Salma Abdulhafiz Almutlak

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Research Title :Modified Class of Estimators Using Ranked Set Sampling

Authors :Bhushan, Shashi, Anoop Kumar, Sana Shahab, Showkat Ahmad Lone, and Salemah A. Almutlak.

Abstract :The present article discusses the issue of population mean estimation in the ranked set sampling framework. A modified class of estimators is proffered and compared in the aspect of its efficacious performance with all salient conventional estimators existing to date. Some well-known existing estimators under 𝑅𝑆𝑆 are recognized as the members of the proffered estimators for appropriately chosen characterizing scalars. The ascendancy of the proposed class of estimators regarding the conventional estimators has been shown through an extensive computational study utilizing some natural and artificially generated populations.

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Research Title :Exact solutions of Euler–Bernoulli beams

Authors : Jamil Abbas Haider, F. D. Zaman, Showkat Ahmad Lone, Sadia Anwar, Salmeh A. Almutlak, and Ibrahim E. Elseesy

Abstract :ABSTRACT In numerous real-world applications, transverse vibrations of beams are nonlinear in nature. It is a task to solve nonlinear beam systems due to their substantial dependence on the 4 variables of the system and the boundary conditions. To comprehend the nonlinear vibration characteristics, it is essential to do a precise parametric analysis. This research demonstrates an approximation solution for odd and even nonlinear transverse vibrating beams using the Laplace-based variation iteration method, and the formulation of the beams depends on the Galerkin approximation. For the solution of the nonlinear differential equation, this method is efficient as compared to the existing methods in the literature because the solutions exactly match with the numerical solutions. The Laplace-based variation iteration method has been used for the first time to obtain the solution to this important problem. To demonstrate the applicability and precision of the Laplace-based iteration method, several initial conditions are applied to the governing equation for nonlinearly vibrating transverse beams. The natural frequencies and periodic response curves are computed using Laplace-based VIM and compared with the Runge–Kutta RK4 method. In contrast to the RK4, the results demonstrate that the proposed method yields excellent consensus. The Lagrange multiplier is widely regarded as one of the most essential concepts in variational theory. The result obtained are displayed in the table form.

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Research Title :Weighted power Maxwell distribution: Statistical inference and COVID-19 applications

Authors : Almuqrin MA, Almutlak SA, Gemeay AM, Almetwally EM, Karakaya K, Makumi N, et al.

Abstract :During the course of this research, we came up with a brand new distribution that is superior; we then presented and analysed the mathematical properties of this distribution; finally, we assessed its fuzzy reliability function. Because the novel distribution provides a number of advantages, like the reality that its cumulative distribution function and probability density function both have a closed form, it is very useful in a wide range of disciplines that are related to data science. One of these fields is machine learning, which is a sub field of data science. We used both traditional methods and Bayesian methodologies in order to generate a large number of different estimates. A test setup might have been carried out to assess the effectiveness of both the classical and the Bayesian estimators. At last, three different sets of Covid-19 death analysis were done so that the effectiveness of the new model could be demonstrated.

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Research Title :Efficient class of ratio cum median estimators for estimating the population median.

Authors : Mir Subzar,Showkat Ahmad Lone ,Emmanuel J. Ekpenyong,Abdul Salam,Muhammad Aslam,T. A. Raja,Salmeh A. Almutlak et al.

Abstract :In estimation theory, the use of auxiliary information significantly improves precision while estimating population parameters. In this paper, an efficient class of ratio cum median estimators of the population median is suggested using simple random sampling without replacement. The expressions for bias and mean square error of the proposed class are derived theoretically. The condition for the asymptotic optimum estimator is obtained with its bias and mean square error expressions. Under certain realistic conditions, the asymptotic optimum estimator is more proficient, based on analytical and numerical comparisons with some existing estimators that are members of the suggested class of estimators. The superiority of the proposed ratio cum median estimators is shown through real data applications. Such a new proposed estimator will be useful in the future for data analysis and making decisions.

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Research Title : Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

Authors :Sadia Anwar, Showkat Ahmad Lone, Aysha Khan, Salmeh Almutlak.

Abstract : we studied the estimation of a stress-strength reliability model (R=P(X>Y)) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes.

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Research Title :Application of Laplace-based variational iteration method to analyze generalized nonlinear oscillations in physical systems

Authors :authors Muhammad Naveed Khan, Jamil Abbas Haider, Zhentao Wang, Showkat Ahmad Lone, Salmeh A. Almutlak, and Ibrahim E. Elseesy.

