On the Estimation Problems for Exponentiated Exponential Distribution under Generalized Progressive Hybrid Censoring

Pandey, Aakriti; Kaushik, Arun; Singh, Sanjay Kumar; Singh, Umesh

doi:10.17713/ajs.v50i1.952

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…It can be used in diverse fields, including reliability engineering, medical research and environmental studies. Many authors have recently reviewed this scheme using some lifetime models, for instance (Abdelwahab et al ., 2023; Alotaibi et al ., 2023; Elshahhat and Abu El Azm, 2022; Nagy and Alrasheedi, 2022; Pandey et al ., 2022; Singh et al ., 2021; Singh et al ., 2023; Zuo et al ., 2021).…”

Section: Introductionmentioning

confidence: 99%

Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

Irfan,

Sharma

2023

IJQRM

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PurposeA progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS.Design/methodology/approachIn this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques.FindingsThe Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study.Originality/valueThe ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature.

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Section: Introductionmentioning

confidence: 99%

Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

Irfan,

Sharma

2023

IJQRM

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“…In recent literature, several authors have considered this scheme using some lifetime distributions, among others see for example. [6][7][8][9][10][11][12][13][14][15] A new two-parameter extended exponential distribution was introduced elsewhere 16 and was recently named NHD as an abbreviation of the author's name. Suppose that the lifetime 𝑋 of a testing unit follows two-parameter NHD(𝛽, 𝜆), then the probability density function (PDF) 𝑓(⋅) and cumulative distribution function (CDF) 𝐹(⋅), survival function (SF) 𝑆(⋅) and hazard rate function (HRF) 𝐻(⋅), for given mission time 𝑡, are given respectively by…”

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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“…Anatolyev and Kosenok 8 stated that the MPSEs are more efficient than the MLEs for skewed distributions. In recent past, several authors have studied the product of spacings function under different types of censoring plans, for example, see references 9–13 . However, for T2‐PCS sample, 14 proposed MPS procedure, which selects parameter values that make the observed data plausibly uniform.…”

Section: Introductionmentioning

confidence: 99%

“…In recent past, several authors have studied the product of spacings function under different types of censoring plans, for example, see references. [9][10][11][12][13] However, for T2-PCS sample, 14 proposed MPS procedure, which selects parameter values that make the observed data plausibly uniform. However, according to reference, 14 the PS function of T2-PCS sample (𝑥 𝑖∶𝑚∶𝑛 , 𝑅 𝑖 ), 𝑖 = 1, 2, … , 𝑚, is defined as…”

Section: Introductionmentioning

confidence: 99%

Analysis of Wilson‐Hilferty distribution under progressive Type‐II censoring

Dey¹,

Elshahhat

2022

Quality & Reliability Eng

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A new re-parameterize form of the Wilson-Hilferty distribution for data modelling with increasing, decreasing and bathtub shape hazard rates has been considered. This paper takes into account the estimation for the unknown model parameters, reliability function and hazard function based on two frequentist methods and Bayesian method of estimation using Type-II progressively censored data. In frequentist method, besides conventional likelihood based estimation, another competitive method, known as maximum product of spacing (MPS) method is proposed to estimate the model parameters, reliability function and hazard function as an alternative approach to the common likelihood method. In Bayesian paradigm, we have also considered the MPS function as an alternative to the traditional likelihood function and both are also discussed under the Bayesian set up for unknown parameters, reliability function and hazard function. Moreover, for all considered unknown quantities, the approximate confidence intervals under the proposed frequentist approaches as well as the Bayes credible intervals are constructed. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates with respect to various criteria quantities. Furthermore, we discuss an optimal progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, to show the applicability of the proposed methodologies in a real-life scenario, an engineering dataset is analysed.

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On the Estimation Problems for Exponentiated Exponential Distribution under Generalized Progressive Hybrid Censoring

Cited by 4 publications

References 18 publications

Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

Reliability characteristics of COVID-19 death rate using generalized progressive hybrid censored data

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

Analysis of Wilson‐Hilferty distribution under progressive Type‐II censoring

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