Fitting Creep-Rupture Life Distribution Using Accelerated Life Testing Data

2000 ◽  
Vol 122 (4) ◽  
pp. 482-487 ◽  
Author(s):  
M. Zuo ◽  
S. Chiovelli ◽  
Y. Nonaka
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Rupture Life ◽  
Creep Rupture ◽  
Accelerated Life Testing ◽  
Likelihood Method ◽  
Linear Regression Method ◽  
Life Distribution ◽  
Accelerated Life ◽  
Life Distributions

This paper comments on using the Larson-Miller parameter to fit the creep-rupture life distribution as a function of temperature and stress. The commonly used least-squares linear regression method assumes that the creep-rupture life follows the lognormal distribution. Most engineering literature does not discuss the validity of this assumption. In this paper, we outline the procedure for validating two critical assumptions when the least-squares method is used. The maximum likelihood method is suggested as an alternative and more powerful method for fitting creep-rupture life distributions. Examples are given to demonstrate the use of these two methods using Microsoft Excel and the LIFEREG procedure in SAS. [S0094-9930(00)00504-7]

A Study on Procedures of the Accelerated Life Testing for Hose Assemblies

2005 ◽  
Vol 297-300 ◽  
pp. 1870-1875
Author(s):  
Y.B. Lee ◽  
Hyoung Eui Kim ◽  
J.H. Park ◽  
J.M. Ko
Keyword(s):  
Accelerated Life Testing ◽  
Test Method ◽  
Life Testing ◽  
Life Test ◽  
Life Distribution ◽  
Burst Test ◽  
Manufacture Process ◽  
Accelerated Life ◽  
Long Time ◽  
Impulse Pressure

There are several types of life test method for hose assemblies. The two major tests used for hose assemblies are impulse test and burst test. And magnification adjustment of impulse pressure, heating of testing oil and repetitive motions of bending and straightening of testing hose are also performed for accelerating the life. According to the manufacture process of hose and swaging process of fitting, there is a difference in the life of hose assemblies from minimum 7 times to maximum 40 times during the life test in the same functioning condition. Like this, the life test of hose which has a wide scope of life distribution gives a problem that observation should take a long time to find out the existence of the bursting from the beginning of the test to the completion of bursting of hose assemblies. Therefore, this research proposes a process of concentrating on the defective section of hose assemblies and maximizing the life acceleration by giving ‘Knockdown stress’ to hose assemblies just until before the hose assemblies get out of order.

An Estimator for the Influence of Service Temperature on Creep Rupture Life

2004 ◽  
Author(s):  
Marvin J. Cohn
Keyword(s):  
Rupture Life ◽  
Safety Margin ◽  
Creep Damage ◽  
Creep Rupture ◽  
Accelerated Life ◽  
Approximate Relationship ◽  
Accelerated Creep ◽  
Technical Basis ◽  
Relationship Of ◽  
The Relationship

The 2001 ASME B31.1 Code (Code) has a warning to the piping designer regarding materials susceptible to creep damage. However, the Code does not prescribe a methodology to determine the accelerated life reduction for a component due to events resulting in operating temperatures in excess of the design temperature. In general, the quantitative evaluation of the service life of a component subject to creep damage is very complex. Nevertheless, the amount of accelerated creep damage due to increased temperature can be approximately estimated. This paper is the technical basis for a recent modification to the Code. It provides an approximate relationship of operating temperature and time for equivalent creep damage of typical power piping materials. Piping designers, plant operators, and plant engineers may use this information as a rough idea of the relationship of temperature and time to maintain an equivalent safety margin on creep rupture life. This evaluation includes a discussion of tolerance to temperature increase for some low chrome ferritic, intermediate chrome martensitic, and austenitic stainless steel alloys.

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

scholarly journals Life Prediction on a T700 Carbon Fiber Reinforced Cylinder with Limited Accelerated Life Testing Data

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Ma Xiaobing ◽  
Zhang Yongbo
Keyword(s):  
Carbon Fiber ◽  
Test Data ◽  
Life Prediction ◽  
Rupture Life ◽  
Accelerated Life Testing ◽  
Accelerated Life Test ◽  
Life Testing ◽  
Life Test ◽  
Failure Data ◽  
Accelerated Life

An accelerated life testing investigation was conducted on a composite cylinder that consists of aluminum alloy and T700 carbon fiber. The ultimate failure stress predictions of cylinders were obtained by the mixing rule and verified by the blasting static pressure method. Based on the stress prediction of cylinder under working conditions, the constant stress accelerated life test of the cylinder was designed. However, the failure data cannot be sufficiently obtained by the accelerated life test due to the time limitation. Therefore, most of the data presented to be high censored in high stress level and zero-failure data in low stress level. When using the traditional method for rupture life prediction, the results showed to be of lower confidence. In this study, the consistency of failure mechanism for carbon fiber and cylinder was analyzed firstly. According to the analysis result, the statistical test information of carbon fiber could be utilized for the accelerated model constitution. Then, rupture life prediction method for cylinder was proposed based on the accelerated life test data and carbon fiber test data. In this way, the life prediction accuracy of cylinder could be improved obviously, and the results showed that the accuracy of this method increased by 35%.

