Results for “test statistics” — Page 39

DOE OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics

The current generation of large galaxy surveys will test the cosmological model by combining multiple types of observational probes. Realising the statistical promise of these new datasets requires rigorous attention to all aspects of analysis including cosmological measurements, modelling, covariance and parameter likelihood. In this paper we present the results of an end-to-end simulation study designed to test the analysis pipeline for the combination of the Dark Energy Spectroscopic Instrument (DESI) Year 1 galaxy redshift dataset and separate weak gravitational lensing information from the Kilo-Degree Survey, Dark Energy Survey and Hyper-Suprime-Cam Survey. Our analysis employs the 3x2-pt correlation functions including cosmic shear and galaxy-galaxy lensing, together with the projected correlation function of the spectroscopic DESI lenses. We build realistic simulations of these datasets including galaxy halo occupation distributions, photometric redshift errors, weights, multiplicative shear calibration biases and magnification. We calculate the analytical covariance of these correlation functions including the Gaussian, noise and super-sample contributions, and show that our covariance determination agrees with estimates based on the ensemble of simulations. We use a Bayesian inference platform to demonstrate that we can recover the fiducial cosmological parameters of the simulation within the statistical error margin of the experiment, investigating the sensitivity to scale cuts. This study is the first in a sequence of papers in which we present and validate the large-scale 3x2-pt cosmological analysis of DESI-Y1.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2005

Regression Analysis of Long-Term Profile Ozone Data Set from BUV Instruments

We have produced a profile merged ozone data set (MOD) based on the SBUV/SBUV2 series of nadir-viewing satellite backscatter instruments, covering the period from November 1978 - December 2003. In 2004, data from the Nimbus 7 SBUV and NOAA 9, ll, and 16 SBUV/2 instruments were reprocessed using the Version 8 (V8) algorithm and most recent calibrations. More recently, data from the Nimbus 4 BUT instrument, which was operational from 1970 - 1977, were also reprocessed using the V8 algorithm. As part of the V8 profile calibration, the Nimbus 7 and NOAA 9 (1993-1997 only) instrument calibrations have been adjusted to match the NOAA 11 calibration, which was established based on comparisons with SSBUV shuttle flight data. Differences between NOAA 11, Nimbus 7 and NOAA 9 profile zonal means are within plus or minus 5% at all levels when averaged over the respective periods of data overlap. NOAA 16 SBUV/2 data have insufficient overlap with NOAA 11, so its calibration is based on pre-flight information. Mean differences over 4 months of overlap are within plus or minus 7%. Given the level of agreement between the data sets, we simply average the ozone values during periods of instrument overlap to produce the MOD profile data set. Initial comparisons of coincident matches of N4 BUV and Arosa Umkehr data show mean differences of 0.5 (0.5)% at 30km; 7.5 (0.5)% at 35 km; and 11 (0.7)% at 40 km, where the number in parentheses is the standard error of the mean. In this study, we use the MOD profile data set (1978-2003) to estimate the change in profile ozone due to changing stratospheric chlorine levels. We use a standard linear regression model with proxies for the seasonal cycle, solar cycle, QBO, and ozone trend. To account for the non-linearity of stratospheric chlorine levels since the late 1990s, we use a time series of Effective Chlorine, defined as the global average of Chlorine + 50 * Bromine at 1 hPa, as the trend proxy. The Effective Chlorine data are taken from the 3-D Goddard CTM. We will show the latest trend results using this statistical model. In addition, the Nimbus 4 BUV data offer an opportunity to test the physical properties of our statistical model. From ground-based comparisons we will establish an uncertainty range for the Nimbus 4 data. We then extrapolate our statistical model fit backwards in time and compare to the Nimbus 4 data. We compare the characteristics of the residual, defined as the difference between the data and statistical regression fit, during the Nimbus 4 time period and the 1978-2003 period over which the statistical model coefficients were estimated, and present these results.

Stolarski, Richard S.↗

DOE OSTI2025

Low responsiveness of machine learning models to critical or deteriorating health conditions

