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83 records · Page 5

Autonomous Performance Monitoring System: Monitoring and Self-Tuning (MAST)

Maintaining the long-term performance of software onboard a spacecraft can be a major factor in the cost of operations. In particular, the task of controlling and maintaining a future mission of distributed spacecraft will undoubtedly pose a great challenge, since the complexity of multiple spacecraft flying in formation grows rapidly as the number of spacecraft in the formation increases. Eventually, new approaches will be required in developing viable control systems that can handle the complexity of the data and that are flexible, reliable and efficient. In this paper we propose a methodology that aims to maintain the accuracy of flight software, while reducing the computational complexity of software tuning tasks. The proposed Monitoring and Self-Tuning (MAST) method consists of two parts: a flight software monitoring algorithm and a tuning algorithm. The dependency on the software being monitored is mostly contained in the monitoring process, while the tuning process is a generic algorithm independent of the detailed knowledge on the software. This architecture will enable MAST to be applicable to different onboard software controlling various dynamics of the spacecraft, such as attitude self-calibration, and formation control. An advantage of MAST over conventional techniques such as filter or batch least square is that the tuning algorithm uses machine learning approach to handle uncertainty in the problem domain, resulting in reducing over all computational complexity. The underlying concept of this technique is a reinforcement learning scheme based on cumulative probability generated by the historical performance of the system. The success of MAST will depend heavily on the reinforcement scheme used in the tuning algorithm, which guarantees the tuning solutions exist.

Peterson, Chariya↗

Personalized Risk Assesment for Adverse Drug Reactions and Treatment Failures

As NASA and other space agencies prepare for future long-term space missions beyond the LEO, the cumulative impact of risk factors encountered in space increases substantially rising concerns about astronauts health. Application of on-board medications to mitigate clinical symptoms associated with certain medical conditions and illnesses is the first line of response to ensure sustainable health and performance of crew. Unfortunately, very limited research has been conducted to determine efficacy of the earth-based pharmaceuticals in a microgravity environment. In some instances, orally administered medications taken during flight were reported to be less effective than expected. Evaluation of series of experiments involving astronauts from shuttle flights shows notable individual variability to several pharmaceuticals during flight. These data provide reasonable assumption of perturbation in CYP450 enzymes during spaceflight, which contribute to the hepatic metabolism of the majority of drugs and therefore may have significant effects on therapeutic efficacy and increase treatment-related toxicity. The genes encoding the CYP450 enzymes are highly variable in humans. Inheritable variations of CYP450 hepatic metabolizer enzymes and transport proteins play a crucial role in the inter-individual variability of drug efficiency and risks of adverse drug reactions. Additionally, there are some reports that document changes in the levels of production of drug-metabolizing enzymes in microgravity. Therefore, in order to provide a safe and effective pharmaceutical treatment in space, medications selection should be based not only on the specific efficacy of medications but also on the individual drug sensitivity and flight-induced changes in metabolism of astronauts chosen for a particular mission. To our knowledge, there was no pre-flight drug sensitivity testing on a genetic level for any of the previous manned NASA space missions. Therefore, technologies capable of predicting and managing medication efficacy, side effects, and toxicity of drugs based on individual genetic variability of crew members are increasingly needed. In this report, we present results of testing the market available Personalized Prescribing System (PPS), a comprehensive, non-invasive solution for safer, targeted medication management for every crew member. Statistical accuracy and simplicity of non-invasive sample analysis demonstrate the feasibility of drug sensitivity assessment and record-keeping tool for flight surgeons and astronauts in applying the recommended medications for situations arising in flight. The information on individual drug sensitivity will translate into personalized risk assessment for adverse drug reactions and treatment failures for each drug from the medication kit as well as predefined outcome. This will address the HHC’s raised “Concern of Clinically Relevant Unpredicted Effects of Medication” as recently updated.

medications↗

Assessing the Viability of Using GEOS-Forecast Product for Landslides Forecasting: A Step Toward Early Warning System

