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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]

Numerous studies have already been attempted to explore the reliability of systems considering mask data, though the mass of them has largely focused on basic series or parallel systems, where component failures are assumed to follow an exponential or Weibull distribution. However, most electrotonic products and systems are made up of numerous components integrated in parallel-series, series-parallel, and other bridge hybrid structures, and the number of studies in the area of accelerated life testing (ALT) employing masked data for hybrid systems is limited. In this paper, the constant-stress ALT (CSALT) is explored based on type-II progressive censoring scheme (TIIPCS) for a four-component hybrid system using geometric process (GmP). The failure times of the components of the system are assumed to follow the generalized Pareto (GP) distribution. The maximum likelihood estimate (MLE) technique is used to establish statistical inference for the model's unknown parameters under the premise that the failure reasons are unknown for the hybrid system. In addition, the asymptotic confidence intervals (ACIs) are also obtained by inverting the fisher information matrix. Finally, a simulation study is given to explain the proposed techniques and to evaluate the performance of the estimates. The performance of MLEs is assessed in terms of root mean square errors (RMSEs) and relative absolute biases (RABs), whereas the performance of ACIs is assessed in terms of their interval length (IL) and coverage probabilities (CPs). The findings show that the technique can deliver good estimation performance with small and intermediate sample sizes, and the estimates are more accurate when more failures are observed, showing the estimation method's efficiency. [ABSTRACT FROM AUTHOR]

The widespread usage of granite in the building sector motivated us to conduct this research and examine the material's sustainability in terms of the investigated characteristics. The purpose of this paper is to discuss the statistical analysis results for the mineralogical impact on radiological hazards indices, such as the equivalent of radium, absorbed gamma dose rate, annual effective dose, internal and external hazard indices, as well as the gamma-ray index, that were calculated to estimate the environmental risks associated with these granites used as building materials, to protect the public from excessive radioactivity exposure. We focused primarily on statistical significance at a 95% confidence level. We employed a non-parametric test (Kruskal–Wallis Test) rather than a one-way ANOVA, to determine the statistical significance of the samples due to the lack of homogeneity or normality among them. To assess the difference between the samples, we used the Mann–Whitney Test on each pair of samples. Additionally, Pearson correlation coefficients for all the mineralogical results are computed. The presence of K-rich minerals (Kefeldspars, biotite) and accessories such as uranophane, uranothorite, allanite, xenotime, fergusonite, aeschynite, zircon, cassiterite, apatite, and sphene, which are mostly found in granitic rocks, determines the level of natural radioactivity of the investigated granites. Most of the rock samples analyzed have indicators of radioactive dangers that are within the acceptable level range, indicating that they are suitable for use as building materials. On the other hand, some samples have environmental criteria that are higher than international standards, indicating that they are unsuitable for use as construction materials. [ABSTRACT FROM AUTHOR]

In this paper, the exponentiated gamma distribution (EGD) with generalized Type-I hybrid censored data under constant-stress partially accelerated life test (CSPALT) model is considered. The Bayesian and E-Bayesian estimation methods, as well as the maximum likelihood estimation method, are discussed for the parameter of the distribution and the acceleration factor. The E-Bayesian and Bayesian estimates are derived by using the squared error loss (SEL) and the LINEX loss functions. The MCMC method is applied for deriving the Bayesian and then E-Bayesian estimates. Moreover, a real data set is given for the illustrative purpose. After all, an evaluation is performed for the results of the proposed methods. [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]

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods. [ABSTRACT FROM AUTHOR]