterly Waves and their evolution into tropical storms. Mineral dust aerosols affect tropical storm development, although their exact role remains to be understood. To better understand the role of dust on tropical cyclogenesis, we have implemented a dust source, transport, and optical model in the NASA Goddard Earth Observing System (GEOS) atmospheric general circulation model and data assimilation system. Our dust source scheme is more physically based scheme than previous incarnations of the model, and we introduce improved dust optical and microphysical processes through inclusion of a detailed microphysical scheme. Here we use A-Train observations from MODIS, OMI, and CALIPSO with NAMMA DC-8 flight data to evaluate the simulated dust distributions and microphysical properties. Our goal is to synthesize the multi-spectral observations from the A-Train sensors to arrive at a consistent set of optical properties for the dust aerosols suitable for direct forcing calculations.

Nowottnick, E.↗
NASA NTRS2019

Comprehensive Assessment of Models and Events Using Library Tools (CAMEL) Framework: Time Series Comparisons

The Comprehensive Assessment of Models and Events using Library Tools (CAMEL) framework leverages existing Community Coordinated Modeling Center services: Run on Request post processing tools that generate model time series outputs and the new Community Coordinated Modeling Center Metadata Registry that describes simulation runs using Space Physics Archive Search and Extract metadata. The new CAMEL visualization tool compares the modeled time series with observational data and computes a suite of skill scores such as Prediction Efficiency, Root Mean Square Error, and Symmetric Signed Percentage Bias. Model data pairs used for skill calculations are obtained considering a user selected maximum difference between the time of observation and the nearest model output. The system renders available data for all locations and time periods selected using interactive visualizations that allow the user to zoom, pan, and pick data values along traces. Skill scores are reported for each selected event or aggregated over all events for all participating model runs. Separately, scores are reported for all locations (satellites or stations) and for each location individually. We are building on past experiences with model data comparisons of magnetosphere and ionosphere model outputs from GEM2008, GEMCEDAR Electrodynamics Thermosphere Ionosphere, and the SWPC Operational Space Weather Model challenges. The CAMEL visualization tool is demonstrated using three validation studies: (a) Wang Sheeley Arge heliosphere simulations compared against OMNI solar wind data, (b) ground magnetic perturbations from several magnetosphere and ionosphere electrodynamics models as observed by magnetometers, and (c) electron fluxes from several ring current simulations compared to Radiation Belt Storm Probes Helium Oxygen Proton Electron instrument measurements, integrated over different energy ranges.

Rastätter, Lutz↗
NASA NTRS2015

A Preliminary Evaluation of Supersonic Transport Category Vehicle Operations in the National Airspace System

Several public sector businesses and government agencies, including the National Aeronautics and Space Administration are currently working on solving key technological barriers that must be overcome in order to realize the vision of low-boom supersonic flights conducted over land. However, once these challenges are met, the manner in which this class of aircraft is integrated in the National Airspace System may become a potential constraint due to the significant environmental, efficiency, and economic repercussions that their integration may cause. Background research was performed on historic supersonic operations in the National Airspace System, including both flight deck procedures and air traffic controller procedures. Using this information, an experiment was created to test some of these historic procedures in a current-day, emerging Next Generation Air Transportation System (NextGen) environment and observe the interactions between commercial supersonic transport aircraft and modern-day air traffic. Data was gathered through batch simulations of supersonic commercial transport category aircraft operating in present-day traffic scenarios as a base-lining study to identify the magnitude of the integration problems and begin the exploration of new air traffic management technologies and architectures which will be needed to seamlessly integrate subsonic and supersonic transport aircraft operations. The data gathered include information about encounters between subsonic and supersonic aircraft that may occur when supersonic commercial transport aircraft are integrated into the National Airspace System, as well as flight time data. This initial investigation is being used to inform the creation and refinement of a preliminary Concept of Operations and for the subsequent development of technologies that will enable overland supersonic flight.