Landslides across the globe are mostly triggered by extreme rainfall events affecting infrastructure, transportation and livelihoods. The risks are rarely quantified due to lack of data, analytical skills and limited modeling techniques. Knowledge of local to global scale landslide risks provides communities and national agencies the ability to adapt disaster management practices to mitigate and recover from these hazards. In order to minimize the risks and improve characterization of community resilience to landslides, it is vital to have reliable information about the factors triggering landslides such as rainfall, well ahead in time. Forecasting potential landslide activity and impacts can be achieved through reliable precipitation forecast models. However, it is challenging because of the temporal and spatial variability of precipitation, an important factor in triggering landslides. Evaluation of the precipitation field, associated errors, and sampling uncertainties is integral for development of efficient and reliable landslide forecasting and early warning system. This study develops a methodology to assess the viability of using a precipitation field provided by a global model and its potential integration in the landslide forecasting system. The study focuses on the comparison between the IMERG (Integrated Multi-satellitE Retrievals for Global Precipitation Mission) and GEOS (NASA Goddard Earth Observing System)-Forecast product over contiguous United States (CONUS). GEOS model assimilates new observations every 6 hours, at 00, 06, 12, and 18 UTC. The framework is tested on the GEOS-Forecast Model initialized at 00 UTC using daily IMERG early product as reference using both categorical and continuous statistics. The categorical statistics includes the probability of detection (POD), success ratio (SR), critical success index (CSI), and the hit bias. Continuous statistics such as correlation, normalized standard deviation, and root-mean-square error are also evaluated. Overall, GEOS-Forecast precipitation field over the analysis period (~1 year) show underestimation with respect to IMERG early for the daily accumulated rainfall. However, the probability distribution function and cumulative distribution function of both show similar patterns. In terms of correlations, POD, SR, CSI, hit bias, the performance varies with respect to the rainfall threshold used.

Sana Khan↗

Real-Time Imaging of Ground Cover: Relationships with Radiation Capture, Canopy Photosynthesis, and Daily Growth Rate

Cumulative absorbed radiation is highly correlated with crop biomass and yield. In this chapter we describe the use of a digital camera and commercial imaging software for estimating daily radiation capture, canopy photosynthesis, and relative growth rate. Digital images were used to determine percentage of ground cover of lettuce (Lactuca sativa L.) communities grown at five temperatures. Plants were grown in a steady-state, 10-chamber CO2 gas exchange system, which was used to measure canopy photosynthesis and daily carbon gain. Daily measurements of percentage of ground cover were highly correlated with daily measurements of both absorbed radiation (r(sup 2) = 0.99) and daily carbon gain (r(sup 2) = 0.99). Differences among temperature treatments indicated that these relationships were influenced by leaf angle, leaf area index, and chlorophyll content. An analysis of the daily images also provided good estimates of relative growth rates, which were verified by gas exchange measurements of daily carbon gain. In a separate study we found that images taken at hourly intervals were effective for monitoring real-time growth. Our data suggests that hourly images can be used for early detection of plant stress. Applications, limitations, and potential errors are discussed. We have long known that crop yield is determined by the efficiency of four component processes: (i) radiation capture, (ii) quantum yield, (iii) carbon use efficiency, and (iv) carbon partitioning efficiency (Charles-Edwards, 1982; Penning de Vries & van Laar, 1982; Thornley, 1976). More than one-half century ago, Watson (1947, 1952) showed that variation in radiation capture accounted for almost all of the variation in yield between sites in temperate regions, because the three other components are relatively constant when the crop is not severely stressed. More recently, Monteith (1977) reviewed the literature on the close correlation between radiation capture and yield. Bugbee and Monje (1992) demonstrated the close relationship between absorbed radiation and yield in an optimal environment.

Klassen, S. P.↗

Ceramic Inclusions in Powder Metallurgy Disk Alloys: Characterization and Modeling

