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Granite rocks are currently one of the foremost raw materials that can be used for various economic purposes such as ornamentation and building materials, because they do not possess radioactive concentrations and have good physical and mechanical properties. The granite rocks of north Um Taghir are connected to neoproterozoic rocks and integrated to the north Arabian-Nubian Shield (ANS), which lies in Northeast Africa. Inductively coupled plasma mass spectrometry (ICP-MS) and X-ray fluorescence analysis, concurrent to some statistical analysis, have been carried for major oxides and some trace elements to extract much fundamental information by following certain mathematical methods. The exposed granite rock units in north Um Taghir are classified into four rock units represented by tonalite, granodiorite, monzogranite, and alkali-feldspar granite which are cut by different types of dikes. The magma of tonalite and granodiorite is low-to-medium K calc-alkaline affinity, while the magma of monzogranite and alkali-feldspar granite is medium-to-high K calc-alkaline affinity, and of metaluminous to peraluminous nature. Granite rocks show a slightly depletion of fractionated patterns from light rare earth elements (LREEs) to heavy rare earth elements (HREEs) with slightly positive to negative Eu anomalies from tonalite to monzogranite and alkali-feldspar granites. The statistical criteria have been achieved to explore the significant differences of radiological hazard parameters among samples. It is obvious that there is no homogeneity among samples; furthermore, in Kruskal–Wallis test, Mann–Whitney test, and Pearson correlation coefficient, it can be noticed that there are significant differences between each pair of samples: tonalite, monzogranite; tonalite, alkali-feldspar granite; granodiorite, monzogranite; and granodiorite, alkali-feldspar granite. There is a strong direct relationship among granodiorite and both tonalite and alkali-feldspar granite, and among alkali-feldspar granite and tonalite and granodiorite. There is a strong inverse relationship among monzogranite and tonalite, granodiorite, and alkali-feldspar granite. As stated by all results, it can be mentioned that the granite rocks have a worthy result of mechanical and physical properties. So that they can be used for various economic purposes.

In this paper, estimates of the parameters and the acceleration factor of a new distribution known as the Weibull Population Mean Distribution (WPMD) are explored. We propose the use of the model suggested by Abd-Elrahman [A better alternative to the generalized Bilal distribution: A new model and applications, Int. J. Reliab. Qual. Saf. Eng. 30(6) (2023) 2350027, doi: 10.1142/S0218539323500274 ] for estimating these parameters. To accomplish this, we employ the maximum likelihood estimation method via a Constant-Stress Partially Accelerated Life Test (CSPALT) model. In this study, we have utilized Unified Hybrid (UH) censored data obtained from the WPMD. Confidence intervals for the model parameters and the acceleration factor are constructed based on the approximate Fisher information matrix. The average and Mean Squared Error (MSE) of estimates are computed to evaluate the performance of the proposed method under the CSPALT model. Additionally, a real data set is provided for illustrative purposes, and a numerical analysis of the UH Censoring Scheme (UHCS) is carried out. Finally, concluding remarks are presented. [ABSTRACT FROM AUTHOR]

In this paper, Burr-X distribution with unified hybrid censored data is considered. The maximum likelihood method, the Bayesian and the E-Bayesian (the expectation of the Bayesian estimate) approaches are studied for the distribution parameter and the associated reliability function. The Bayesian and the E-Bayesian estimates are derived under LINEX and squared error loss (SEL) functions. We apply Markov chain Monte Carlo (MCMC) techniques to derive the Bayesian and the E-Bayesian estimates. Also, confidence intervals (CIs) of the maximum likelihood estimates, as well as credible intervals (CRIs) of the Bayesian and the E-Bayesian estimates, are computed. On the other hand, an example of a real data set is provided for the purpose of illustration. Finally, a numerical comparison among the proposed methods is performed. [ABSTRACT FROM AUTHOR]

In this paper, Burr-X distribution with Type-I hybrid censored data is considered. E-Bayesian estimation (expectation of the Bayesian estimate) and the corresponding maximum likelihood and Bayesian estimation methods are discussed for the distribution parameter and the reliability function. Bayesian and E-Bayesian estimates are derived by using LINEX and squared error loss (SEL) functions. By applying Markov chain Monte Carlo (MCMC) techniques Bayesian and E-Bayesian estimates are obtained. An illustrative examples of Type-I hybrid censored samples and real data set are presented. Finally, a comparison among the proposed estimation methods is conducted. [ABSTRACT FROM AUTHOR]