scholarly journals Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 192-199 ◽  
Author(s):  
Hanaa H. Abu-Zinadah ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Risk Factors ◽  
Risk Model ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Life Tests ◽  
Censoring Scheme

Abstract The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study.

scholarly journals Accelerated competing risks model from Gompertz lifetime distributions with type-II censoring scheme

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 165-175
Author(s):  
Abdullah Almarashi ◽  
Gamal Abd-Elmougod
Keyword(s):  
Accelerated Life Test ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Model ◽  
Time To Failure ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Accelerated Life ◽  
Interval Estimators ◽  
Censoring Scheme

Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two boot?strap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity.

scholarly journals Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Vikas Kumar Sharma
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Model Parameters ◽  
Type Ii ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Highest Posterior Density ◽  
Censoring Scheme

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.

scholarly journals Accelerated competing risks model from Gompertz lifetime distributions with type-II censoring scheme

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 165-175
Author(s):  
Abdullah Almarashi ◽  
Gamal Abd-Elmougod
Keyword(s):  
Accelerated Life Test ◽  
Likelihood Method ◽  
Model Parameters ◽  
Test Model ◽  
Time To Failure ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Accelerated Life ◽  
Interval Estimators ◽  
Censoring Scheme

Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two boot?strap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity.

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

scholarly journals Analysis of Type-II Censored Competing Risks’ Data under Reduced New Modified Weibull Distribution

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Saad J. Almalki ◽  
Tahani A. Abushal ◽  
M. D. Alsulami ◽  
G. A. Abd-Elmougod
Keyword(s):  
Competing Risks ◽  
Hazard Rate ◽  
Rate Function ◽  
Likelihood Method ◽  
Mcmc Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Hazard Rate Function ◽  
Monte Carlo Simulation Study ◽  
Modified Weibull

Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study.

scholarly journals Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 100
Author(s):  
Hisham M. Almongy ◽  
Fatma Y. Alshenawy ◽  
Ehab M. Almetwally ◽  
Doaa A. Abdo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Transformer Insulation ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

scholarly journals Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 557-565 ◽  
Author(s):  
Hanaa H. Abu-Zinadah
Keyword(s):  
Confidence Intervals ◽  
Life Time ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data ◽  
Data Set ◽  
Censored Samples ◽  
Credible Intervals ◽  
Life Tests ◽  
Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

scholarly journals Statistical Analysis of Joint Type-I Generalized Hybrid Censoring Data from Burr XII Lifetime Distributions

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mahmoud Ragab ◽  
Aisha Fayomi ◽  
Ali Algarni ◽  
G. A. Abd-Elmougod ◽  
Neveen Sayed-Ahmed ◽  
...  
Keyword(s):  
Model Parameters ◽  
Type I ◽  
Bayes Method ◽  
Monte Carlo Simulation Study ◽  
Lifetime Distributions ◽  
Hybrid Censoring ◽  
Life Tests ◽  
Censoring Scheme ◽  
Theoretical Results

The quality of the products coming from different lines of production requires some tests called comparative life tests. For lines having the same facility, the lifetime of the product is distributed by Burr XII, the lifetime distribution, and units are tested under type-I generalized hybrid censoring scheme. The observed censoring data are used under maximum likelihood and the Bayes method to estimate the model parameters. The theoretical results are discussed and assessed through data analysis and Monte Carlo simulation study. Finally, we reported some brief comments obtained from numerical computation.

scholarly journals Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1997
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi ◽  
Devendra Kumar ◽  
Salem A. Alyami
Keyword(s):  
Maximum Likelihood ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Right Censored Order Statistics ◽  
Censoring Scheme ◽  
Two Parameter ◽  
Progressive Type Ii Censoring

In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the scale and location parameters of two parameter reduced Kies distribution. The parameters of the two parameter reduced Kies distribution are estimated under progressive type-II censoring scheme. The model parameters are estimated using the maximum likelihood estimation method. Further, we explore the asymptotic confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. Based on our study, we can conclude that maximum likelihood estimators is decreasing with respect to an increase of the schemes and comparing the three censoring schemes, it is clear that the mean sum of squares, confidence interval lengths are smaller for scheme 1 than schemes 2 and 3.

scholarly journals Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1679
Author(s):  
R. Alshenawy ◽  
Ali Al-Alwan ◽  
Ehab M. Almetwally ◽  
Ahmed Z. Afify ◽  
Hisham M. Almongy
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Confidence Intervals ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likelihood estimation methods. Further, we explore the asymptotic confidence intervals and bootstrap confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. An empirical study using two real datasets form engineering and medicine fields to validate the introduced methods of inference. Based on our study, we can conclude that the maximum product of spacing method outperforms the maximum likelihood method for estimating the extended odd Weibull exponential (EOWE) parameters under a progressive type-II censoring scheme in both numerical and empirical cases.

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