Powder metallurgy alloys are increasingly used in gas turbine engines, especially in turbine disk applications. Although powder metallurgy materials have many advantages over conventionally cast and wrought alloys (higher strength, higher temperature capability, etc.), they suffer from the rare occurrence of ceramic defects (inclusions) that are inherent to the powder atomization process. These inclusions can have a potentially large detrimental effect on the durability of individual components. An inclusion in a high stress location can act as a site for premature crack initiation and thereby considerably reduce the fatigue life. Because these inclusions are exceedingly rare, they typically do not reveal themselves in the process of characterizing the material for a particular application (the cumulative volume of the test bars in a fatigue life characterization is typically on the order of a single actual component). Ceramic inclusions have, however, been found to be the root cause of a number of catastrophic engine failures. To investigate the effect of these inclusions in detail, we have undertaken a study where known populations of ceramic particles, whose composition and morphology are designed to mimic the "natural" inclusions, are added to the precursor powder. Surface-connected inclusions have been found to have a particularly large detrimental effect on fatigue life; therefore, the quantity of ceramic "seeds" added is calculated to ensure that a minimum number will intersect the surface of the fatigue test bars. Because the ceramic inclusions are irregularly shaped and have a tendency to break up in the process of extrusion and forging, a method of calculating the probability of occurrence and expected intercepted surface area was needed. We have developed a Monte Carlo simulation to determine the distributions of these parameters and have verified the simulated results with observations of ceramic inclusions found in macroscopic slices from extrusions and forgings. Fatigue specimens have been machined from Udimet 720 (a powder metallurgy superalloy) forgings, to determine the effects of the inclusions on fatigue life. The ultimate goal of this study will be to use probabilistic methods to determine the reliability detriment that can be attributed to these ceramic inclusions. This work has been supported by the Ultra Safe and Ultra- Efficient Engine Technologies programs.

Bonacuse, Peter J.↗

Three Paradigms of Lunar Regolith Evolution

Integration of diverse datasets on the Moon may render some paradigms of lunar science either better-defended or vulnerable. We will consider three paradigms commonly used for understanding the processes of lunar regolith evolution in light of new and accumulated data. Our premise is that all data-sets should converge to a single interpretation if a concept or model is to be accepted as a paradigm. If a convergence is lacking, the paradigm needs fresh scrutiny. SteadyState: Lunar regolith evolution is currently understood in terms of comminution, agglutination, and replenishment as described by McKay and coworkers). Briefly, the model envisages continued micrometeoritic bombardment to comminute exposed soil particles to finer sizes while continued agglutination consumes finer sizes to produce larger constructional particles. Eventually, a balance between these two opposing processes achieves a steady state; soils at steady state maintain their mean grain size (M(sub z)). Episodic higher-energy impacts excavate fresh coarse material from below the soil cover, disturb the steady state, and restart the process to achieve a new steady state. It follows that the thickness of the regolith at any site would control the frequency of replenishment; indeed, the thickness of the regolith at Apollo landing sites was predicted by McKay et al. from the average M(sub z) of local soils. However, replenishment may come also from disintegrating boulders and cobbles at the lunar surface, and rates of comminution and agglutination may depend on the properties of target material. Regression between M(sub z) and I(sub s)/Fe(sup 0) (a measure of maturity or total surface exposure) of Apollo soils at different sites shows the following relations and estimated M(sub z) at a high maturity of I(sub s)/Fe(sup 0)= 100. It is possible that Apollo 12 and 15 sites have the thickest regolith and the Apollo 16 site has the thinnest. It is also possible that Apollo 12 and 15 basalts are comminuted faster than Apollo 16 highland rocks and Apollo 14 and 17 soils are products of mixed parentage. If a soil becomes continually finer as it matures until agglutination catches up, and if comminution is differential-dependent on the physical properties of the constituents, then the composition of the bulk soil has to match the composition of some "fulcrum" grain size fraction, say X Grain size fractions >X and <X will complement each other; their mass balance is the bulk soil. It appears that the 10-20-micron size fraction may be the fulcrum. In general, trace-element chemistry and IR reflectance spectra of this size fraction are closest to that of the bulk soil, regardless of maturity that is surprising. Disaggregated products of regolith breccias may also show similar relationships. If the 10-20 gm is the fulcrum (i.e., X as above) for many soil properties (e.g., major element composition, FMR, solar-wind-implanted elements), then this may be the ultimate mean grain size of lunar soils at steady state. However, different properties of soils may find steady states at different grain size fractions. The steady state of solar-wind-implanted elements, on the other hand, will climb up the grain-size scale as agglutinates transfer surface-correlated components into volume correlated components until a saturation level is reached or the rates of replenishment and implantation become equal. The same will be the case with vapor-deposited reduced metals as they too are incorporated inside constructional particles. Properties that are directly affected by soil-maturation processes will thus have different pathways of achieving steady states. Maturity, i.e., cumulative surface exposure, of lunar soils is best quantified by the amount of nanophase superparamagnetic Fe(sup 0) (np-Fe(sup 0)) normalized to Fe content (=I(sub s)/Fe(sup 0). The majority consensus (paradigm?) for the production of np-Fe(sup 0) is associated with the production of agglutinates. Because large doses of solar-wind H are implanted in all lunar soils upon exposure, any melting (e.g., during agglutinate production) triggers a chemical reduction of Fe-bearing minerals resulting in np-Fe(sup 0) production. The quantity of np-Fe(sup 0) is thus dependent on melting events, (i.e., exposure), and limited by the Fe content of the soil. All freshly produced np-Fe(sup 0) resides in agglutinitic glass, as new TEM images show. Apparently, the correction procedure developed by Lucey et al. to estimate the Fe content of the lunar surface from IR-reflectance spectra depends on accepting the above. However, the process of producing np-Fe(sup 0) may be physical rather than chemical. All np-Fe(sup 0) could be deposits from a vapor produced by micrometeoritic impact on lunar soils. If metal-O bonds in target phases are broken, O being "most volatile" will escape leaving an O-deficient vapor to facilitate the production of np-Fe(sup 0). If so, the quantity of np-Fe(sup 0) is dependent on the vaporizing events, (i.e., exposure), and limited by the efficiency of breaking metal-O bonds and the escape of 0. To the extent that strengths of metal-O bonds are dependent on the local crystal field, production of np-Fe(sup 0) may be limited by the mineral composition of target soils and not by their total Fe content. According to this model, vapor-deposited np-Fe(sup 0) should be found at any retentive sites on lunar soil grains. Indeed, TEM images show np-Fe(sup 0) on plagioclase and ilmenite. Incorporation of such pre-irradiated np-Fe(sup 0)-bearing grains into agglutinates may account for eventual increased emplacement of np-Fe(sup 0) in agglutinates. Such a paradigm shift in understanding the origin of np-Fe(sup 0) will raise questions ranging from the unquestionable use of Is/FeO as the universal maturity parameter of lunar soils to global elemental maps of the Moon from remote-sensing data. Additional information is contained in the original.

