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In recent years, several novel modeling applications have been able to better fit complex datasets, and they can provide insights that would not be possible with traditional distributions. A new model developed by mixing the exponential and gamma models, called the Garima model, is discussed in this article. This model exhibits a better behavior fit than exponential and Lindley, among others. When the reliability practitioner wishes to score a specific number of failed units, a generalized progressive-hybrid-censored Type-II technique has been proposed to reduce both the length and expense of a life test. Given the availability of the presented data, the difficulty of estimating the scale parameter and various reliability time aspects of the Garima model is investigated using likelihood and Bayes inferential approaches. In addition, when the Garima parameter is assumed to have gamma density prior, the Markovian-Chain via Monte-Carlo sampler from a symmetric loss is performed to obtain the symmetric Bayes' infer. Besides the asymptotic confidence intervals, the highest intervals for all unknown subjects are also developed. Simulation comparisons are also carried out, and useful recommendations are provided. A real data application is examined based on genuine datasets from the physical sector to see how the examined approaches may be implemented in real-life situations. [ABSTRACT FROM AUTHOR]

Let K + (μ i) = { Q s i μ i , s i ∈ (m 0 μ i , m + μ i) } , i = 1 , 2 , be two CSK families generated by the nondegenerate probability measures μ 1 and μ 2 with support bounded from above. Define the set of measures L = K + (μ 1) • K + (μ 2) = { Q s 1 μ 1 • Q s 2 μ 2 , s 1 ∈ (m 0 μ 1 , m + μ 1) and s 2 ∈ (m 0 μ 2 , m + μ 2) } , where Q s 1 μ 1 • Q s 2 μ 2 denotes the Fermi convolution of Q s 1 μ 1 and Q s 2 μ 2 . We prove that if L is still a CSK family (that is, L = K + (σ) for some nondegenerate probability measure () σ), then the probability measures σ , μ 1 and μ 2 are of the free Poisson type and follow the free Poisson law up to affinity. The same result, regarding the free Poisson measure, is obtained if we consider the t-deformed free convolution t replacing the Fermi convolution • in the family of measures L. [ABSTRACT FROM AUTHOR]

Nowadays, the increasing demands of smart cities require innovative technologies to optimize resource utilization and minimize costs. This research focuses on the construction sector, specifically the production of advanced high-strength steel. We address practical application problems from the iron and steel factory in Annaba, Algeria, known as fuzzy multi-objective linear programming problems. Two methods are applied: a mathematical model and Artificial Neural Networks (ANNs). Results indicate that the ANN approach offers significant time and effort savings. [ABSTRACT FROM AUTHOR]

This article covers the issue of evaluating the two shape parameters and reliability metrics of a novel Kumaraswamy-exponential lifetime distribution, whose density exhibits a left-skewed, right-skewed, or symmetric shape, through a type-II improved adaptive progressively censored sample. Both conventional and Bayesian viewpoints are used to evaluate the various parameters, which include point and interval estimations. While the estimation of one of the shape parameters requires a numerical solution, the other shape parameter estimation can be carried out in closed form by the classical method. Besides, the likelihood method's asymptotic traits are employed to provide interval estimations for all parameters. Leveraging the Markov chain Monte Carlo process, the symmetric squared loss function and independent gamma priors are taken into account for calculating Bayes points and the highest posterior density interval estimations. To illustrate the accuracy, compare estimation methods, and show the applicability of the various suggested methods, a simulation examination and a pair of applications are looked at. In the end, four accuracy indicators are taken into consideration to figure out the best progressive censoring pattern. The numerical results indicate that when collecting samples using the suggested censored procedure, it is advisable to use the Bayesian estimation approach for evaluating the Kumaraswamy-exponential distribution. [ABSTRACT FROM AUTHOR]