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All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Leonard Johnson published a methodology for establishing the confidence that two populations of data are different. Johnson's methodology is dependent on limited combinations of test parameters (Weibull slope, mean life ratio, and degrees of freedom) and a set of complex mathematical equations. In this report, a simplified algebraic equation for confidence numbers is derived based on the original work of Johnson. The confidence numbers calculated with this equation are compared to those obtained graphically by Johnson. Using the ratios of mean life, the resultant values of confidence numbers at the 99 percent level deviate less than 1 percent from those of Johnson. At a 90 percent confidence level, the calculated values differ between +2 and 4 percent. The simplified equation is used to rank the experimental lives of three aluminum alloys (AL 2024, AL 6061, and AL 7075), each tested at three stress levels in rotating beam fatigue, analyzed using the Johnson- Weibull method, and compared to the ASTM Standard (E739 91) method of comparison. The ASTM Standard did not statistically distinguish between AL 6061 and AL 7075. However, it is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers using the Johnson- Weibull analysis. AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median, or L(sub 50), lives

Vlcek, Brian L.↗
NASA NTRS1975

Decision-related cortical potentials during an auditory signal detection task with cued observation intervals

Cortical-evoked potentials were recorded from human subjects performing an auditory detection task with confidence rating responses. Unlike earlier studies that used similar procedures, the observation interval during which the auditory signal could occur was clearly marked by a visual cue light. By precisely defining the observation interval and, hence, synchronizing all perceptual decisions to the evoked potential averaging epoch, it was possible to demonstrate that high-confidence false alarms are accompanied by late-positive P3 components equivalent to those for equally confident hits. Moreover the hit and false alarm evoked potentials were found to covary similarly with variations in confidence rating and to have similar amplitude distributions over the scalp. In a second experiment, it was demonstrated that correct rejections can be associated with a P3 component larger than that for hits. Thus it was possible to show, within the signal detection paradigm, how the two major factors of decision confidence and expectancy are reflected in the P3 component of the cortical-evoked potential.

Squires, K. C.↗
NASA NTRS1992

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗
NASA NTRS2006

Final Results from the BIMA CMB Anisotropy Survey and Search for Signature of the SZ Effect

We report the final results of our study of the cosmic microwave background (CMB) with the BIMA array. Over 1000 hours of observation were dedicated to this project exploring CMB anisotropy on scales between 1' and 2' in eighteen 6'.6 FWHM fields. In the analysis of the CMB power spectrum, the visibility data is divided into two bins corresponding to different angular scales. Modeling the observed excess power as a flat band of average multipole l(sub eff)= 5237, we find deltaT(sup 2)(sub 1) = 220(sup +140)(sub -120) mu K(sup 2) at 68% confidence and deltaT(sup 2)(sub 1) greater than 0 muK(sup 2) with 94.7% confidence. In a second band with average multipole of l(sub eff) = 8748, we find deltaT(sup 2)(sub 2) consistent with zero, and an upper limit 880 muK(sup 2) at 95% confidence. An extensive series of tests and supplemental observations with the VLA provide strong evidence against systematic errors or radio point sources being the source of the observed excess power. The dominant source of anisotropy on these scales is expected to arise from the Sunyaev-Zel'dovich (SZ) effect in a population of distant galaxy clusters. If the excess power is due to the SZ effect, we can place constraints on the normalization of the matter power spectrum sigma(sub 8) = 1.03(sup +0.20)(sub -0.29) at 68% confidence. The distribution of pixel fluxes in the BIMA images are found to be consistent with simulated observations of the expected SZ background and rule out instrumental noise or radio sources as the source of the observed excess power with similar confidence to the detection of excess power. Follow-up optical observations to search for galaxy over-densities anti-correlated with flux in the BIMA images, as might be expected from the SZ effect, proved to be inconclusive.

Dawson, K. S.↗
NASA NTRS2007

Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Probabilistic failure analysis is essential when analysis of stress-life (S-N) curves is inconclusive in determining the relative ranking of two or more materials. In 1964, L. Johnson published a methodology for establishing the confidence that two populations of data are different. Simplified algebraic equations for confidence numbers were derived based on the original work of L. Johnson. Using the ratios of mean life, the resultant values of confidence numbers deviated less than one percent from those of Johnson. It is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers. These equations were applied to rotating beam fatigue tests that were conducted on three aluminum alloys at three stress levels each. These alloys were AL 2024, AL 6061, and AL 7075. The results were analyzed and compared using ASTM Standard E739-91 and the Johnson-Weibull analysis. The ASTM method did not statistically distinguish between AL 6010 and AL 7075. Based on the Johnson-Weibull analysis confidence numbers greater than 99 percent, AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median or L(sub 50) lives.