Basu, A.↗

Impact experiments into multiple-mesh targets: Concept development of a lightweight collisional bumper

The utility of multiple-mesh targets as potential lightweight shields to protect spacecraft in low-Earth orbit against collisional damage is explored. Earlier studies revealed that single meshes comminute hypervelocity impactors with efficiencies comparable to contiguous targets. Multiple interaction of projectile fragments with any number of meshes should lead to increased comminution, deceleration, and dispersion of the projectile, such that all debris exiting the mesh stack possesses low specific energies (ergs/sq cm) that would readily be tolerated by many flight systems. The study is conceptually exploring the sensitivity of major variables such as impact velocity, the specific areal mass (g/sq cm) of the total mesh stack (SM), and the separation distance (S) between individual meshes. Most experiments employed five or ten meshes with total SM typically less than 0.5 the specific mass of the impactor, and silicate glass impactors rather than metal projectiles. While projectile comminution increases with increasing impact velocity due to progressively higher shock stresses, encounters with multiple-meshes at low velocity (1-2 km/s) already lead to significant disruption of the glass impactors, with the resulting fragments being additionally decelerated and dispersed by subsequent meshes, and, unlike most contiguous single-plate bumpers, leading to respectable performance at low velocity. Total specific bumper mass must be the subject of careful trade-off studies; relatively massive bumpers will generate too much debris being dislodged from the bumper itself, while exceptionally lightweight designs will not cause sufficient comminution, deceleration, or dispersion of the impactor. Separation distance was found to be a crucial design parameter, as it controls the dispersion of the fragment cloud. Substantial mass savings could result if maximum separation distances were employed. The total mass of debris dislodged by multiple-mesh stacks is modestly smaller than that of single, contiguous-membrane shields. The cumulative surface area of all penetration holes in multiple mesh stacks is an order of magnitude smaller than that in analog multiple-foil shields, suggesting good long-term performance of the mesh designs. Due to different experimental conditions, direct and quantitative comparison with other lightweight shields is not possible at present.