Underwood, Matthew C.↗
NASA NTRS1995

Propulsion Controlled Aircraft design and development

This paper describes the design, development, and ground testing of the propulsion controlled aircraft (PCA) flight control system. A backup flight control system which uses only engine thrust, the PCA system utilizes collective and differential thrust changes to steer an aircraft that experiences partial or complete failure of the hydraulically actuated control surfaces. The objective of the program was to investigate, in flight, the throttles-only control capability of the F-15, using manual control, and also an augmented PCA mode in which computer-controlled thrust was used for flight control. The objective included PCA operation in up-and-away flight and, if performance was adequate, a secondary objective to make actual PCA landings. The PCA design began with a feasibility study which evaluated many control law designs. The study was done using off-line control analysis, simulation, and on-line manned flight simulator tests. Control laws, cockpit displays, and cockpit controls were evaluated by NASA test pilots. A flight test baseline configuration was selected based on projected flight performance, applicability to transport and fighter aircraft, and funding costs. During the PCA software and hardware development, the initial design was updated as data became available from throttle-only flight experiments conducted by NASA on the F-15. This information showed basic airframe characteristics that were not observed in the F-15 flight simulator and resulted in several design changes. After the primary objectives of the PCA flight testing were accomplished, additional PCA modes of operation were developed and implemented. The evolution of the PCA system from the initial feasibility study, control law design, simulation, hardware-in-the-loop tests, pilot-in-the-loop tests, and ground tests is presented.

Wells, Edward A.↗
NASA NTRSDate not supplied

Experimental Investigation of a Physisorption-Based Hydrogen Storage System

This study discusses a practical system utilizing the principle of physisorption where hydrogen is weakly bound to the surface of a nanoporous silica aerogel blanket as an alternative to high-pressure and cryogenic hydrogen storage. Three different experiments are conducted to simulate various scenarios of such a storage method: change in pressure and change of scale. Transient responses of the charging and discharging cycles are of particular interest. It is observed that hydrogen uptake can be increased by up to 36-38 % at ambient conditions and 77 K when utilizing the aerogel blankets. Packing density, or the artificial increase of surface per volume, increases storage capacity as it is a mainly surface-driven phenomenon. High-pressure testing up to 50 bar showed benefits of the aerogel addition whereas the maximum uptake improvement was observed for 2 bar with a 105.3 % improvement over an empty vessel at identical conditions corresponding to 6.43 wt%. The scale-up of the system is highly sensitive to the design of the internal cooling design as aerogels are poor thermal conductors reducing the transient response of such systems. Furthermore, the high mass of metal-based pressure vessels further delays the thermal response. This makes the system suitable for day to week-long hydrogen storage but not for peak-shaving or load balancing.

Marcel Otto↗
NASA NTRS1989

Modeling, simulation, and analysis of optical remote sensing systems

Remote Sensing of the Earth's resources from space-based sensors has evolved in the past 20 years from a scientific experiment to a commonly used technological tool. The scientific applications and engineering aspects of remote sensing systems have been studied extensively. However, most of these studies have been aimed at understanding individual aspects of the remote sensing process while relatively few have studied their interrelations. A motivation for studying these interrelationships has arisen with the advent of highly sophisticated configurable sensors as part of the Earth Observing System (EOS) proposed by NASA for the 1990's. Two approaches to investigating remote sensing systems are developed. In one approach, detailed models of the scene, the sensor, and the processing aspects of the system are implemented in a discrete simulation. This approach is useful in creating simulated images with desired characteristics for use in sensor or processing algorithm development. A less complete, but computationally simpler method based on a parametric model of the system is also developed. In this analytical model the various informational classes are parameterized by their spectral mean vector and covariance matrix. These class statistics are modified by models for the atmosphere, the sensor, and processing algorithms and an estimate made of the resulting classification accuracy among the informational classes. Application of these models is made to the study of the proposed High Resolution Imaging Spectrometer (HRIS). The interrelationships among observational conditions, sensor effects, and processing choices are investigated with several interesting results.