Abstract :In this paper, the variational iterative method (VIM) with the Laplace transform is utilized to solve the nonlinear problems of a simple pendulum and mass spring oscillator, which corresponds to the Duffing equation. Finding the Lagrange multiplier (LM) is a significant phase in the VIM, and variational theory is frequently employed for this purpose. This paper demonstrates how the Laplace transform can be utilized to locate the LM in a more efficient manner. The frequency obtained by Laplace-based VIM is the same as that defined in the already existing methods in the literature in order to ensure the clarity of the results. Numerous analytical techniques can be used to solve the Duffing equation, but we are the first to do it using a Laplace-based VIM and a distinctive LM. The fundamental results of my paper are that LM is also the same in the Elzaki transformation. In the vast majority of instances, Laplace-based VIM only requires one iteration to arrive at an answer with high precision and linearization, discretization or intensive computational work is required for this purpose. Comparing analytical results of VIM by Laplace transform to the built-in Simulink command in MATLAB which gives us the surety about the method’s applicability for solving nonlinear problems. Future work on the basic pendulum may examine the effects of nonlinearities and damping on its motion and the application of advanced control mechanisms to regulate its behavior. Future research on mass spring oscillators could examine the system’s response to random or harmonic input. The mass spring oscillator could also be used in vibration isolation to minimize vibrations from one building to another.

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Research Title :Stochastically analysis by using fixed point approach of pendulum with rolling wheel via translational and rotational motion

Authors : Jamil Abbas Haider, Farhan Saeed, Showkat Ahmad Lone, Salmeh A Almutlak, and Mohamed Abdelghany Elkot

Abstract :This paper presents an analytical solution for a complex mechanical system consisting of a pendulum with a rolling wheel, which combines translational and rotational motion. The system’s dynamics are described by a set of coupled differential equations that are challenging to solve analytically using traditional methods. To overcome this challenge, the variation iteration method (VIM) is employed to derive an analytical solution. VIM is a powerful technique that allows for the approximate solution of differential equations by constructing a series solution iteratively. The Lagrange multiplier, a crucial component in the solution process, is determined for the first time using the Elzaki transformation. Interestingly, the Lagrange multiplier obtained through the Elzaki transformation matches the result obtained from Laplace transformation, which is a fundamental finding of this paper. Also we compared its results with the by employing the VIM and the derived Lagrange multiplier, a comprehensive analytical solution for the complex pendulum with a rolling wheel system is obtained. The solution provides insights into the system’s behavior, such as the oscillation amplitudes, angular velocities and other relevant dynamic parameters. The proposed approach demonstrates the efficacy of the VIM in tackling complex mechanical systems and showcases the equivalence between the Lagrange multiplier derived through Elzaki transformation and the well-established Laplace transformation. The results obtained from this study contribute to the understanding and analysis of coupled translational and rotational systems, providing a valuable tool for researchers and engineers working in the field of mechanical dynamics. Sketches are made of the phase portraits close to the equilibrium points.

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Research Title :Designing an efficient adaptive EWMA model for normal process with engineering applications

Authors : Zahid Rasheed , Majid Khanc , Syed Masroor Anwar , Muhammad Usman Aslam , Showkat Ahmad Lone , Salmeh A. Almutlak (June 2024)

Abstract :Stability in process parameters is required to ensure the quality of the finished item. Control charts, as one of the critical parts of statistical process monitoring (SPM), have seen widespread use across many disciplines for detecting and responding to shifts in process parameters. The adaptive EWMA (AEWMA) control chart is a well-known scheme that detects both small and large process shifts by integrating the features of the Shewhart and classical EWMA charts. In this study, we propose an enhanced AEWMA chart, termed the EAEWMA chart, that efficiently monitors small and large process mean shifts simultaneously. The proposed EAEWMA chart enhances the existing AEWMA chart using the shift estimator, based on the hybrid EWMA (HEWMA) statistic. The Monte Carlo simulation approach is employed as the computational method to obtain the numerical findings for the various performance metrics. The EAEWMA chart is compared with various existing charts, including AEWMA, HEWMA, EWMA, ACSUM, and IACCUSUM, in zero- and steady-state scenarios. Conclusively, two practical applications of the EAEWMA chart are presented, demonstrating its value for practitioners and engineers, and illustrating its efficacy in real-world scenarios.