Hoerz, Friedrich↗

Search for Olivine Spectral Signatures on the Surface of Vesta

The occurrence of olivines on Vesta were first postulated from traditional petrogenetic models which suggest the formation of olivine as lower crustal cumulates. An indirect confirmation is given by their presence as a minor component in some samples of diogenite meteorites, the harzburgitic diogenites and the dunitic diogenites, and as olivine mineral clasts in howardites. Another indication for this mineral was given by interpretations of groundbased and Hubble Space Telescope observations that suggested the presence of local olivine-bearing units on the surface of Vesta. The VIR instrument onboard the DAWN mission has been mapping Vesta since July 2011. VIR acquired hyperspectral images of Vesta s surface in the wavelength range from 0.25 to 5.1 m during Approach, Survey and High Altitude Mapping (HAMO) orbits that allowed a 2/3 of the entire asteroid surface to be mapped. The VIR operative spectral interval, resolution and coverage is suitable for the detection and mapping of any olivine rich regions that may occur on the Vesta surface. The abundance of olivine in diogenites is typically lower than 10% but some samples richer in olivine are known. However, we do not expect to have extensive exposures of olivine-rich material on Vesta. Moreover, the partial overlap of olivine and pyroxene spectral signatures will make olivine difficult to detect. Different spectral parameters have been used to map olivine on extraterrestrial bodies, and here we discuss the different approaches used, and develop new ones specifically for Vesta. Our new methods are based on combinations of the spectral parameters relative to the 1 and 2 micron bands (the most prominent spectral features of Vesta surface in the visible and the infrared), such as band center locations, band depths, band areas, band area ratios. Before the direct application to the VIR data, the efficiency of each approach is evaluated by means of analysis of laboratory spectra of HED meteorites, pyroxenes, olivines and their mixtures.

Palomba, E.↗

Derivation and Testing of Consumptive Water Use Fraction for Specialty Crops

The Crop Consumptive Use Fraction (CCUF) expresses beneficial water use in the form of seasonal evapotranspiration of applied water (ETAW), relative to total irrigation volume. The metric is an indicator of the efficiency of agricultural water use and is a recommended component for preparation of agricultural water management plans in California. An FAO-56 based web application has been developed to facilitate retrospective evaluation of ETAW, and hence CCUF, at field level. The current application is optimized for prevailing climate in four of the state’s main growing regions: San Joaquin Valley, Sacramento Valley, Central Coast, and North Coast. User inputs include crop type, soil texture, irrigation method, daily irrigation volume, daily rainfall, and seasonal start/stop dates to define the analysis period. Time series of fractional green canopy cover (Fc), based on Landsat and Sentinel-2 Earth-resource satellite observations, are imported from NASA’s Satellite Irrigation Management Support (SIMS) system. Grass reference evapotranspiration (ETo) time series are accessed from Spatial CIMIS (California Irrigation Management Information System). Daily crop height (h) is estimated as a simple function of typical maximum height for the given crop type (from FAO-56) and Fc. A vegetation density coefficient (Kd) is derived from Fc and h. Stomatal control factors during mid-and late-season are applied to tree and vine crops. Typical values for minimum daily relative humidity and mean daily windspeed, derived from historical CIMIS weather data, are used to correct for regional deviations from standard climate (defined as RHmin=45%, windspeed =2m/s). The resulting daily basal crop coefficient (Kcb) represents the ET of a well-watered crop with minimal soil evaporation, relative to ETo. A soil water balance sub-model for the top 0.1 m is used to calculate daily evaporation coefficients (Ke). A second sub-model applies to the root zone to calculate crop water stress coefficients (Ks) and effective precipitation (Pe), which is the fraction of rainfall that is available for crop use. Those coefficients are combined with Kcb and ETo to calculate daily ETc. ETAW is then derived as cumulative ETc less cumulative Pe. For verification purposes, sensor installations were used to measure seasonal ETc in commercial fields for several annual and perennial specialty crops by soil water balance and energy balance methods. Model estimates of seasonal ETc show mean absolute error of <10% compared to the ground measurements.