Hendricks, Robert C.↗
NASA NTRS1978

Automotive Stirling engine development program

The Ford/DOE automotive Stirling engine development program is directed towards establishing the technological and developmental base that would enable a decision on whether an engineering program should be directed at Stirling engine production. The fuel economy assessment aims to achieve, with a high degree of confidence, the ERDA proposal estimate of 20.6 MPG (gasoline) for a 4500 lb 1WC Stirling engine passenger car. The current M-H fuel economy projection for the 170 HP Stirling engine is 15.7 MPG. The confidence level for this projection is 32%. A confidence level of 29% is projected for a 22.1 MPG estimate. If all of the planned analyses and test work is accomplished at the end of the one year effort, and the projected improvements are substantiated, the confidence levels would rise to 59% for the 20.6 MPG projection and 54% for the 22.1 MPG projection. Progress achieved thus far during the fuel economy assessment is discussed.

Kitzner, E. W.↗
NASA NTRS1978

Search for X-ray polarization in the Crab pulsar

Results of a search for X-ray polarization in the Crab pulsar are presented which were obtained by observing the pulsar at 2.6 and 5.2 keV with identical X-ray polarimeters aboard OSO 8. The polarization in different portions of the X-ray light curve is analyzed, the polarization contribution due to the nebula is removed, and the results of the analysis are given for isolated portions of both the primary pulse and the interpulse at 2.6 and 5.2 keV. No evidence for X-ray polarization is found at the 99% confidence level; 3-sigma upper limits to the polarization at 2.6 keV are given along with the largest polarization allowed at 5.2 keV by the 99% confidence counter. It is noted that the trailing edge of the interpulse at 2.6 keV is 26% polarized at the 92% confidence level, while the 5.2-keV polarization measurement of 40% in the leading edge of the primary pulse is different from zero at 96% confidence. X-ray and optical polarization measurements are compared.

Silver, E. H.↗
NASA NTRS1993

Longitudinal study of astronaut health: Mortality in the years 1959-1991

We conducted a historical cohort study of mortality among 195 astronauts who were exposed to space and medical sources of radiation between 1959 and 1991. Cumulative occupational and medical radiation exposures were obtained from the astronaut radiation exposure history data base. Causes of death were obtained from obligatory death certificates and autopsy reports that were on file in the medical records. A total of 18 deaths occurred during the 32-year follow-up period for which the all-cause standardized mortality ratio (SMR) was 142 (95 percent confidence interval 84 225). There was one cancer death in the buccal cavity and pharynegeal ICD-9 rubric whose occurrence was significantly beyond expectation. Mortality for coronary disease was 59 percent lower than expected (2 deaths; SMR = 41; 95 percent confidence limit 5 147). The crude death rate for 10 occupationally related accidents was 400 deaths per 100,000 person-years, which is an order of magnitude greater than accidental death rates in mining industries. The SMR of 1027 for fatal accidents was significantly beyond expectation (14 deaths; 95 percent confidence limit 561 1723) and was similar to SMRs for accidents among aerial pesticide applications. The 10-year cumulative risk of occupational fatalities based on the exponential, Weibull, Gompertz, and linear-exponential distributions was 10 percent. Mortality from motor vehicle accidents was slightly higher than expected but was not significant (1 death; SMR = 145; 95 percent confidence limit 2 808). Radiation exposures from medical procedures accounted for a majority of cumulative dose when compared with space radiation exposures. The results of the study do not confirm the impression that astronauts are at increased risk of cancer, but this does not obviate the need for further study. Overall, it was found that astronauts are at a health disadvantage as a result of catastrophic accidents.

Peterson, Leif E.↗
NASA NTRS1994

The massive halos of spiral galaxies

We use a sample of satellite galaxies to demonstrate the existence of extended massive dark halos around spiral galaxies. Isolated spirals with rotation velocities near 250 km/s have a typical halo mass within 200 kpc of 1.5-2.6 x 10(exp 12) solar mass (90% confidence range for H(sub 0) = 75 km/s/Mpc). This result is most easily derived using standard mass estimator techniques, but such techniques do not account for the strong observational selection effects in the sample, nor for the extended mass distributions that the data imply. These complications can be addressed using scale-free models similar to those previously employed to study binary galaxies. When satellite velocities are assumed isotropic, both methods imply massive and extended halos. However, the derived masses depend sensitively on the assumed shape of satellite orbits. Furthermore, both methods ignore the fact that many of the satellites in the sample have orbital periods comparable to the Hubble time. The orbital phases of such satellites cannot be random, and their distribution in radius cannot be freely adjusted; rather these properties reflect ongoing infall onto the outer halos of their primaries. We use detailed dynamical models for halo formation to evaluate these problems, and we devise a maximum likelihood technique for estimating the parameters of such models from the data. The most strongly constrained parameter is the mass within 200-300 kpc, giving the confidence limits quoted above. The eccentricity, e, of satellite orbits is also strongly constrained, 0.50 less than e less than 0.88 at 90% confidence, implying a near-isotropic distribution of satellite velocities. The cosmic density parameter in the vicinity of our isolated halos exceeds 0.13 at 90% confidence, with preferred values exceeding 0.3.

