Inference on progressive-stress model for the exponentiated exponential distribution under type-II progressive hybrid censoring

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Based on failures of a parallel‐series system, a new distribution called geometric‐Poisson‐Rayleigh distribution is proposed. Some properties of the distribution are discussed. A real data set is used to compare the new distribution with other 6 distributions. The progressive‐stress accelerated life tests are considered when the lifetime of an item under use condition is assumed to follow the geometric‐Poisson‐Rayleigh distribution. It is assumed that the scale parameter of the geometric‐Poisson‐Rayleigh distribution satisfies the inverse power law such that the stress is a nonlinear increasing function of time and the cumulative exposure model for the effect of changing stress holds. Based on type‐I progressive hybrid censoring with binomial removals, the maximum likelihood and Bayes (using linear‐exponential and general entropy loss functions) estimation methods are considered to estimate the involved parameters. Some point predictors such as the maximum likelihood, conditional median, best unbiased, and Bayes point predictors for future order statistics are obtained. The Bayes estimates are obtained using Markov chain Monte Carlo algorithm. Finally, a simulation study is performed, and numerical computations are performed to compare the performance of the implemented methods of estimation and prediction.

Section: Andmentioning

confidence: 99%

“…where Ω j (t) and (c j , d) are given, respectively, by (18) and (19). HRF (21) of GPRD under progressive-stress ALT is plotted in Figure 5 for different values of a and b.…”

Section: Gprd Under Progressive-stress Modelmentioning

confidence: 99%

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Inference for a geometric‐poisson‐Rayleigh distribution under progressive‐stress accelerated life tests based on type‐I progressive hybrid censoring with binomial removals

Nadarajah

Abdel-Hamid

Hashem

2018

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“…AL-Hussaini et al 20 derived Bayesian prediction intervals based on progressively type-II censored data from the half-logistic distribution under progressive-stress model. Abdel-Hamid and Abushul 21 obtained the Bayes estimates (BEs) of exponentiated exponential distribution under type-II progressive hybrid censoring, assuming the inverse power law and the cumulative exposure model.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian inference on progressive‐stress accelerated life testing for the extension of the exponential distribution under progressive type‐II censoring

El-Din

Abu-Youssef

Ali

et al. 2017

In this paper, a progressive‐stress accelerated life test under progressive type‐II censoring is considered. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. The maximum likelihood and Bayes estimates of the model parameters are obtained. The approximate and credible confidence intervals of the estimators are derived. Furthermore, a real lifetime data set is analyzed to illustrate the proposed procedures. Finally, the simulation studies are used to compare between 2 different designs of the progressive‐stress test (simple and multiple ramp‐stress tests).

“…Notable among them are Yin and Sheng 19 considered the MLE for exponential failure times under progressive stress, Bai et al 20 considered optimum testing plan with linearly increasing progressive stress, ie, simple ramp stress for Weibull distribution under type-I censoring scheme, Abdel-Hamid and AL-Hussaini 21 studied progressive-stress ALT under progressive censoring for Weibull distribution. Hussaini et al 22 considered one-sample Bayesian prediction intervals based on progressively type-II censored data from the half-logistic distribution under progressive stress ALT, Abdel-Hamid and Abushal 23 considered exponentiated exponential distribution based on progressive-stress ALT under progressively hybrid censored data. Recently, El-Din et al 24 considered classical and Bayesian inference on progressively type-II censored progressive-stress ALT for the extension of the exponential distribution.…”

mentioning

confidence: 99%

Statistical inference on progressive‐stress accelerated life testing for the logistic exponential distribution under progressive type‐II censoring

Mahto

Dey²,

Tripathi

2019

The accelerated life testing (ALT) is an efficient approach and has been used in several fields to obtain failure time data of test units in a much shorter time than testing at normal operating conditions. In this article, a progressivestress ALT under progressive type-II censoring is considered when the lifetime of test units follows logistic exponential distribution. We assume that the scale parameter of the distribution satisfying the inverse power law. First, the maximum likelihood estimates of the model parameters and their approximate confidence intervals are obtained. Next, we obtain Bayes estimators under squared error loss function with the help of Metropolis-Hasting (MH) algorithm. We also derive highest posterior density (HPD) credible intervals of the model parameters. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation. Finally, one data set has been analyzed for illustrative purposes. KEYWORDS accelerated life testing, cumulative exposure model, highest posterior density, Markov chain Monte Carlo, maximum likelihood estimation