Estimation Uncertainty in the Determination of the Master Curve Reference Temperature

2010 ◽  
Author(s):  
T.-L. Sam Sham ◽  
Daniel R. Eno
Keyword(s):  
Standard Error ◽  
Master Curve ◽  
Asymptotic Properties ◽  
Test Methods ◽  
Reference Temperature ◽  
Finite Sample ◽  
Estimation Uncertainty ◽  
Single Temperature ◽  
Rigorous Treatment ◽  
Temperature Test

The Master Curve Reference Temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology. Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.

Procedure for Uncertainty Estimation in Determining the Master Curve Reference Temperature1

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
T.-L. Sham ◽  
Daniel R. Eno
Keyword(s):  
Standard Error ◽  
Master Curve ◽  
Asymptotic Properties ◽  
Test Methods ◽  
Test Method ◽  
Reference Temperature ◽  
Finite Sample ◽  
Transition Range ◽  
Single Temperature ◽  
Temperature Test

The master curve reference temperature, T0, characterizes the fracture performance of structural steels in the ductile-to-brittle transition region. For a given material, this reference temperature is estimated via fracture toughness testing. A methodology is presented to compute the standard error of an estimated T0 value from a finite sample of toughness data, in a unified manner for both single temperature and multiple temperature test methods. Using the asymptotic properties of maximum likelihood estimators, closed-form expressions for the standard error of the estimate of T0 are presented for both test methods. This methodology includes statistically rigorous treatment of censored data, which represents an advance over the current ASTM E1921 methodology (“E1921-10, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range,” ASTM International, West Conshohocken, PA, 2010). Through Monte Carlo simulations of realistic single temperature and multiple temperature test plans, the recommended likelihood-based procedure is shown to provide better statistical performance than the methods in the ASTM E1921 standard.

A weighted Fama-MacBeth two-step panel regression procedure: asymptotic properties, finite-sample adjustment, and performance

2020 ◽  
Vol 37 (2) ◽  
pp. 347-360
Author(s):  
Kyuseok Lee
Keyword(s):  
Asymptotic Distribution ◽  
Standard Error ◽  
Asymptotic Properties ◽  
Formal Proof ◽  
Error Estimator ◽  
Panel Regression ◽  
Finite Sample ◽  
Asymptotic Results ◽  
Content Type ◽  
Regression Procedure

Purpose In a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error. Design/methodology/approach First, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed. Findings It is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%. Originality/value The findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.

Surface Temperature Test Methods Per IEEE 1349

2007 ◽  
Vol 43 (3) ◽  
pp. 821-828 ◽  
Author(s):  
Daniel E. Delaney ◽  
Michael K. Bruin
Keyword(s):  
Surface Temperature ◽  
Test Methods ◽  
Temperature Test

International Round Robin Test on Master Curve Reference Temperature Evaluation Utilizing Miniature C(T) Specimen

2014 ◽  
pp. 1-17 ◽  
Author(s):  
Yamamoto Masato ◽  
Onizawa Kunio ◽  
Yoshimoto Kentaro ◽  
Ogawa Takuya ◽  
Mabuchi Yasuhiro ◽  
...  
Keyword(s):  
Master Curve ◽  
Round Robin ◽  
Reference Temperature ◽  
Round Robin Test ◽  
International Round

scholarly journals Gradient and Likelihood Ratio Tests in Cure Rate Models

2016 ◽  
Vol 5 (4) ◽  
pp. 9 ◽  
Author(s):  
Hérica P. A. Carneiro ◽  
Dione M. Valença
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Survival Models ◽  
Finite Sample ◽  
Cure Rate ◽  
Time Model ◽  
Cure Rate Models ◽  
Large Sample ◽  
Finite Samples

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently  a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we  performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

scholarly journals Heterogeneous individual risk modelling of recurrent events

Biometrika ◽  
2020 ◽  
Author(s):  
Huijuan Ma ◽  
Limin Peng ◽  
Chiung-Yu Huang ◽  
Haoda Fu
Keyword(s):  
Recurrent Events ◽  
Asymptotic Properties ◽  
Dynamic Modelling ◽  
Individual Risk ◽  
Simulation Studies ◽  
Finite Sample ◽  
Risk Modelling ◽  
Modelling Framework ◽  
Proposed Model

Summary Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. We propose a new sensible measure of individual risk of recurrent events and present a dynamic modelling framework thereof, which accounts for both observed covariates and unobservable frailty. The proposed modelling requires no distributional specification of the unobservable frailty, while permitting exploration of the dynamic effects of the observed covariates. We develop estimation and inference procedures for the proposed model through a novel adaptation of the principle of conditional score. The asymptotic properties of the proposed estimator, including the uniform consistency and weak convergence, are established. Extensive simulation studies demonstrate satisfactory finite-sample performance of the proposed method. We illustrate the practical utility of the new method via an application to a diabetes clinical trial that explores the risk patterns of hypoglycemia in type 2 diabetes patients.