scholarly journals Weibull accelerated life testing analysis with several variables using multiple linear regression

DYNA ◽  
2015 ◽  
Vol 82 (191) ◽  
pp. 156-162 ◽  
Author(s):  
Manuel R. Piña-Monarrez ◽  
Carlos A. Ávila-Chávez ◽  
Carlos D. Márquez-Luévano
Keyword(s):  
Life Stress ◽  
Shape Parameter ◽  
Accelerated Life Testing ◽  
Accelerated Life Test ◽  
Likelihood Method ◽  
Test Analysis ◽  
Operational Level ◽  
Accelerated Life ◽  
Response Variance ◽  
Joint Form

In Weibull accelerated life test analysis (ALT) with two or more variables (<em>X<sub>2</sub>, X<sub>3</sub>, ... X<sub>k</sub></em>), we estimated, in joint form, the parameters of the life stress model r{X(t)} and one shape parameter β. These were then used to extrapolate the conclusions to the operational level. However, these conclusions are biased because in the experiment design (DOE) used, each combination of the variables presents its own Weibull family (β<sub>i</sub>, η<sub>i</sub>). Thus the estimated β is not representative. On the other hand, since (β<sub>i</sub>, η<sub>i</sub>) is determined by the variance of the logarithm of the lifetime data σ<sub>t</sub><sup>2</sup> , the response variance σ<sub>y</sub><sup>2</sup> and the correlation coefficient R<sup>2</sup>, which increases when variables are added to the analysis, β is always overestimated. In this paper, the problem is statistically addressed and based on the Weibull families (β<sub>i</sub>, η<sub>i</sub>) a vector Y<sub>η</sub> is estimated and used to determine the parameters of r{X(t)}. Finally, based on the variance σ<sub>y</sub><sup>2</sup> of each level, the variance of the operational level σ<sub>op</sub><sup>2</sup> is estimated and used to determine the operational shape parameter β<sub>op</sub>. The efficiency of the proposed method is shown by numerical applications and by comparing its results with those of the maximum likelihood method (ML).

scholarly journals Uncertainty in Multi-Scale Creep Rupture Life Modeling and a New Approach to Estimating Frequency of In-Service Inspection of Components at Elevated Temperatures

2018 ◽  
Author(s):  
Jeffrey T. Fong ◽  
N. Alan Heckert ◽  
James J. Filliben ◽  
Marvin J. Cohn
Keyword(s):  
Least Squares ◽  
Rupture Life ◽  
Creep Rupture ◽  
Full Scale ◽  
Time To Failure ◽  
New Approach ◽  
Full Size ◽  
Inspection Strategy ◽  
Least Squares Fit ◽  
Service Inspection

Uncertainty in modeling the creep rupture life of a full-scale component using experimental data at microscopic (Level 1), specimen (Level 2), and full-size (Level 3) scales, is addressed by applying statistical theory of prediction intervals, and that of tolerance intervals based on the concept of coverage, p. Using a nonlinear least squares fit algorithm and the physical assumption that the one-sided Lower Tolerance Limit ( LTL ), at 95 % confidence level, of the creep rupture life, i.e., the minimum time-to-failure, minTf, of a full-scale component, cannot be negative as the lack or “Failure” of coverage ( Fp ), defined as 1 - p, approaches zero, we develop a new creep rupture life model, where the minimum time-to-failure, minTf, at extremely low “Failure” of coverage, Fp, can be estimated. Since the concept of coverage is closely related to that of an inspection strategy, and if one assumes that the predominent cause of failure of a full-size component is due to the “Failure” of inspection or coverage, it is reasonable to equate the quantity, Fp, to a Failure Probability, FP, thereby leading to a new approach of estimating the frequency of in-service inspection of a full-size component. To illustrate this approach, we include a numerical example using the published creep rupture time data of an API 579-1/ASME FFS-1 Grade 91 steel at 571.1 C (1060 F) (API-STD-530, 2007), and a linear least squares fit to generate the necessary uncertainties for ultimately performing a dynamic risk analysis, where a graphical plot of an estimate of risk with uncertainty vs. a predicted most likely date of a high consequence failure event due to creep rupture becomes available for a risk-informed inspection strategy associated with an energy-generation or chemical processing plant equipment.

