Inference for two‐parameter Rayleigh competing risks data under generalized progressive hybrid censoring

Singh, Devendra P.; Lodhi, Chandrakant; Tripathi, Yogesh Mani; Wang, Liang

doi:10.1002/qre.2791

Cited by 13 publications

(9 citation statements)

References 53 publications

(70 reference statements)

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“…Theorem 2. Suppose that observation (2) comes from Weibull population (5); the MLE of α obtained from (10) uniquely exists which can be derived from the following equation:…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…In addition, the Bayes credible intervals under NIP also have better performance than ACIs in terms of interval length. Besides, to illustrate eorem 2 and Lemma 1, the curves of the profile log-likelihood function (10) and the logarithmic function of posterior marginal density (21) with respect to NIP are plotted in Figure 4 under the censored failure data. It is observed that the profile log-likelihood function of α has a unique maximum point and the posterior marginal density function π(α|data) is log-concave.…”

Section: Real-life Illustrationmentioning

confidence: 99%

“…Taking derivative for (10) and setting it to zero, one has likelihood equation (11). Next, it is shown that equation (11) has a unique root with respect to α.…”

Section: Appendixmentioning

confidence: 99%

“…To overcome such problems, hybrid censoring schemes were further introduced in practice, which can be viewed as a mixture of Type-I and Type-II censoring in conventional and progressive censoring procedures, respectively. For instance, Prajapati et al [6] and Algarni et al [7] discussed inference based on Type-I and Type-II hybrid censoring, and Basu et al [8], Gorny and Cramer [9], and Singh et al [10] studied progressive hybrid censored data under different cases. For an exhaustive amount of references and further details on hybrid censoring, one can see the recent review paper [11] and the monograph of Balakrishnan and Cramer [5] within related sections.…”

Section: Introductionmentioning

confidence: 99%

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Estimation for Weibull Parameters with Generalized Progressive Hybrid Censored Data

Zuo

Wang

Lin

et al. 2021

Journal of Mathematics

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In this paper, the interest is in estimating the Weibull products when the available data is obtained via generalized progressive hybrid censoring. The testing scheme conducts products of interest under a more flexible way and allows collecting failure data in efficient and adaptable experimental scenarios than traditional lifetime testing. When the latent lifetime of products follows Weibull distribution, classical and Bayesian inferences are considered for unknown parameters. The existence and uniqueness of maximum likelihood estimates are established, and approximate confidence intervals are also constructed via asymptotic theory. Bayes point estimates as well as the credible intervals of the parameters are obtained, and correspondingly, Monte Carlo sampling technique is also provided for complex posterior computation. Extensive numerical analysis is carried out, and the results show that the generalized progressive hybrid censoring is an adaptive procedure in practical lifetime experiment, both proposed classical and Bayesian inferential approaches perform satisfactorily, and the Bayesian results are superior to conventional likelihood estimates.

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“…Theorem 2. Suppose that observation (2) comes from Weibull population (5); the MLE of α obtained from (10) uniquely exists which can be derived from the following equation:…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Section: Real-life Illustrationmentioning

confidence: 99%

“…Taking derivative for (10) and setting it to zero, one has likelihood equation (11). Next, it is shown that equation (11) has a unique root with respect to α.…”

Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation for Weibull Parameters with Generalized Progressive Hybrid Censored Data

Zuo

Wang

Lin

et al. 2021

Journal of Mathematics

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“…On the basis of GPHCS, Ref. [ 14 ] investigated the two-parameter Rayleigh competing risk data adopting the maximum likelihood estimation and Gibbs sampling technique was employed to approximate the associated Bayes estimates.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring

Zeng

Gui

2021

Entropy

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In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the Newton–Raphson algorithm and the expectation maximization algorithm. Based on the asymptotic normality of the maximum likelihood estimators, we develop the asymptotic confidence intervals. The percentile bootstrap method is also employed in the case of the small sample size. Further, the Bayes estimates are evaluated under various loss functions like squared error, general entropy, and linex loss functions. Tierney and Kadane approximation, as well as the importance sampling approach, is applied to obtain the Bayesian estimates under proper prior distributions. The associated Bayesian credible intervals are constructed in the meantime. Extensive numerical simulations are implemented to compare the performance of different estimation methods. Finally, an authentic example is analyzed to illustrate the inference approaches.

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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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Inference for two‐parameter Rayleigh competing risks data under generalized progressive hybrid censoring

Cited by 13 publications

References 53 publications

Estimation for Weibull Parameters with Generalized Progressive Hybrid Censored Data

Estimation for Weibull Parameters with Generalized Progressive Hybrid Censored Data

Statistical Inference of Truncated Normal Distribution Based on the Generalized Progressive Hybrid Censoring

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

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