scholarly journals Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1786 ◽  
Author(s):  
A. M. Abd El-Raheem ◽  
M. H. Abu-Moussa ◽  
Marwa M. Mohie El-Din ◽  
E. H. Hafez
Keyword(s):  
Simulation Study ◽  
Stress Test ◽  
Real Data ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Model Parameters ◽  
Data Set ◽  
Accelerated Life

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

scholarly journals On Bayesian estimation of step stress accelerated life testing for exponentiated Lomax distribution based on censored samples

2020 ◽  
pp. 239-248
Author(s):  
Refah Mohamed Alotaibi ◽  
Hoda Ragab Rezk
Keyword(s):  
Numerical Study ◽  
Real Data ◽  
Operating Conditions ◽  
Stress Factors ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Life Testing ◽  
Unknown Parameters ◽  
Accelerated Life ◽  
Credible Intervals

In reliability analysis and life-testing experiments, the researcher is often interested in the effects of changing stress factors such as “temperature”, “voltage” and “load” on the lifetimes of the units. Step-stress (SS) test, which is a special class from the well-known accelerated life-tests, allows the experimenter to increase the stress levels at some constant times to obtain information on the unknown parameters of the life models more speedily than under usual operating conditions. In this paper, a simple SS model from the exponentiated Lomax (ExpLx) distribution when there is time limitation on the duration of the experiment is considered. Bayesian estimates of the parameters assuming a cumulative exposure model with lifetimes being ExpLx distribution are resultant using Markov chain Monte Carlo (M.C.M.C) procedures. Also, the credible intervals and predicted values of the scale parameter, reliability and hazard are derived. Finally, the numerical study and real data are presented to illustrate the proposed study

scholarly journals Optimal Plan and Estimation for Bivariate Step-Stress Accelerated Life Test under Progressive Type-I Censoring

2021 ◽  
pp. 683-694
Author(s):  
Mashroor Ahmad Khan ◽  
Navin Chandra
Keyword(s):  
Maximum Likelihood ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Type I ◽  
Life Test ◽  
Type I Censoring ◽  
Accelerated Life ◽  
Progressive Type ◽  
Stress Levels

 In this paper, a step-stress accelerated life test with two stress variables for Weibull distribution under progressive type-I censoring is considered. The stress-life relationship as a log-linear function of stress levels, and for each combination of stress levels, a cumulative exposure model is assumed. The maximum likelihood and Bayes estimates of the model parameters are obtained. The optimum test plan is developed using variance-optimality criterion, which consists in finding out the optimal stress change time by minimizing asymptotic variance of the maximum likelihood estimates of the log of the scale parameter at the design stress. The proposed study illustrated by using simulated data.

scholarly journals The Beta Weibull-G Family of Distributions: Model, Properties and Application

2018 ◽  
Vol 7 (2) ◽  
pp. 12 ◽  
Author(s):  
Boikanyo Makubate ◽  
Broderick O. Oluyede ◽  
Gofaone Motobetso ◽  
Shujiao Huang ◽  
Adeniyi F. Fagbamigbe
Keyword(s):  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Generalized Distributions ◽  
Special Cases

A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series expansion of the density function, hazard function, moments, mean deviations, Lorenz and Bonferroni curves, R\'enyi entropy, distribution of order statistics and maximum likelihood estimates of the model parameters are given. Application of the model to real data set is presented to illustrate the importance and usefulness of the special case beta Weibull-log-logistic distribution.

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

scholarly journals Estimation in Step-Stress Accelerated Life Tests for Power Generalized Weibull Distribution with Progressive Censoring

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. M. Mohie EL-Din ◽  
S. E. Abu-Youssef ◽  
Nahed S. A. Ali ◽  
A. M. Abd El-Raheem
Keyword(s):  
Weibull Distribution ◽  
Asymptotic Variance ◽  
Acceleration Factor ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Progressive Censoring ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.

The odd Nadarajah-Haghighi family of distributions: properties and applications

2019 ◽  
Vol 56 (2) ◽  
pp. 185-210 ◽  
Author(s):  
Abraão D. C. Nascimento ◽  
Kássio F. Silva ◽  
Gauss M. Cordeiro ◽  
Morad Alizadeh ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
New Family ◽  
Mathematical Properties ◽  
The Family ◽  
Family Of Distributions

Abstract We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

scholarly journals Statistical Analysis for Generalized Progressive Hybrid Censored Data from Lindley Distribution under Step-Stress Partially Accelerated Life Test Model

2021 ◽  
Vol 50 (1) ◽  
pp. 105-120
Author(s):  
Aakriti Pandey ◽  
Arun Kaushik ◽  
Sanjay K. Singh ◽  
Umesh Singh
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Estimation Procedure ◽  
Accelerated Life Test ◽  
Test Model ◽  
Life Test ◽  
Data Set ◽  
Lindley Distribution ◽  
Accelerated Life ◽  
Censoring Scheme

The aim of this paper is to present the estimation procedure for the step-stress partially accelerated life test model under the generalized progressive hybrid censoring scheme. The uncertainties are assumed to be governed by Lindley distribution. The problem with point and interval estimation of the parameters as well as the acceleration factor using maximum likelihood approach for the step-stress partially accelerated life test model has been considered. A simulation study is conducted to monitor the performance of the estimators on the basis of the mean squared error under the considered censoring scheme. The expected total time of the test under an accelerated condition is computed to examine the effects of the parameters on the duration of the test. In addition, a graph of the expected total time of the test under accelerated and un-accelerated conditions is provided to highlight the effect due to acceleration. One real data set has been analyzed for illustrative purposes.

scholarly journals A new generalization of Aradhana distribution: Properties and applications

2020 ◽  
Vol 16 (2) ◽  
pp. 51-66
Author(s):  
A. Hassan ◽  
S. A. Dar ◽  
P. B. Ahmad ◽  
B. A. Para
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Model Parameters ◽  
R Software ◽  
Data Set

AbstractIn this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

scholarly journals Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data

2015 ◽  
Vol 3 (1) ◽  
pp. 72 ◽  
Author(s):  
Amal S. Hassan ◽  
Salwa M. Assar ◽  
Ahmed N. Zaky
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
High Reliability ◽  
Asymptotic Variance ◽  
Constant Stress ◽  
Acceleration Factor ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Accelerated Life

<p>Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weibull distribution. Maximum likelihood estimates are obtained for the model parameters and acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators is given. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample sizes. Simulation studies are performed to investigate the performance of the estimators.</p>

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