Zaritsky, Dennis↗
NASA NTRS1994

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗
NASA NTRS2002

Measurement of Arcminute Scale Cosmic Microwave Background Anisotropy with the BIMA Array

We report the results of our continued study of arcminute scale anisotropy in the Cosmic Microwave Background (CMB) with the Berkeley-Illinois-Maryland Association (BIMA) array. The survey consists of ten independent fields selected for low infrared dust emission and lack of bright radio point sources. With observations from the VLA (Very Large Array) at 4.8 GHz, we have identified point sources which could act as contaminants in estimates of the CMB power spectrum and removed them in the analysis. Modeling the observed power spectrum with a single. flat band power with average multipole of l(sub eff) = 6864, we find Delta T = 14.2((sup +4.8)(sub -6.0)) micro K at 68% confidence. The signal in the visibility data exceeds the expected contribution from instrumental noise with 96.5% confidence. We have also divided the data into two bins corresponding to different spatial resolutions in the power spectrum. We find Delta T(sub 1) = 16.6((sup +5.3)(sub -5.9)) micro K at 68% confidence for CMB flat band power described by an average multipole of l(sub eff) = 5237 and Delta T(sub 2) is less than 26.5 micro K at 95% confidence for l(sub eff) = 8748.

Dawson, K. S.↗
NASA NTRS2002

Integrating Formal Methods and Testing 2002

Traditionally, qualitative program verification methodologies and program testing are studied in separate research communities. None of them alone is powerful and practical enough to provide sufficient confidence in ultra-high reliability assessment when used exclusively. Significant advances can be made by accounting not only tho formal verification and program testing. but also the impact of many other standard V&V techniques, in a unified software reliability assessment framework. The first year of this research resulted in the statistical framework that, given the assumptions on the success of the qualitative V&V and QA procedures, significantly reduces the amount of testing needed to confidently assess reliability at so-called high and ultra-high levels (10-4 or higher). The coming years shall address the methodologies to realistically estimate the impacts of various V&V techniques to system reliability and include the impact of operational risk to reliability assessment. Combine formal correctness verification, process and product metrics, and other standard qualitative software assurance methods with statistical testing with the aim of gaining higher confidence in software reliability assessment for high-assurance applications. B) Quantify the impact of these methods on software reliability. C) Demonstrate that accounting for the effectiveness of these methods reduces the number of tests needed to attain certain confidence level. D) Quantify and justify the reliability estimate for systems developed using various methods.

Cukic, Bojan↗
NASA NTRS2010

Verifying Algorithms for Autonomous Aircraft by Simulation Generalities and Example

An open question in Air Traffic Management is what procedures can be validated by simulation where the simulation shows that the probability of undesirable events is below the required level at some confidence level. The problem is including enough realism to be convincing while retaining enough efficiency to run the large number of trials needed for high confidence. The paper first examines the probabilistic interpretation of a typical requirement by a regulatory agency and computes the number of trials needed to establish the requirement at an equivalent confidence level. Since any simulation is likely to consider only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. The paper establishes a separation algorithm at the required confidence level where the aircraft operates under feedback control as is subject to perturbations. There is a discussion where it is shown that a scenario three of four orders of magnitude more complex is feasible. The question of what can be validated by simulation remains open, but there is reason to be optimistic.

White, Allan L.↗
NASA NTRS2011

Binomial Test Method for Determining Probability of Detection Capability for Fracture Critical Applications

The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that for a minimum flaw size and all greater flaw sizes, there is 0.90 probability of detection with 95% confidence (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields estimates of POD and confidence bounds for both Hit-Miss or signal amplitude testing, where signal amplitudes are reduced to Hit-Miss by using a signal threshold Directed DOEPOD uses a nonparametric approach for the analysis or inspection data that does require any assumptions about the particular functional form of a POD function. The DOEPOD procedure identifies, for a given sample set whether or not the minimum requirement of 0.90 probability of detection with 95% confidence is demonstrated for a minimum flaw size and for all greater flaw sizes (90/95 POD). The DOEPOD procedures are sequentially executed in order to minimize the number of samples needed to demonstrate that there is a 90/95 POD lower confidence bound at a given flaw size and that the POD is monotonic for flaw sizes exceeding that 90/95 POD flaw size. The conservativeness of the DOEPOD methodology results is discussed. Validated guidelines for binomial estimation of POD for fracture critical inspection are established.