Kerekes, John Paul↗
NASA NTRS2007

Calculational and Experimental Investigations of the Pressure Effects on Radical - Radical Cross Combinations Reactions: C2H5 + C2H3

Pressure-dependent product yields have been experimentally determined for the cross-radical reaction C2H5 + C2H3. These results have been extended by calculations. It is shown that the chemically activated combination adduct, 1-C4H8*, is either stabilized by bimolecular collisions or subject to a variety of unimolecular reactions including cyclizations and decompositions. Therefore the "apparent" combination/disproportionation ratio exhibits a complex pressure dependence. The experimental studies were performed at 298 K and at selected pressures between about 4 Torr (0.5 kPa) and 760 Torr (101 kPa). Ethyl and vinyl radicals were simultaneously produced by 193 nm excimer laser photolysis of C2H5COC2H3 or photolysis of C2H3Br and C2H5COC2H5. Gas chromatograph/mass spectrometry/flame ionization detection (GC/MS/FID) were used to identify and quantify the final reaction products. The major combination reactions at pressures between 500 (66.5 kPa) and 760 Torr are (1c) C2H5 + C2H3 yields 1-butene, (2c) C2H5 + C2H5 yields n-butane, and (3c) C2H3 + C2H3 yields 1,3-butadiene. The major products of the disproportionation reactions are ethane, ethylene, and acetylene. At moderate and lower pressures, secondary products, including propene, propane, isobutene, 2-butene (cis and trans), 1-pentene, 1,4-pentadiene, and 1,5-hexadiene are also observed. Two isomers of C4H6, cyclobutene and/or 1,2-butadiene, were also among the likely products. The pressure-dependent yield of the cross-combination product, 1-butene, was compared to the yield of n-butane, the combination product of reaction (2c), which was found to be independent of pressure over the range of this study. The [ 1-C4H8]/[C4H10] ratio was reduced from approx.1.2 at 760 Torr (101 kPa) to approx.0.5 at 100 Torr (13.3 kPa) and approx.0.1 at pressures lower than about 5 Torr (approx.0.7 kPa). Electronic structure and RRKM calculations were used to simulate both unimolecular and bimolecular processes. The relative importance of C-C and C-H bond ruptures, cyclization, decyclization, and complex decompositions are discussed in terms of energetics and structural properties. The pressure dependence of the product yields were computed and dominant reaction paths in this chemically activated system were determined. Both modeling and experiment suggest that the observed pressure dependence of [1-C4H8]/[C4H10] is due to decomposition of the chemically activated combination adduct 1-C4H8* in which the weaker allylic C-C bond is broken: H2C=CHCH2CH3 yields C3H5 + CH3. This reaction occurs even at moderate pressures of approx.200 Torr (26 kPa) and becomes more significant at lower pressures. The additional products detected at lower pressures are formed from secondary radical-radical reactions involving allyl, methyl, ethyl, and vinyl radicals. The modeling studies have extended the predictions of product distributions to different temperatures (200-700 K) and a wider range of pressures (10(exp -3) - 10(exp 5) Torr). These calculations indicate that the high-pressure [1-C4H8]/[C4H10] yield ratio is 1.3 +/- 0.1.

Fahr, Askar↗
NASA NTRS1980

Report on the Summer MONEX Field Phase

The Summer Monsoon Experiment (MONEX) which was conducted over the Indian Ocean and adjacent land areas from May to August 1979, and overlapped with the second Special Observing Period of the Global Weather Experiment (FGGE). Attention is given to the scientific goals of Summer MONEX which cover (1) planetary scale aspects, (2) synoptic scale aspects, (3) interactions with atmospheric circulation in the Pacific, Southern Hemisphere, Northern midlatitudes, and stratosphere, and (4) numerical simulation and prediction. The observing system and field operations designed to attain these goals are discussed in detail. In conclusion, it is noted that the combined MONEX and FGGE observations should provide an unprecedented data set for a basic study of the monsoon phenomena.

Fein, J. S.↗
NASA NTRS2015

NASA Controller Acceptability Study 1(CAS-1) Experiment Description and Initial Observations

This paper describes the Controller Acceptability Study 1 (CAS-1) experiment that was conducted by NASA Langley Research Center personnel from January through March 2014 and presents partial CAS-1 results. CAS-1 employed 14 air traffic controller volunteers as research subjects to assess the viability of simulated future unmanned aircraft systems (UAS) operating alongside manned aircraft in moderate-density, moderate-complexity Class E airspace. These simulated UAS were equipped with a prototype pilot-in-the-loop (PITL) Detect and Avoid (DAA) system, specifically the Self-Separation (SS) function of such a system based on Stratway+ software to replace the see-and-avoid capabilities of manned aircraft pilots. A quantitative CAS-1 objective was to determine horizontal miss distance (HMD) values for SS encounters that were most acceptable to air traffic controllers, specifically HMD values that were assessed as neither unsafely small nor disruptively large. HMD values between 0.5 and 3.0 nautical miles (nmi) were assessed for a wide array of encounter geometries between UAS and manned aircraft. The paper includes brief introductory material about DAA systems and their SS functions, followed by descriptions of the CAS-1 simulation environment, prototype PITL SS capability, and experiment design, and concludes with presentation and discussion of partial CAS-1 data and results.

