Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life

Author(s):  
D. Gary Harlow

Abstract Uncertainty in the prediction of lower tail fatigue life behavior is a combination of many causes, some of which are aleatoric and some of which are systemic. The error cannot be entirely eliminated or quantified due to microstructural variability, manufacturing processing, approximate scientific modeling, and experimental inconsistencies. The effect of uncertainty is exacerbated for extreme value estimation for fatigue life distributions because by necessity those events are rare. In addition, typically, there is a sparsity of data in the region of smaller stress levels in stress–life testing where the lives are considerably longer, extending to giga cycles for some applications. Furthermore, there is often over an order of magnitude difference in the fatigue lives in that region of the stress–life graph. Consequently, extreme value estimation is problematic using traditional analyses. Thus, uncertainty must be statistically characterized and appropriately managed. The primary purpose of this paper is to propose an empirically based methodology for estimating the lower tail behavior of fatigue life cumulative distribution functions, given the applied stress. The methodology incorporates available fatigue life data using a statistical transformation to estimate lower tail behavior at much smaller probabilities than can be estimated by traditional approaches. To assess the validity of the proposed methodology confidence bounds will be estimated for the stress–life data. The development of the methodology and its subsequent validation will be illustrated using extensive fatigue life data for 2024–T4 aluminum alloy specimens readily available in the open literature.


Extremes ◽  
2016 ◽  
Vol 19 (2) ◽  
pp. 325-349 ◽  
Author(s):  
Bikramjit Das ◽  
Souvik Ghosh

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.


Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.


Author(s):  
Suman Debnath ◽  
Anirban Banik ◽  
Tarun Kanti Bandyopadhyay ◽  
Mrinmoy Majumder ◽  
Apu Kumar Saha

2017 ◽  
pp. 8-17
Author(s):  
A. A. Ermakova ◽  
O. Yu. Borodin ◽  
M. Yu. Sannikov ◽  
S. D. Koval ◽  
V. Yu. Usov

Purpose: to investigate the diagnostic opportunities of contrast  magnetic resonance imaging with the effect of magnetization transfer effect in the diagnosis of focal metastatic lesions in the brain.Materials and methods.Images of contrast MRI of the brain of 16  patients (mean age 49 ± 18.5 years) were analysed. Diagnosis of  the direction is focal brain lesion. All MRI studies were carried out  using the Toshiba Titan Octave with magnetic field of 1.5 T. The  contrast agent is “Magnevist” at concentration of 0.2 ml/kg was  used. After contrasting process two T1-weighted studies were  performed: without T1-SE magnetization transfer with parameters of pulse: TR = 540 ms, TE = 12 ms, DFOV = 24 sm, MX = 320 × 224  and with magnetization transfer – T1-SE-MTC with parameters of pulse: ΔF = −210 Hz, FA(МТС) = 600°, TR = 700 ms, TE = 10 ms,  DFOV = 23.9 sm, MX = 320 x 224. For each detected metastatic  lesion, a contrast-to-brain ratio (CBR) was calculated. Comparative  analysis of CBR values was carried out using a non-parametric  Wilcoxon test at a significance level p < 0.05. To evaluate the  sensitivity and specificity of the techniques in the detection of  metastatic foci (T1-SE and T1-SE-MTC), ROC analysis was used. The sample is divided into groups: 1 group is foci ≤5 mm in size, 2  group is foci from 6 to 10 mm, and 3 group is foci >10 mm. Results.Comparative analysis of CBR using non-parametric Wilcoxon test showed that the values of the CBR on T1-weighted  images with magnetization transfer are significantly higher (p  <0.001) that on T1-weighted images without magnetization transfer. According to the results of the ROC analysis, sensitivity in detecting  metastases (n = 90) in the brain on T1-SE-MTC and T1-SE was  91.7% and 81.6%, specificity was 100% and 97.6%, respectively.  The accuracy of the T1-SE-MTC is 10% higher in comparison with  the technique without magnetization transfer. Significant differences (p < 0.01) between the size of the foci detected in post-contrast T1- weighted images with magnetization transfer and in post-contrast  T1-weighted images without magnetization transfer, in particular for  foci ≤5 mm in size, were found. Conclusions1. Comparative analysis of CBR showed significant (p < 0.001)  increase of contrast between metastatic lesion and white matter on  T1-SE-MTC in comparison with T1-SE.2. The sensitivity, specificity and accuracy of the magnetization transfer program (T1-SE-MTC) in detecting foci of  metastatic lesions in the brain is significantly higher (p < 0.01), relative to T1-SE.3. The T1-SE-MTC program allows detecting more foci in comparison with T1-SE, in particular foci of ≤5 mm (96% and 86%, respectively, with p < 0.05).


2014 ◽  
Vol 4 (2) ◽  
Author(s):  
Sayyida Sayyida ◽  
Nurdody Zakki

Diversity of Indonesian Batik hanging area. One of the very well-known Indonesian batik is Batik Madura. Batik Madura has become a pride for Indonesia, especially for Madura. The purpose of the study is to model the Sumenep pride to Batik Madura and to see the level of risk or tendency of batik madura pride for the community group Sumenep. This research method uses a non parametric regression used a non-parametric regression because the dependent variable in this study is the variable Y are variables not normally distributed. The results of this study states that the level of risk of the village in Sumenep proud of batik is almost 5 times higher than the islands while people in this city who live in the district town at risk Sumenep proud of Batik Madura 8-fold compared to the archipelago. So it can be concluded that the city is much more proud of batik than those who reside in rural areas especially those who reside in the islands. This study uses data from 100 questionnaires were analyzed using logistic regression analysis. The conclusion of this study is the pride of the batik model as follows: Function logistic regression / logit function: g (x) = 0,074 + 1,568X4(1)+2,159X4(2 this is case the islands as a comparison, X4(1)  is the place to stay in the village and X4(2)  is the place to stay in town, so the Model Opportunities p(x) = EXP(g(x))/1+EXP(g(x)).  Hopes for further research is to conduct research on the development of batik in an integrated region, the need to be disseminated to potential areas of particular potential in Madura batik, especially for residents who reside in the Islands.Keywords: Pride, Batik, Sumenep.


Sign in / Sign up

Export Citation Format

Share Document