Generazio, Edward R.↗
NASA NTRS2011

Probabilistic Solar Energetic Particle Models

To plan and design safe and reliable space missions, it is necessary to take into account the effects of the space radiation environment. This is done by setting the goal of achieving safety and reliability with some desired level of confidence. To achieve this goal, a worst-case space radiation environment at the required confidence level must be obtained. Planning and designing then proceeds, taking into account the effects of this worst-case environment. The result will be a mission that is reliable against the effects of the space radiation environment at the desired confidence level. In this paper we will describe progress toward developing a model that provides worst-case space radiation environments at user-specified confidence levels. We will present a model for worst-case event-integrated solar proton environments that provide the worst-case differential proton spectrum. This model is based on data from IMP-8 and GOES spacecraft that provide a data base extending from 1974 to the present. We will discuss extending this work to create worst-case models for peak flux and mission-integrated fluence for protons. We will also describe plans for similar models for helium and heavier ions.

Adams, James H., Jr.↗
NASA NTRS2016

Impacts of Extreme Events on Human Health

Increased Exposure to Extreme Events Key Finding 1: Health impacts associated with climate-related changes in exposure to extreme events include death, injury, or illness; exacerbation of underlying medical conditions; and adverse effects on mental health[High Confidence]. Climate change will increase exposure risk in some regions of the United States due to projected increases in the frequency and/or intensity of drought, wildfires, and flooding related to extreme precipitation and hurricanes [Medium Confidence].Disruption of Essential Infrastructure Key Finding 2: Many types of extreme events related to climate change cause disruption of infrastructure, including power, water, transportation, and communication systems, that are essential to maintaining access to health care and emergency response services and safeguarding human health [High Confidence].Vulnerability to Coastal Flooding Key Finding 3: Coastal populations with greater vulnerability to health impacts from coastal flooding include persons with disabilities or other access and functional needs, certain populations of color, older adults, pregnant women and children, low-income populations, and some occupational groups [High Confidence].Climate change will increase exposure risk to coastal flooding due to increases in extreme precipitation and in hurricane intensity and rainfall rates, as well as sea level rise and the resulting increases in storm surge.

floods↗
NASA NTRS2016

Defining Baconian Probability for Use in Assurance Argumentation

The use of assurance cases (e.g., safety cases) in certification raises questions about confidence in assurance argument claims. Some researchers propose to assess confidence in assurance cases using Baconian induction. That is, a writer or analyst (1) identifies defeaters that might rebut or undermine each proposition in the assurance argument and (2) determines whether each defeater can be dismissed or ignored and why. Some researchers also propose denoting confidence using the counts of defeaters identified and eliminated-which they call Baconian probability-and performing arithmetic on these measures. But Baconian probabilities were first defined as ordinal rankings which cannot be manipulated arithmetically. In this paper, we recount noteworthy definitions of Baconian induction, review proposals to assess confidence in assurance claims using Baconian probability, analyze how these comport with or diverge from the original definition, and make recommendations for future practice.

Graydon, Patrick J.↗
NASA NTRS2017

Chapter 8: Droughts, Floods, and Wildfires

Recent droughts and associated heat waves have reached record intensity in some regions of the United States; however, by geographical scale and duration, the Dust Bowl era of the 1930s remains the benchmark drought and extreme heat event in the historical record (very high confidence). While by some measures drought has decreased over much of the continental United States in association with long-term increases in precipitation, neither the precipitation increases nor inferred drought decreases have been confidently attributed to anthropogenic forcing. The human effect on recent major U.S. droughts is complicated. Little evidence is found for a human influence on observed precipitation deficits, but much evidence is found for a human influence on surface soil moisture deficits due to increased evapotranspiration caused by higher temperatures. Future decreases in surface (top 10 cm) soil moisture from anthropogenic forcing over most of the United States are likely as the climate warms under higher scenarios. Substantial reductions in western U.S. winter and spring snowpack are projected as the climate warms. Earlier spring melt and reduced snow water equivalent have been formally attributed to human-induced warming (high confidence) and will very likely be exacerbated as the climate continues to warm (very high confidence). Under higher scenarios, and assuming no change to current water resources management, chronic, long-duration hydrological drought is increasingly possible by the end of this century. Detectable changes in some classes of flood frequency have occurred in parts of the United States and are a mix of increases and decreases. Extreme precipitation, one of the controlling factors in flood statistics, is observed to have generally increased and is projected to continue to do so across the United States in a warming atmosphere. However, formal attribution approaches have not established a significant connection of increased riverine flooding to human-induced climate change, and the timing of any emergence of a future detectable anthropogenic change in flooding is unclear. The incidence of large forest fires in the western United States and Alaska has increased since the early 1980s and is projected to further increase in those regions as the climate warms, with profound changes to certain ecosystems.

Wehner, M. F.↗