Chamberlain, James P.↗
NASA NTRS1990

Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model

Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.

Bell, Thomas L.↗
NASA NTRS2005

Postural Control Disturbances Produced By Exposure to HMD and Dome Vr Systems

Two critical and unresolved human factors issues in VR systems are: 1) potential "cybersickness", a form of motion sickness which is experienced in virtual worlds, and 2) maladaptive sensorimotor performance following exposure to VR systems. Interestingly, these aftereffects are often quite similar to adaptive sensorimotor responses observed in astronauts during and/or following space flight. Most astronauts and cosmonauts experience perceptual and sensorimotor disturbances during and following space flight. All astronauts exhibit decrements in postural control following space flight. It has been suggested that training in virtual reality (VR) may be an effective countermeasure for minimizing perceptual and/or sensorimotor disturbances. People adapt to consistent, sustained alterations of sensory input such as those produced by microgravity, and experimentally-produced stimulus rearrangements (e.g., reversing prisms, magnifying lenses, flight simulators, and VR systems). Adaptation is revealed by aftereffects including perceptual disturbances and sensorimotor control disturbances. The purpose of the current study was to compare disturbances in postural control produced by dome and head-mounted virtual environment displays. Individuals recovered from motion sickness and the detrimental effects of exposure to virtual reality on postural control within one hour. Sickness severity and initial decrements in postural equilibrium decreases over days, which suggests that subjects become dual-adapted over time. These findings provide some direction for developing training schedules for VR users that facilitate adaptation, and address safety concerns about aftereffects.

Harm, D. L.↗
NASA NTRS2023

Oxidation of Silicon Particles Suspended in Mullite Matrix With Dual-Mode Vacancy Diffusion of Oxygen

Mullite bond coats filled with silicon particles have recently been proposed for the next generation of environmental barrier coatings (EBCs). The sacrificial oxidation of the silicon particles eliminates some of the environmental durability issues associated with traditional EBC designs. To investigate this novel design approach, a mathematical formulation and resulting numerical method have been developed for simulating the oxidation of silicon particles embedded in a mullite matrix. The focus is on the oxidation of the silicon in a dry oxygen environment where the oxidant is presumably oxygen. Oxygen transport from the exterior environment through the mullite is assumed to occur via two lattice defect diffusion mechanisms. As a result, the rate of oxygen transport is dictated by the self-diffusivity of the lattice defects. The numerical method is implemented using the COMSOL Multiphysics® program (COMSOL, Inc.). The method is applied to simulate the oxidation of silicon particles in a mullite pellet in recent oxidation experiments. Numerical results compare favorably with the oxidation behavior observed in the oxidation experiments. The numerical method is also used to investigate the effects of various features of the mullite-silicon particle system on the oxidation behavior.

silicon oxidation↗
NASA NTRS2021

Establishing Fault Tolerance for a Class of Systems by Experiment

A long-standing problem in system verification is establishing fault tolerance at the ultra-high level by experiment. It is considered impossible because of system complexity and the enormous number of trials needed. This paper considers the problem for a class of digital systems that use redundancy to achieve reliability. The class is the systems that operate for a period of time without maintenance followed by a maintenance check that replaces components identified as faulty. The paper considers simulating a natural life test where a natural life test observes a number of operating periods. If the system does not fail during the test, it can be said to have a certain reliability at a certain confidence level. The approach in this paper is to make the simulated life test more efficient while maintaining realism by integrating structural arguments, information on fault occurrence, and fault injection in the lab. The major result of this paper is constructing a global fault model using the failure rate of the components and proving theorems about the model that tell how many, what kind, when, and where to inject faults. A simple example illustrates applying the theorems.

design of experiments↗