Machine learning (ML) based mortality prediction models can be immensely useful in intensive care units. Such a model should generate warnings to alert physicians when a patient’s condition rapidly deteriorates, or their vitals are in highly abnormal ranges. Before clinical deployment, it is important to comprehensively assess a model’s ability to recognize critical patient conditions. We develop multiple medical ML testing approaches, including a gradient ascent method and neural activation map. We systematically assess these machine learning models’ ability to respond to serious medical conditions using additional test cases, some of which are time series. Guided by medical doctors, our evaluation involves multiple machine learning models, resampling techniques, and four datasets for two clinical prediction tasks. We identify serious deficiencies in the models’ responsiveness, with the models being unable to recognize severely impaired medical conditions or rapidly deteriorating health. For in-hospital mortality prediction, the models tested using our synthesized cases fail to recognize 66% of the injuries. In some instances, the models fail to generate adequate mortality risk scores for all test cases. Our study identifies similar kinds of deficiencies in the responsiveness of 5-year breast and lung cancer prediction models. Using generated test cases, we find that statistical machine-learning models trained solely from patient data are grossly insufficient and have many dangerous blind spots. Most of the ML models tested fail to respond adequately to critically ill patients. How to incorporate medical knowledge into clinical machine learning models is an important future research direction.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2016

Helicopter Acoustic Flight Test with Altitude Variation and Maneuvers

A cooperative flight test campaign between NASA and the U.S. Army was performed from September 2014 to February 2015. The purposes of the testing were to: investigate the effects of altitude variation on noise generation, investigate the effects of gross weight variation on noise generation, establish the statistical variability in acoustic flight testing of helicopters, and characterize the effects of transient maneuvers on radiated noise for a medium-lift utility helicopter. This test was performed at three test sites (0, 4000, and 7000 feet above mean sea level) with two aircraft (AS350 SD1 and EH-60L) tested at each site. This report provides an overview of the test, documents the data acquired and describes the formats of the stored data.

Watts, Michael E.↗

DOE OSTI2019

Statistical Determination of Fatigue Strength

A cyclic test method for the fatigue strength of metals is proposed. In this method, fatigue curves characterizing the stress dependence of the number of cycles to failure are plotted and statistically described. The number of cycles to failure is described by a Weibull distribution, using the lowest guaranteed values.

42 ENGINEERING↗

NASA NTRS2005

Liquid Rocket Engine Testing Overview

Contents include the following: Objectives and motivation for testing. Technology, Research and Development Test and Evaluation (RDT&E), evolutionary. Representative Liquid Rocket Engine (LRE) test compaigns. Apollo, shuttle, Expandable Launch Vehicles (ELV) propulsion. Overview of test facilities for liquid rocket engines. Boost, upper stage (sea-level and altitude). Statistics (historical) of Liquid Rocket Engine Testing. LOX/LH, LOX/RP, other development. Test project enablers: engineering tools, operations, processes, infrastructure.

Rahman, Shamim↗

NASA NTRS2008

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

Vlcek, Brian L.↗

NASA NTRS2012

Test Population Selection from Weibull-Based, Monte Carlo Simulations of Fatigue Life

Fatigue life is probabilistic and not deterministic. Experimentally establishing the fatigue life of materials, components, and systems is both time consuming and costly. As a result, conclusions regarding fatigue life are often inferred from a statistically insufficient number of physical tests. A proposed methodology for comparing life results as a function of variability due to Weibull parameters, variability between successive trials, and variability due to size of the experimental population is presented. Using Monte Carlo simulation of randomly selected lives from a large Weibull distribution, the variation in the L10 fatigue life of aluminum alloy AL6061 rotating rod fatigue tests was determined as a function of population size. These results were compared to the L10 fatigue lives of small (10 each) populations from AL2024, AL7075 and AL6061. For aluminum alloy AL6061, a simple algebraic relationship was established for the upper and lower L10 fatigue life limits as a function of the number of specimens failed. For most engineering applications where less than 30 percent variability can be tolerated in the maximum and minimum values, at least 30 to 35 test samples are necessary. The variability of test results based on small sample sizes can be greater than actual differences, if any, that exists between materials and can result in erroneous conclusions. The fatigue life of AL2024 is statistically longer than AL6061 and AL7075. However, there is no statistical difference between the fatigue lives of AL6061 and AL7075 even though AL7075 had a fatigue life 30 percent greater than AL6061.

Vlcek, Brian L.↗

DOE OSTI2019

Active Subspace Methods for Data-Intensive Inverse Problems (Final Report)

Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Active Subspace Methods for Data-Intensive Inverse Problems