Derivation↗

Using the Space Glove to Teach Spatial Thinking

The challenge of extending students' skills in spatial thinking to astronomical scales was the central focus of our K-8 curriculum development. When the project's lead teacher requested a curriculum that cumulatively built on each prior year's learning in a spiral fashion, I knew exactly what the school was asking for. Second and third graders began by noticing the cyclical patters that the sun, moon, and stars make in the sky. Fourth graders explored the phases of the moon by taking turns modeling and sketching them in their classroom and then comparing them to the real sky. Sixth !graders used real telescopes to observe a moving model of our solar system and walked a scale model of the planets' orbits. The curriculum is designed to expand students' capacity to visualize space in a hierarchical fashion that asks them to imagine themselves from a broader number of spatial perspectives through hands-on activities. The "situational awareness" Peter's story describes is a hallmark of high-performance engineering and innovation. Keeping in mind the potential outcomes of multiple paths of pursuit from multiple perspectives while keeping track of their relative merits and performance requirements is a demanding spatial task. What made it possible for Peter to transform the failure of his first glove into triumph was the mental space in which that failure provided exactly the information needed for a new breakthrough. In at least two cases, Peter could immediately "see" the full implications of what his hands were telling him. He tells the story of how putting his hands in a Phase VI astronaut glove instantly transformed his understanding of the glove challenge. Six months into his development, the failure of circumferentially wrapped cords to produce a sufficiently flexible glove again forced him to abandon his assumptions. His situational awareness was so clear and compelling it became a gut-level response. Peter's finely developed spatial skills enabled him to almost instinctively focus his full energy on a carefully constructed set of experiments. The finger's ability to sense pressure, force, and work gave him the immediate feedback required to solve this one central problem. Once properly understood, his failure quickly led to the magical "Aha!" moment of discovery; the rest is history. Just as children need opportunities to develop hands-on understanding, engineers need to explore new possibilities through incremental hands-on failure. High-performance innovation is all about learning to make maximum use of thinking spatially to direct this process. Peter Homer's glove also reminds us that efficient engineering decisions need to be made as close to the hardware as possible. Whether we're doing hands-on education or hands-on engineering, it is when we trust in our ability to "feel our way" through failure that we reach our highest potential.

Lord, Peter↗

Reliability and Confidence Interval Analysis of a CMC Turbine Stator Vane

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight, enable higher operating temperatures requiring less cooling and thus leading to increased engine efficiencies. However, these materials are brittle and show degradation with time at high operating temperatures due to creep as well as cyclic mechanical and thermal loads. In addition, these materials are heterogeneous in their make-up and various factors affect their properties in a specific design environment. Most of these advanced composites involve two- and three-dimensional fiber architectures and require a complex multi-step high temperature processing. Since there are uncertainties associated with each of these in addition to the variability in the constituent material properties, the observed behavior of composite materials exhibits scatter. Traditional material failure analyses employing a deterministic approach, where failure is assumed to occur when some allowable stress level or equivalent stress is exceeded, are not adequate for brittle material component design. Such phenomenological failure theories are reasonably successful when applied to ductile materials such as metals. Analysis of failure in structural components is governed by the observed scatter in strength, stiffness and loading conditions. In such situations, statistical design approaches must be used. Accounting for these phenomena requires a change in philosophy on the design engineer s part that leads to a reduced focus on the use of safety factors in favor of reliability analyses. The reliability approach demands that the design engineer must tolerate a finite risk of unacceptable performance. This risk of unacceptable performance is identified as a component's probability of failure (or alternatively, component reliability). The primary concern of the engineer is minimizing this risk in an economical manner. The methods to accurately determine the service life of an engine component with associated variability have become increasingly difficult. This results, in part, from the complex missions which are now routinely considered during the design process. These missions include large variations of multi-axial stresses and temperatures experienced by critical engine parts. There is a need for a convenient design tool that can accommodate various loading conditions induced by engine operating environments, and material data with their associated uncertainties to estimate the minimum predicted life of a structural component. A probabilistic composite micromechanics technique in combination with woven composite micromechanics, structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Since the measured data for the ceramic matrix composite properties is very limited, obtaining a probabilistic distribution with their corresponding parameters is difficult. In case of limited data, confidence bounds are essential to quantify the uncertainty associated with the distribution. Usually 90 and 95% confidence intervals are computed for material properties. Failure properties are then computed with the confidence bounds. Best estimates and the confidence bounds on the best estimate of the cumulative probability function for R-S (strength - stress) are plotted. The methodologies and the results from these analyses will be discussed in the presentation.

Murthy, Pappu L. N.↗