A Method for Estimating Parameters of P-S-N Curves Based on Weibull Distribution

2011 ◽  
Author(s):  
Dan Ling ◽  
Shun-Peng Zhu ◽  
Hong-Zhong Huang ◽  
Li-Ping He ◽  
Zhong-Lai Wang
Keyword(s):  
Fatigue Life ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Stress Level ◽  
Likelihood Estimation ◽  
Probability Of Failure ◽  
Unknown Parameters ◽  
Curve Model ◽  
The Relationship

An S-N curve is a traditional tool for design against fatigue. Because there is often a considerable amount of scatter in fatigue performance of specimens, The P-S-N curves capturing the probability of failure should be employed instead of S-N curves. In order to minimize the time and the number of specimens required for fatigue test, many researches had been done. Most studies were focused on a three-parameter S-N curve model; lognormal distribution and maximum likelihood estimation were employed to estimate unknown parameters. In this paper, a three-parameter Weibull distribution is used to describe the scatter of fatigue life. The relationship among survival probability, stress level and fatigue life is considered. A method for estimating parameters of P-S-N curves is proposed. According to this method, three groups of specimens are needed. Each group is submitted to a stress level. The parameters of P-S-N curves can be estimated by solving a set of nonlinear equations. And a numerical example shows that the method is effective.

scholarly journals On the Transmuted AdditiveWeibull Distribution

2016 ◽  
Vol 42 (2) ◽  
pp. 117-132 ◽  
Author(s):  
Ibrahim Elbatal ◽  
Gokarna Aryal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Random Number ◽  
Continuous Distribution ◽  
Random Number Generation ◽  
Likelihood Estimation ◽  
Unknown Parameters ◽  
Real World Data ◽  
New Distribution

In this article a continuous distribution, the so-called transmuted additive Weibull distribution, that extends the additive Weibull distribution and some other distributions is proposed and studied. We will use the quadratic rank transmutation map proposed by Shaw and Buckley (2009) in order to generate the transmuted additiveWeibull distribution. Various structural properties of the new distribution including explicit expressions for the moments, random number generation and order statistics are derived. Maximum likelihood estimation of the unknown parameters of the new model for completesample is also discussed. It will be shown that the analytical results are applicable to model real world data.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

2022 ◽  
Vol 7 (2) ◽  
pp. 2820-2839
Author(s):  
Saurabh L. Raikar ◽  
◽  
Dr. Rajesh S. Prabhu Gaonkar ◽  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Jaya Algorithm ◽  
Two Parameter

<abstract> <p>Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.</p> </abstract>

Maximum likelihood estimation for the poly-Weibull distribution

2019 ◽  
Vol 31 (4) ◽  
pp. 545-552
Author(s):  
Jason K. Freels ◽  
Daniel A. Timme ◽  
Joseph J. Pignatiello ◽  
Richard L. Warr ◽  
Raymond R. Hill
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

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