Fostered by advances in computing, simulation and data science have emerged as the third and fourth paradigms enabling scientific discovery. Many mathematical challenges arise when integrating these paradigms to produce new knowledge. One of the most important challenges is the inverse or calibration problem: find the inputs of a simulation such that its outputs agree with a given set of measurements. As both the cost of the complex simulations and the volume of measurement data sets increase, intuition-driven trial-and-error methods for calibration quickly become untenable; modern scientists need more computationally efficient and mathematically rigorous methods. When measurements and simulated predictions contain uncertainty, the Bayesian perspective on statistical inference provides a popular mathematical framework for developing computational methods to solve inverse problems. Markov chain Monte Carlo (MCMC) methods are a mainstay of this framework; they characterize a probability distribution on the space of model inputs that is conditioned on the given measurements. However, despite recent advances, MCMC methods remain impractical for expensive simulations with more than a handful of inputs. At its heart, MCMC searches the space of inputs for corresponding outputs that match measurements, and so it is afflicted with the curse of dimensionality. Additionally, MCMC methods become less efficient as the volume of the measurement data increases, particularly if the measurements are redundant. To make MCMC—and Bayesian methods, in general—amenable to today’s computer models with millions of inputs and terabytes of measurement data, one must devise methods to reduce the dimension of both the simulation inputs and the measurements. For many models used in practice, the outputs vary primarily on a low-dimensional manifold of the nominally high-dimensional input space. Recently developed active subspace methods discover this low-dimensional manifold and exploit it to enable analyses typically suited for low-dimensional settings (e.g., statistical inversion of complex systems). We hypothesize that active subspace methods can provide the necessary dimension reduction, enabling existing Bayesian methods to find solutions for a large class of otherwise intractable statistical inverse problems. We will test the hypothesis with a series of mathematical analyses and computational experiments that will proceed along three research veins: (i) integrating active subspace methods into methods for statistical inversion, (ii) addressing current challenges in active subspace methods, and (iii) incorporating methods for nonlinear dimensionality reduction into active subspace methods. We will apply the methods we develop to real inverse problems in chemical kinetics and turbulent flame modeling. Our team combines expertise in methods for inverse problems, dimension reduction, and reduced order modeling. With a history of active collaboration and thoughtful engagement, we bring enthusiasm and fresh perspectives to a well studied subject. We are excited by the potential opportunity to work together to extend and apply active subspace methods to data-intensive inverse problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Failure risk assessment by analysis and testing

The sources of information on which to base an evaluation of reliability or failure risk of an aerospace flight system are (1) experience from tests and flights and (2) engineering analysis. It is rarely feasible to establish high reliability at high confidence by testing aerospace systems or components. Moreover, failure prediction by conventional, deterministic methods of engineering analysis can become arbitrary and subject to serious misinterpretation when uncertain or approximate information is used to establish analysis parameter values and to calibrate the accuracy of engineering models. The limitations of testing to evaluate failure risk are discussed, and a statistical approach which incorporates both engineering analysis and testing is presented.

Moore, N.↗

NASA NTRS1993

Digital test signal generation: An accurate SNR calibration approach for the DSN

In support of the on-going automation of the Deep Space Network (DSN) a new method of generating analog test signals with accurate signal-to-noise ratio (SNR) is described. High accuracy is obtained by simultaneous generation of digital noise and signal spectra at the desired bandwidth (base-band or bandpass). The digital synthesis provides a test signal embedded in noise with the statistical properties of a stationary random process. Accuracy is dependent on test integration time and limited only by the system quantization noise (0.02 dB). The monitor and control as well as signal-processing programs reside in a personal computer (PC). Commands are transmitted to properly configure the specially designed high-speed digital hardware. The prototype can generate either two data channels modulated or not on a subcarrier, or one QPSK channel, or a residual carrier with one biphase data channel. The analog spectrum generated is on the DC to 10 MHz frequency range. These spectra may be up-converted to any desired frequency without loss on the characteristics of the SNR provided. Test results are presented.

Gutierrez-Luaces, Benito O.↗

NASA NTRSDate not supplied

Preliminary Steps in Developing Rapid Aero Modeling Technology

The Rapid Aero Modeling (RAM) approach is a method to efficiently and automatically obtain aerodynamic models during testing, significantly saving time and resources. Motivation for this technology results from demand for experimental efficiency and model fidelity that has increased with growing aircraft complexity and aerodynamic nonlinearities. These issues are typical in the responses presented by a class of vehicles categorized as Urban Air Mobility aircraft where many features from both airplane and rotorcraft are present. For UAM configurations, with typically many more factors than conventional aircraft, traditional test methods can lead to increased costs and missed interactions. RAM guides the test to obtain high-fidelity, statistically rigorous aircraft models, and the approach is applicable to computational, ground, or flight-test experiments. It combines concepts from Design of Experiment theory and Aircraft System Identification theory that allow the user the freedom to choose, in advance of the test, a specific level of fidelity typically, in terms of prediction error. RAM only collects data required to meet the user-specified fidelity and fidelity is only limited by the facility and test article capabilities. An initial wind tunnel test to support development of RAM was conducted to assess potential metrics, algorithms, and procedures. This paper presents results from initial tests for the development of RAM technology and highlights some of the unique features of RAM applied toa conventional configuration during a ground-based, static, wind-tunnel test.

