Analysis of adaptive type-II progressively hybrid censoring with binomial removals

Elshahhat, Ahmed; Nassar, Mazen

doi:10.1080/00949655.2022.2127149

Cited by 12 publications

(7 citation statements)

References 20 publications

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“…Combining the information created by LF (7) with the prior information about µ and γ in (18) into the Bayes' methodology, the posterior PDF of µ and γ becomes…”

Section: Bayes Lf-based Estimationmentioning

confidence: 99%

“…Utilizing the joint SF ( 13) and joint prior information (18), the joint posterior density of µ and γ can be formulated as…”

Section: Bayes Sf-based Estimationmentioning

confidence: 99%

“…where k is a constant. Using the AT2PHC strategy, several works have been performed in the literature; for example, see Hemmati and Khorram [10], Liu and Gui [11], Kohansal and Bakouch [12], Elshahhat and Nassar [13], Du and Gui [14], Ateya et al [15], Alotaibi et al [16], Nassar et al [17], Elshahhat and Nassar [18], and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Elshahhat

Mohammed

2023

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A new two-parameter extended exponential lifetime distribution with an increasing failure rate called the Poisson–exponential (PE) model was explored. In the reliability experiments, an adaptive progressively Type-II hybrid censoring strategy is presented to improve the statistical analysis efficiency and reduce the entire test duration on a life-testing experiment. To benefit from this mechanism, this paper sought to infer the unknown parameters, as well as the reliability and failure rate function of the PE distribution using both the likelihood and product of spacings estimation procedures as a conventional view. For each unknown parameter, from both classical approaches, an approximate confidence interval based on Fisher’s information was also created. Additionally, in the Bayesian paradigm, the given classical approaches were extended to Bayes’ continuous theorem to develop the Bayes (or credible interval) estimates of the same unknown quantities. Employing the squared error loss, the Bayesian inference was developed based on independent gamma assumptions. Because of the complex nature of the posterior density, the Markov chain with the Monte Carlo methodology was used to obtain data from the whole conditional distributions and, therefore, evaluate the acquired Bayes point/interval estimates. Via extensive numerical comparisons, the performance of the estimates provided was evaluated with respect to various criteria. Among different competing progressive mechanisms, using four optimality criteria, the best censoring was suggested. Two real chemical engineering datasets were also analyzed to highlight the applicability of the acquired point and interval estimators in an actual practical scenario.

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“…Combining the information created by LF (7) with the prior information about µ and γ in (18) into the Bayes' methodology, the posterior PDF of µ and γ becomes…”

Section: Bayes Lf-based Estimationmentioning

confidence: 99%

“…Utilizing the joint SF ( 13) and joint prior information (18), the joint posterior density of µ and γ can be formulated as…”

Section: Bayes Sf-based Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Elshahhat

Mohammed

2023

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“…See also the work of Kohansal and Shoaee [19], Panahi and Asadi [20], Ahmad et al [21], Du and Gui [22], Ateya et al [23], Alotaibi et al [24,25], and Nassar et al [26]. Recently, Elshahhat and Nassar [27] extended the APT-II HC scheme to binomial random removals.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

et al. 2022

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In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.

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“…Mohan & Chacko (2021) studied the estimation of parameters for a two parameter Kumaraswamy-exponential distribution based on AT-II PCS. An adaptive type-II progressive hybrid censored sampling with random removals is considered by Elshahhat & Nassar (2022). Lv et al (2022) studied the statistical inference of Gompertz distribution based on AT-II PCS.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring

Zhang

Gui

2022

Mathematics

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This paper discusses statistical inference and optimal design of constant-stress accelerated life testing for the Chen distribution under progressive Type-II censoring. The scale parameter of the life distribution is assumed to be a logarithmic linear function of the stress level. The maximum likelihood estimates of the parameters are obtained. Then, the observed Fisher information matrix is derived and utilized to construct asymptotic confidence intervals. Meanwhile, the parametric bootstrap methods are provided for the interval estimation. In addition, the Bayes estimates under the squared error loss function are obtained by applying the Tierney and Kadane technique and Lindley’s approximation. As for the optimal design, D- and A-optimality criteria are considered to determine the optimal transformed stress level. Finally, the simulation is carried out to demonstrate the proposed estimation techniques and the optimal criteria, and a real data set is discussed.

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Analysis of adaptive type-II progressively hybrid censoring with binomial removals

Cited by 12 publications

References 20 publications

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring

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