Investigation of the Beltline Welding Seam and Base Metal of the Greifswald WWER-440 Unit 1 Reactor Pressure Vessel

2009 ◽  
Author(s):  
Jan Schuhknecht ◽  
Hans-Werner Viehrig ◽  
Udo Rindelhardt
Keyword(s):  
Weld Metal ◽  
Base Metal ◽  
Pressure Vessel ◽  
Master Curve ◽  
Reactor Pressure Vessel ◽  
Reference Temperature ◽  
Metal Ring ◽  
Welding Seam ◽  
Root Region ◽  
Reactor Pressure

The investigation of reactor pressure vessel (RPV) materials from decommissioned NPPs offers the unique opportunity to scrutinize the irradiation behaviour under real conditions. Material samples taken from the RPV wall enable a comprehensive material characterisation. The paper describes the investigation of trepans taken from the decommissioned WWER-440 first generation RPVs of the Greifswald NPP. Those RPVs represent different material conditions such as irradiated (I), irradiated and recovery annealed (IA) and irradiated, recovery annealed and re-irradiated (IAI). The working program is focussed on the characterisation of the RPV steels (base and weld metal) through the RPV wall. The key part of the testing is aimed at the determination of the reference temperature T0 following the ASTM Test Standard E1921-05 to determine the fracture toughness of the RPV steel in different thickness locations. In a first step the trepans taken from the RPV Greifswald Unit 1 containing the X-butt multilayer submerged welding seam and from base metal ring 0.3.1 both located in the beltline region were investigated. Unit 1 represents the IAI condition. It is shown that the Master Curve approach as adopted in ASTM E1921 is applicable to the investigated original WWER-440 weld metal. The evaluated T0 varies through the thickness of the welding seam. The lowest T0 value was measured in the root region of the welding seam representing a uniform fine grain ferritic structure. Beyond the welding root T0 shows a wavelike behaviour. The highest T0 of the weld seam was not measured at the inner wall surface. This is important for the assessment of ductile-to-brittle temperatures measured on sub size Charpy specimens made of weld metal compact samples removed from the inner RPV wall. Our findings imply that these samples do not represent the most conservative condition. Nevertheless, the Charpy transition temperature TT41J estimated with results of sub size specimens after the recovery annealing was confirmed by the testing of standard Charpy V-notch specimens. The evaluated Charpy-V TT41J shows a better accordance with the irradiation fluence along the wall thickness than the Master Curve reference temperature T0. The evaluated T0 from the trepan of base metal ring 0.3.1 varies through the thickness of the RPV wall. T0 increases from −120°C at the inner surface to −104°C at a distance of 33 mm from it and again to −115°C at the outer RPV wall. The KJc values generally follow the course of the MC, although the scatter is large. The re-embrittlement during 2 campaigns operation can be assumed to be low for the weld and base metal.

A Combined Model Approach for Estimating T0

2019 ◽  
Author(s):  
Marjorie Erickson
Keyword(s):  
Fracture Toughness ◽  
Master Curve ◽  
Reference Temperature ◽  
Initiation Toughness ◽  
Correlation Model ◽  
Combined Model ◽  
Best Estimate ◽  
Curve Model ◽  
Asme Code ◽  
Model Approach

Abstract The current best-estimate model describing the fracture toughness of ferritic steels is the Master Curve methodology standardized in ASTM E1921. Shortly following standardization by ASTM, efforts were undertaken to incorporate this best-estimate model into the framework of the ASME Code to reduce the conservatisms resulting from use of a reference temperature based on the nil-ductility temperature (RTNDT) to index the plane strain fracture initiation toughness (KIc). The reference temperature RTT0, which is based on the ASTM E1921-defined T0 value, was introduced in ASME Code Cases N-629 (replaced by Code Case N-851) and N-631 to replace RTNDT for indexing the ASME KIc curve. Efforts are continuing within the ASME Code to implement direct use of the Master Curve model; using the T0 reference temperature to index an elastic-plastic, KJc fracture toughness curve. Transitioning to a direct T0-based fracture toughness assessment methodology requires the availability of T0 estimates for all materials to be assessed. The historical Charpy and NDT-based regulatory approach to characterizing toughness for reactor pressure vessel (RPV) steels results in a lack of T0 values for a large population of the US nuclear fleet. The expense of the fracture toughness testing required to estimate a valid T0 value makes it unlikely that T0 will ever be widely available. Since direct implementation of best-estimate, fracture toughness models in codes and regulatory actions requires an estimate of T0 for all materials of interest it is necessary to develop an alternative means of estimating T0. A project has been undertaken to develop a combined model approach to estimating T0 from data that may include limited elastic-plastic fracture toughness KJc, Charpy, tensile, ductile initiation toughness, arrest toughness, and/or nil-ductility temperature data. Using correlations between these properties and T0 a methodology for combining estimates of T0 from several sources of data was developed. T0 estimates obtained independently from the Master Curve model, the Simple T28J correlation model, and a more complex Charpy correlation model were combined using the Mixture Probability Density Function (PDF) method to provide a single estimate for T0. Using this method, the individual T0 estimates were combined using weighting factors that accounted for sample size and individual model accuracy to optimize the accuracy and precision of the combined T0 estimate. Combining weighted estimates of T0 from several sources of data was found to provide a more refined estimate of T0 than could be obtained from any of the models alone.

Learning Block Structures in U-statistic Based Matrices

Biometrika ◽  
2020 ◽  
Author(s):  
Weiping Zhang ◽  
Baisuo Jin ◽  
Zhidong Bai
Keyword(s):  
Matrix Theory ◽  
Block Structure ◽  
Group Structure ◽  
Asymptotic Properties ◽  
Finite Sample ◽  
Eigenvalues And Eigenvectors ◽  
Sample Matrix ◽  
U Statistics ◽  
Large Matrix ◽  
Block Structures

Abstract We introduce a conceptually simple, efficient and easily implemented approach for learning the block structure in a large matrix. Using the properties of U-statistics and large dimensional random matrix theory, the group structure of many variables can be directly identified based on the eigenvalues and eigenvectors of the scaled sample matrix. We also established the asymptotic properties of the proposed approach under mild conditions. The finite-sample performance of the approach is examined by extensive simulations and data examples.

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