Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

El-Din, M. M. Mohie; Abu-Youssef, S. E.; Ali, Nahed S. A.; El-Raheem, A. M. Abd

doi:10.5351/csam.2016.23.4.269

Cited by 19 publications

(12 citation statements)

References 19 publications

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“…Haghighi [42] proposed a design for the step-stress accelerated life test for the NH distribution in the presence of type-I censoring and then estimated model parameters for such circumstances. El-Din et al [43] also proposed a simple step-stress accelerated life test for the NH model under type-II progressive censoring, obtained maximum likelihood and Bayes estimates for NH model parameters, and also derived approximate, bootstrap, and credible intervals for the estimators. El-Din et al [44] considered the progressive stress accelerated life test under progressive type-II censoring and obtained parameter estimates of the NH model through maximum likelihood and Bayes methods of estimation along with Bayes credible intervals.…”

Section: Order Statistics Andmentioning

confidence: 99%

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Ahmadini

Tahir

Alamri

et al. 2021

Mathematical Problems in Engineering

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The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.

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Section: Order Statistics Andmentioning

confidence: 99%

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Ahmadini

Tahir

Alamri

et al. 2021

Mathematical Problems in Engineering

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“…We can use this algorithm with one dimension and two dimensions data. For more reading see [24][25][26][27][28][29][30][31].…”

Section: The Metropolis-hasting Algorithmmentioning

confidence: 99%

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Hussam¹,

Riad

Mubarak

et al. 2020

Symmetry

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Saving money and time are very important in any research project, so we must find a way to decrease the time of the experiment. This method is called the accelerated life tests (ALT) under censored samples, which is a very efficient method to reduce time, which leads to a decrease in the cost of the experiment. This research project includes inference on Lindley distribution in a simple step-stress ALT for the Type II progressive censored sample. The paper contains two major sections, which are a simulation study and a real-data application on the experimental design of an industry experiment on lamps. These sections are used to conduct results on the study of the distribution. The simulation was done using Mathematica 11 program. To use real data in the censored sample, we fitted them to be compatible with the Lindley distribution using the modified Kolmogorov–Smirnov (KS) goodness of fit test for progressive Type II censored data. We used the tampered random variable (TRV) acceleration model to generate early failures of items under stress. We also found the values of the distribution parameter and the accelerating factor using the maximum likelihood estimation of (MLEs) and Bayes estimates (BEs) using symmetric loss function for both simulated data and real data. Next, we estimated the upper and lower bounds of the parameters using three methods, namely approximate confidence intervals (CIs), Bootstrap CIs, and credible CIs, for both parameters of the distribution, ψ and ζ. Finally, we found the value of the parameter for the real data set under normal use conditions and stress conditions and graphed the reliability functions under normal and accelerated use.

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“…22,23 studied the constant-stress and simple step-stress accelerated life-tests for the NHD in presence data obtained from PCS-TII. 24 investigated classical and Bayes estimates of the NHD parameters based on progressive-stress accelerated life-test. Based on both frequentist and Bayesian view points, 25 presented a comparison between several estimation methods for the unknown parameters of NHD under complete data.…”

Section: Introductionmentioning

confidence: 99%

Statistical reliability analysis of electronic devices using generalized progressively hybrid censoring plan

Elshahhat

Azm

2022

Quality & Reliability Eng

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Generalized progressive hybrid censoring plan proposed to overcome the limitation of the progressive hybrid censoring scheme is that it cannot be applied when very few failures may occur before pre-specified terminal time 𝑇. In this paper, the estimating problems of the model parameters, reliability and hazard rate functions of Nadarajah-Haghighi distribution when a sample is available from generalized progressive hybrid censoring have been considered. The maximum likelihood and Bayes estimators have been obtained for any function of the model parameters. Approximate confidence intervals for the unknown parameters and any function of them are constructed. Using independent gamma informative priors, the Bayes estimators of the unknown parameters are derived under the squared-error loss function. Two approximation techniques, namely: Lindley approximation method and Metropolis Hastings algorithm have been used to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. The performance of the proposed methods are evaluated through a Monte Carlo simulation study. To select the optimum censoring scheme among different competing censoring plans, different optimality criteria have been considered. A real-life dataset, representing the failure times of electronic devices, is analyzed to demonstrate how the applicability of the proposed methodologies in real phenomenon.

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Parametric inference on step-stress accelerated life testing for the extension of exponential distribution under progressive type-II censoring

Cited by 19 publications

References 19 publications

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Study on Lindley Distribution Accelerated Life Tests: Application and Numerical Simulation

Statistical reliability analysis of electronic devices using generalized progressively hybrid censoring plan

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