Multispectral Analysis for Quantitative Measurements of Myoglobin Oxygen Fractional Saturation in the Presence of Hemoglobin Interference

1992 ◽  
Vol 46 (12) ◽  
pp. 1919-1928 ◽  
Author(s):  
Lorilee S. L. Arakaki ◽  
David H. Burns
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Least Squares ◽  
Partial Least Squares ◽  
Least Squares Method ◽  
Linear Regression Method ◽  
Saturation Curve ◽  
Visible Absorption ◽  
Oxygen Tensions

Quantitative values for myoglobin oxygen fractional saturation were extracted from visible absorption spectra of myoglobin and hemoglobin solutions by analysis with three algorithms: classical least-squares, partial least-squares, and stagewise multiple linear regression. In an effort to mimic in vivo conditions, oxygen tensions and concentrations of myoglobin and hemoglobin solutions in separate cuvettes were varied independently. Transmission measurements were made through both cuvettes so that spectra contained contributions from both myoglobin and hemoglobin. Oxygen tensions in the myoglobin solutions spanned the rapidly varying region of the myoglobin oxygen saturation curve with pO2 ranging from 0 to 4.79 Torr, corresponding to fractional saturation values between 0 and 0.903. A range of hemoglobin oxygenations from fully oxygenated to fully deoxygenated was used. Estimation of myoglobin fractional saturation by the classical least-squares algorithm had a standard error (SEest) of 0.094, while the partial least-squares method resulted in an SEest of 0.070. Partial least-squares estimations resulted in an SEest of 0.041 when a limited wavelength range was used. The stagewise multiple linear regression method had an SEest of 0.052. Results indicate that stagewise regression and partial least-squares yielded estimates of myoglobin fractional saturation that were more accurate than those obtained from classical least-squares.

Analysis of Accelerated Life Test Data Involving Two Failure Modes

2011 ◽  
Vol 211-212 ◽  
pp. 1002-1006 ◽  
Author(s):  
R. Jiang
Keyword(s):  
Shape Parameter ◽  
Failure Modes ◽  
Risk Model ◽  
Accelerated Life Testing ◽  
Accelerated Life Test ◽  
Life Testing ◽  
Life Test ◽  
Life Distribution ◽  
Accelerated Life ◽  
Step Procedure

This paper presents an approach to analyze accelerated life testing (ALT) data involving two failure modes. The approach first transforms the ALT dataset into two new datasets that correspond to individual failure modes. Each transformed dataset is modeled using a two-step procedure, and the resulted models associated with individual failure modes are combined into a competing risk model. The approach is illustrated using the ALT data of industrial heaters from the literature. The analysis shows that the shape parameter of the life distribution can change with stress level.

scholarly journals Bayesian and Classical Estimation for the One Parameter Double Lindley Model

2020 ◽  
pp. 409-420 ◽  
Author(s):  
Mohamed Ibrahim ◽  
Wahhab Mohammed ◽  
Haitham M. Yousof
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Weighted Least Squares Method ◽  
Von Mises ◽  
New Distribution

The main motivation of this paper is to show how the different frequentist estimators of the new distribution perform for different sample sizes and different parameter values and to raise a guideline in choosing the best estimation method for the new model. The unknown parameters of the new distribution are estimated using the maximum likelihood method, ordinary least squares method, weighted least squares method, Cramer-Von-Mises method and Bayesian method. The obtained estimators are compared using Markov Chain Monte Carlo simulations and we observed that Bayesian estimators are more efficient compared to other the estimators.

scholarly journals Validation and Comparison of Different Statistical Models for the Prediction of Water Main Pipe Breaks in a Municipal Network in Québec, Canada

2016 ◽  
Vol 29 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Sophie Duchesne ◽  
Babacar Toumbou ◽  
Jean-Pierre Villeneuve
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Method ◽  
Water Main ◽  
Pipe Replacement ◽  
The Impact ◽  
Over Time ◽  
Observation Period

In this study, three models for the simulation of the number of breaks in a water main network are presented and compared: linear regression, the Weibull-Exponential-Exponential (WEE), and the Weibull-Exponential-Exponential-Exponential (WEEE) models. These models were calibrated using a database of recorded breaks in a real water main network of a municipality in the province of Québec, for the observation period 1976 to 1996, with the least squares and the maximum likelihood methods. The ability of these models to predict breaks over time was then evaluated by comparing the predicted number of breaks for the years 1997 to 2007 with the observed breaks in the network over the same time period. Results show that if the period of observation is short (around 20 years), calibration of the WEE and WEEE models with the maximum likelihood method leads to estimates that are closer to the observations than when these models are calibrated with the least squares method. When the observation period is longer (around 30 years), the predictions obtained with the models calibrated using the maximum likelihood or the least squares methods are similar. However, the use of the maximum likelihood method for calibration is only possible when data for the occurrence of each break for each pipe of the network are available (a pipe being a homogeneous network segment between two adjacent street junctions). If this is not the case, a trend line will be sufficient to predict the number of breaks over time, though this type of curve does not allow to account for pipe replacement scenarios. If the only information available is the total number of breaks on the network each year, then the impact of replacement scenarios could be simulated with the WEE and WEEE models calibrated using the least squares method.

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