scholarly journals APPLICATION OF THE BOOTSTRAP METHOD FOR STATISTICAL CHARACTERISTICS ASSESSMENT OF AIRCRAFT COMPONENTS’ SMALL SAMPLES

2018 ◽  
Vol 19 (3) ◽  
pp. 482-488
Author(s):  
D.S. Gerasimova ◽  
◽  
A.V. Sayapin ◽  
A.A. Palukhin ◽  
A.V. Katsura ◽  
...  
Keyword(s):  
Bootstrap Method ◽  
Statistical Characteristics ◽  
Small Samples ◽  
The Bootstrap Method

scholarly journals Conservative Estimations of Reliability With Limited Sampling

2007 ◽  
Author(s):  
Victor Picheny ◽  
Nam-Ho Kim ◽  
Raphael T. Haftka
Keyword(s):  
Normal Distribution ◽  
Thermal Loading ◽  
Bootstrap Method ◽  
Composite Panel ◽  
Small Samples ◽  
Normal Distribution Function ◽  
Limited Sampling ◽  
Bootstrap Approach ◽  
The Relationship ◽  
The Bootstrap Method

The objective of this paper is to provide a method of safely estimating reliability based on small samples. First, it is shown that the commonly used estimators of the parameters of the normal distribution function are biased, and they tend to lead to unconservative estimates of reliability. Then, two ways of making this estimation conservative are proposed: (1) adding constraints when a distribution is fitted to the data to bias it to be conservative, and (2) using the bootstrap method to estimate the bias needed for a given level of conservativeness. The relationship between the accuracy and the conservativeness of the estimates is explored for a normal distribution. In particular, detailed results are presented for the case when the goal is 95% likelihood to be conservative. The bootstrap approach is found to be more accurate for this level of conservativeness. It is then applied to the reliability analysis of a composite panel under thermal loading. Finally, we explore the influence of sample sizes and target probability of failure on estimates quality, and show that for a constant level of conservativeness, small samples and low probabilities can lead to a high risk of large overestimation while this risk is limited to a very reasonable value for samples above.

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Haiyan Ge ◽  
Xintian Liu ◽  
Yu Fang ◽  
Haijie Wang ◽  
Xu Wang ◽  
...  
Keyword(s):  
Normal Distribution ◽  
Bootstrap Method ◽  
Small Samples ◽  
Estimation Of Parameters ◽  
Error Ellipse ◽  
Content Type ◽  
Ellipse Model ◽  
Ellipse Method ◽  
Virtual Samples ◽  
The Bootstrap Method

Purpose The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

Parameter distribution characteristics of material fatigue life using improved bootstrap method

2018 ◽  
Vol 28 (5) ◽  
pp. 772-793 ◽  
Author(s):  
Minghui Zhang ◽  
Xintian Liu ◽  
Yansong Wang ◽  
Xiaolan Wang
Keyword(s):  
Fatigue Life ◽  
Test Data ◽  
Bootstrap Method ◽  
Small Sample ◽  
Statistical Characteristics ◽  
Average Error ◽  
Parameter Distribution ◽  
Virtual Test ◽  
Sample Data ◽  
The Bootstrap Method

The bootstrap method is mostly used to estimate statistical characteristics of small sample data. However, the limitations of the bootstrap method itself lead to a reduction in the reliability of small-sample estimates. In this article, an improved bootstrap method is developed to address this problem. In the statistically significant error range (the sample average error and the limit error of sampling) of the original single sample data, expanding the virtual test data that obey two distributions to overcome the limitations of the bootstrap method itself. This article compares and analyses these two methods through the case; the result indicates that the improved bootstrap method can enhance the reliability of the estimation results without changing its probability distribution. We also discussed how to reduce the fluctuation of the improved bootstrap method. And the effectiveness and feasibility of this improved method are discussed in the analysis of fatigue life test data.

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

The Bootstrap-Method: Discussion and Proposal for Improvement / Das bootstrap-Verfahren: Diskussion und Verbesserungsvorschlag

1998 ◽  
Vol 217 (1) ◽  
Author(s):  
Hans Schneeberger
Keyword(s):  
Bootstrap Method ◽  
Law School ◽  
Mean Deviation ◽  
Alternative Method ◽  
Doubling Method ◽  
The Mean ◽  
The Bootstrap Method

SummaryWith Efron’s law-school example the bootstrap method is compared with an alternative method, called doubling. It is shown, that the mean deviation of the estimator is always smaller for the doubling method.

Application of the bootstrap method to quantify uncertainty in seismic hazard estimates

1992 ◽  
Vol 82 (1) ◽  
pp. 104-119
Author(s):  
Michéle Lamarre ◽  
Brent Townshend ◽  
Haresh C. Shah
Keyword(s):  
Confidence Interval ◽  
Seismic Hazard ◽  
Statistical Method ◽  
Bootstrap Method ◽  
Earthquake Magnitude ◽  
Earthquake Catalog ◽  
Uncertainty Measure ◽  
Attenuation Models ◽  
The Bootstrap Method

Abstract This paper describes a methodology to assess the uncertainty in seismic hazard estimates at particular sites. A variant of the bootstrap statistical method is used to combine the uncertainty due to earthquake catalog incompleteness, earthquake magnitude, and recurrence and attenuation models used. The uncertainty measure is provided in the form of a confidence interval. Comparisons of this method applied to various sites in California with previous studies are used to confirm the validity of the method.

Standard Error Estimation of 3PL IRT True Score Equating With an MCMC Method

2008 ◽  
Vol 33 (3) ◽  
pp. 257-278 ◽  
Author(s):  
Yuming Liu ◽  
E. Matthew Schulz ◽  
Lei Yu
Keyword(s):  
Bootstrap Method ◽  
Standard Errors ◽  
True Score ◽  
Mcmc Method ◽  
Test Form ◽  
True Score Equating ◽  
Standard Error Estimation ◽  
Equivalent Test ◽  
Mean Square Errors ◽  
The Bootstrap Method

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills®. For parallel and congeneric test forms within valid IRT true score ranges, the pattern and magnitude of standard errors of IRT true score equating estimated by the MCMC method were very close to those estimated by the bootstrap method. For tau-equivalent test forms, the pattern of standard errors estimated by the two methods was also similar. Bias and mean square errors of equating produced by the MCMC method were smaller than those produced by the bootstrap method; however, standard errors were larger. In educational testing, the MCMC method may be used as an additional or alternative procedure to the bootstrap method when evaluating the precision of equating results.

scholarly journals ACCURACY AND ERROR FACTORS OF SENSITOMETRIC CURVE USING THE BOOTSTRAP METHOD

1991 ◽  
Vol 47 (6) ◽  
pp. 811-817 ◽  
Author(s):  
AKIO OGURA ◽  
HIDEHARU NIIDA ◽  
KENICHI OGAWA ◽  
YOSHINORI KOMAI ◽  
HIDEHIKO TODOROKI ◽  
...  
Keyword(s):  
Bootstrap Method ◽  
The Bootstrap Method
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