Patrick C Murphy↗

DOE OSTI2023

Hemispherical power asymmetry in intensity and polarization for Planck PR4 data

Abstract One of the foundations of the Standard Model of Cosmology is statistical isotropy, which can be tested, among other probes, through the study of the Cosmic Microwave Background (CMB). However, a hemispherical power asymmetry on large scales has been reported for WMAP and Planck data by different works.The statistical significance is above 3σfor temperature, suggesting a directional dependence of the local power spectrum, and thus a feature beyond the ΛCDM model. With the third release of the Planck data (PR3), a new analysis was performed including the E-mode polarization maps, finding an asymmetry at a modest level of significance. In this work, we perform an asymmetry analysis in intensity and polarization maps for the latest Planck processing pipeline (PR4). We obtain similar results to those obtained with PR3, with a slightly lower significance (2.8% for the Sevem method)for the amplitude of the E-mode local variance dipole as well as a significant variability with the considered mask.In addition, a hint of a possible T-E alignment between the asymmetry axes is found at the level of ∼ 5%. For the analysis, we have implemented an alternative inpainting approach in order to get an accurate reconstruction of the E-modes. More sensitive all-sky CMB polarization data, such as those expected from the future LiteBIRD experiment, are needed to reach a more robust conclusion on the possible existence of deviations from statistical isotropy in the form of a hemispherical power asymmetry.

Astronomy & Astrophysics↗

NASA NTRS1984

Methodology for predictive testing of fuel cells

A perturbation testing method has been developed and tested for predictive testing of fuel cells. This method involves application of small changes to the operating conditions of the cell in a predetermined sequence. The resultant response of the cell is then measured and statistically correlated with the corresponding test conditions. This method has been applied to the phosphoric acid fuel cell, and the effect of operating and cell-component variables on cell-performance degradation has been studied. A strong effect of the cell temperature and cathode potential on fuel-cell-performance degradation has been observed. A cell-performance degradation model has been formulated, and the unknown parameters in the model have been estimated by a regression analysis of the experimental data. A reasonable agreement between the fuel cell performance predicted by this model (derived from the perturbation experiments) and the unperturbed test data supports fthe applicability of the perturbation method.

Patel, D. N.↗

DOE OSTI2025

Statistical fracture behavior of doped UO 2 using a ball-on-ring equibiaxial flexure test method

Metal oxide dopants, such as titanium and chromium oxides, have garnered considerable attention for their potential to increase grain size (≥ 30 µm) in UO 2 fuel, purportedly enhancing fission gas retention during reactor operation. Fuel performance is significantly impacted by fuel fracture behavior, so it is important to understand the effects of enhanced grain size and dopant content on UO 2 fuel fracture. UO 2 pellets were doped with 0.1 wt% TiO 2 and 0.3 wt% Cr 2 O 3 to alter density and grain size. Inductively coupled plasma mass spectroscopy measured dopant levels pre- and post-sintering. X-ray diffraction revealed lattice changes and microstrain via Rietveld refinement. Field emission scanning electron microscopy determined grain sizes of approximately 30 µm for TiO 2 doping and 7 µm for Cr 2 O 3 doping. Transverse rupture strength tests were performed on over 30 samples per dataset to obtain characteristic strength and Weibull modulus. Results indicate no statistical difference in fracture strength between 0.1 wt% TiO 2 doped UO 2 and undoped UO 2 , while 0.3 wt% Cr 2 O 3 doped UO 2 exhibited a 20% decrease in fracture strength. Doped UO 2 samples also showed reduced Weibull modulus compared to undoped UO 2 , suggesting increased scatter in fracture strength. This study's findings suggest that titanium and chromium oxide doping in UO 2 , regardless of grain size, induce residual stresses, decreasing fracture strength and increasing variability in fracture behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2011

Rolling-Element Fatigue Testing and Data Analysis - A Tutorial

In order to rank bearing materials, lubricants and other design variables using rolling-element bench type fatigue testing of bearing components and full-scale rolling-element bearing tests, the investigator needs to be cognizant of the variables that affect rolling-element fatigue life and be able to maintain and control them within an acceptable experimental tolerance. Once these variables are controlled, the number of tests and the test conditions must be specified to assure reasonable statistical certainty of the final results. There is a reasonable correlation between the results from elemental test rigs with those results obtained with full-scale bearings. Using the statistical methods of W. Weibull and L. Johnson, the minimum number of tests required can be determined. This paper brings together and discusses the technical aspects of rolling-element fatigue testing and data analysis as well as making recommendations to assure quality and reliable testing of rolling-element specimens and full-scale rolling-element bearings.

Vlcek, Brian L.↗