Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution

Nassar, Mazen; Elshahhat, Ahmed

doi:10.1080/02664763.2023.2230536

Cited by 16 publications

(7 citation statements)

References 29 publications

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“…To highlight the utility of methodologies proposed for an actual phenomenon, an engineering application representing the failure times for 30 items of repairable mechanical machines (RMM) is analyzed in this subsection; see Table 11. Nassar et al [23] reanalyzed the RMM data set after it was first provided by Murthy et al [24]. From the full RMM data, to check the effectiveness of the CJ model, we shall compare its fit to other five models in the literature, namely: XLindley (XL(μ)) by Chouia et al [25], Xgamma (XG(μ)) by Sen et al [26], Muth (M(μ)) discussed by Irshad et al [27], Lindley (L(μ)) by Ghitany et al [28], and exponential (E(μ)) reviewed by Tomy et al [29].…”

Section: Mechanical Equipment Datamentioning

confidence: 99%

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

Alotaibi,

Rezk,

Elshahhat

2024

CMES

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A new one-parameter Chris-Jerry distribution, created by mixing exponential and gamma distributions, is discussed in this article in the presence of incomplete lifetime data. We examine a novel generalized progressively hybrid censoring technique that ensures the experiment ends at a predefined period when the model of the test participants has a Chris-Jerry (CJ) distribution. When the indicated censored data is present, Bayes and likelihood estimations are used to explore the CJ parameter and reliability indices, including the hazard rate and reliability functions. We acquire the estimated asymptotic and credible confidence intervals of each unknown quantity. Additionally, via the squared-error loss, the Bayes' estimators are obtained using gamma prior. The Bayes estimators cannot be expressed theoretically since the likelihood density is created in a complex manner; nonetheless, Markovchain Monte Carlo techniques can be used to evaluate them. The effectiveness of the investigated estimations is assessed, and some recommendations are given using Monte Carlo results. Ultimately, an analysis of two engineering applications, such as mechanical equipment and ball bearing data sets, shows the applicability of the proposed approaches that may be used in real-world settings.

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Section: Mechanical Equipment Datamentioning

confidence: 99%

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

Alotaibi,

Rezk,

Elshahhat

2024

CMES

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“…In this application, from the engineering field, we will explain our theoretical results based on the time between consecutive failures for repairable mechanical equipment (RME) items depicted in Table 7. Murthy et al [36] initially conveyed this data and it has also been examined by Elshahhat et al [37], Nassar et al [38], and Elshahhat et al [39]. Employing the competitive statistical distributions as well as the model selection criteria proposed in Subsection 5.1, the MOL distribution based on the complete RME data is compared.…”

Section: Mechanical Equipmentsmentioning

confidence: 99%

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

CMES

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A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing, bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is studied. In this research, using a progressive Type-II censored, various inferences of the MOL model parameters of life are introduced. Utilizing the maximum likelihood method as a classical approach, the estimators of the model parameters and various reliability measures are investigated. Against both symmetric and asymmetric loss functions, the Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) technique with the assumption of independent gamma priors. From the Fisher information data and the simulated Markovian chains, the approximate asymptotic interval and the highest posterior density interval, respectively, of each unknown parameter are calculated. Via an extensive simulated study, the usefulness of the various suggested strategies is assessed with respect to some evaluation metrics such as mean squared errors, mean relative absolute biases, average confidence lengths, and coverage percentages. Comparing the Bayesian estimations based on the asymmetric loss function to the traditional technique or the symmetric loss function-based Bayesian estimations, the analysis demonstrates that asymmetric loss function-based Bayesian estimations are preferred. Finally, two data sets, representing vinyl chloride and repairable mechanical equipment items, have been investigated to support the approaches proposed and show the superiority of the proposed model compared to the other fourteen lifetime models.

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“…where θ j , β j > 0, j = 1, 2. The joint posterior distribution of the unknown parameters can be determined by merging the data from observations produced by the LF, as provided by ( 6), with the prior information that is already known, as supplied by the joint prior distribution in (11), as follows…”

Section: Prior and Posterior Distributionsmentioning

confidence: 99%

“…The IT2-APC plan has not received much attention, according to a review of the literature. Several estimation issues for some lifetime models were examined using the IT2-APC scheme by Nassar and Elshahhat [11], Elshahhat and Nassar [12], Elbatal et al [13], Alam and Nassar [14] and Dutta and Kayal [15]. Let us now assume the observed IT2-APC sample with PSP, denoted, respectively, as x = (x…”

Section: Introductionmentioning

confidence: 99%

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

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To gather enough data from studies that are ongoing for an extended duration, a newly improved adaptive Type-II progressive censoring technique has been offered to get around this difficulty and extend several well-known multi-stage censoring plans. This work, which takes this scheme into account, focuses on some conventional and Bayesian estimation missions for parameter and reliability indicators, where the unit log-log model acts as the base distribution. The point and interval estimations of the various parameters are looked at from a classical standpoint. In addition to the conventional approach, the Bayesian methodology is examined to derive credible intervals beside the Bayesian point by leveraging the squared error loss function and the Markov chain Monte Carlo technique. Under varied settings, a simulation study is carried out to distinguish between the standard and Bayesian estimates. To implement the proposed procedures, two actual data sets are analyzed. Finally, multiple precision standards are considered to pick the optimal progressive censoring scheme.

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Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution

Cited by 16 publications

References 29 publications

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data

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