Designing Advanced Reliability Testing Mathematical Model for Modern Products

The modern era is the age of science, technology and at the same time it is the age of competition. The advancement of new technology and increased global competition have emphasized the importance of product strength and reliability estimation. As a result, producers and manufacturers must now verify the strength and reliability of their products prior to releasing them to the market. In the past, reliability data analysis was a critical tool for this purpose. Traditionally, reliability data analysis entails quantifying these life characteristics through the examination of failure data. However, in many situations, obtaining such failure data has been extremely difficult, if not impossible, due to the length of time between designing and releasing a product, and the difficulty of designing a product that will last a long period due to its continuous use and operation. Faced with this challenge, reliability statisticians developed a technique called Accelerated Reliability Testing to rapidly determine the reliability and life characteristics of products. This technique increases product reliability and identifies when and how a product will fail in its intended environment. In the present work, we plan to investigate these mathematical reliability models to determine the costs associated with the various product guarantees. If component lifetimes follow the power-function distribution, the problem is examined under increasing stress using percent failure censoring. The method is referred as a process that applies accelerated testing to estimate the cost of age-replacement for goods sold under warranty. Additionally, a mathematical illustration is presented to illustrate the results

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains

Unification of Adomian decomposition method and ZZ transformation for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems

This paper presents a novel approach for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems by using the unification of the Adomian decomposition method and ZZ transformation. The suggested method combines the Aboodh transform and the Adomian decomposition method, both of which are trustworthy and efficient mathematical tools for solving fractional differential equations (FDEs). This method's theoretical analysis is addressed for nonlinear FDE systems. To find exact solutions to the equations, the method is applied to fractional Kersten-Krasil'shchik linked KdV-mKdV systems. The results show that the suggested method is efficient and practical for solving fractional Kersten-Krasil'shchik linked KdV-mKdV systems and that it may be applied to other nonlinear FDEs. The suggested method has the potential to provide new insights into the behavior of nonlinear waves in fluid and plasma environments, as well as the development of new mathematical tools for modeling and studying complicated wave phenomena

Structure Preserving Splitting Techniques for Ebola Reaction–Diffusion Epidemic System

In this paper, we deal with the numerical solution of the reaction–diffusion Ebola epidemic model. The diffusion which is an important phenomenon for the epidemic model is included in the model. This inclusion has made the model more comprehensive for studying the disease dynamics in the human population. The quantities linked with the model indicate the population sizes which are taken as absolute, therefore, the numerical schemes utilized to solve the underlying Ebola epidemic system should sustain the positivity. The numerical approaches used to solve the underlying epidemic models are explicit nonstandard finite difference operator splitting (ENSFD-OS) and implicit nonstandard finite difference operator splitting (INSFD-OS) techniques. These schemes preserve all the physical features of the state variables, i.e. projected schemes hold the positive solution acquired by the Ebola diffusive epidemic model. The underlying epidemic model illustrates two stable steady states, a virus-free state, and a virus existence state. The suggested approaches retain the stability of each of the steady states possessed by the assumed epidemic model. A numerical example and simulations for validation of all the characteristics of suggested techniques are also investigated

Lacunary sequences related to statistical convergence

<p>In this manuscript, our concern is to introduce the new approach of studying the lacunary almost statistical convergence and strongly almost convergence of the generalized difference sequences of fuzzy numbers. Some interesting and basic properties concerning them will be studied. </p&gt

Some Sequence Spaces of Sigma Means Defined by Orlicz Function

Ganie and Sheikh [12] have recently studied the space V∞(θ) adopting the notion of sigma means and lacunary sequence θ = (kr ). In the present paper, we introduce and explore V∞ (M , θ ) and V∞ (M , p, θ ), where M is an Orlicz function. Some inclusion relations will be defined between the concerned spaces

A Fractional Analysis of Zakharov–Kuznetsov Equations with the Liouville–Caputo Operator

In this study, we used two unique approaches, namely the Yang transform decomposition method (YTDM) and the homotopy perturbation transform method (HPTM), to derive approximate analytical solutions for nonlinear time-fractional Zakharov–Kuznetsov equations (ZKEs). This framework demonstrated the behavior of weakly nonlinear ion-acoustic waves in plasma containing cold ions and hot isothermal electrons in the presence of a uniform magnetic flux. The density fraction and obliqueness of two compressive and rarefactive potentials are depicted. In the Liouville–Caputo sense, the fractional derivative is described. In these procedures, we first used the Yang transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. The results of these methods also made clear the connections between the precise solutions to the issues under study. Illustrations of the reliability of the proposed techniques are provided. The results are clarified through graphs and tables. The reliability of the proposed procedures is demonstrated by illustrative examples. The proposed approaches are attractive, though these easy approaches may be time-consuming for solving diverse nonlinear fractional-order partial differential equations

Computational Analysis of Fractional-Order KdV Systems in the Sense of the Caputo Operator via a Novel Transform

The main features of scientific efforts in physics and engineering are the development of models for various physical issues and the development of solutions. In order to solve the time-fractional coupled Korteweg–De Vries (KdV) equation, we combine the novel Yang transform, the homotopy perturbation approach, and the Adomian decomposition method in the present investigation. KdV models are crucial because they can accurately represent a variety of physical problems, including thin-film flows and waves on shallow water surfaces. The fractional derivative is regarded in the Caputo meaning. These approaches apply straightforward steps through symbolic computation to provide a convergent series solution. Different nonlinear time-fractional KdV systems are used to test the effectiveness of the suggested techniques. The symmetry pattern is a fundamental feature of the KdV equations and the symmetrical aspect of the solution can be seen from the graphical representations. The numerical outcomes demonstrate that only a small number of terms are required to arrive at an approximation that is exact, efficient, and trustworthy. Additionally, the system’s approximative solution is illustrated graphically. The results show that these techniques are extremely effective, practically applicable for usage in such issues, and adaptable to other nonlinear issues

The dynamics of fractional KdV type equations occurring in magneto-acoustic waves through non-singular kernel derivatives

To study magneto-acoustic waves in plasma, we will use a numerical method based on the Natural Transform Decomposition Method (NTDM) to find the approximative solutions of nonlinear fifth-order KdV equations. The method combines the familiar Natural transform (NT) with the standard Adomian decomposition method. The fractional derivatives considered are the Caputo–Fabrizio and the Atangana–Baleanu derivatives in the sense of Caputo derivatives. Adomian polynomials may be employed to tackle nonlinear terms. In this method, the solution is calculated as a convergent series, and it is demonstrated that the NTDM solutions converge to the exact solutions. A range of two- and three-dimensional figures have been used to illustrate the dynamic behavior of the derived solutions. The tables provide a visual representation of numerical data. The physical behavior of the derived solutions about fractional order is further demonstrated by several simulations. When addressing nonlinear wave equations in science and engineering, the NTDM offers a broad range of applications. Several examples are given to highlight the importance of this work and to demonstrate the simplicity and trustworthiness of the method

Quantitative Features Analysis of Water Carrying Nanoparticles of Alumina over a Uniform Surface

Little is known about the rising impacts of Coriolis force and volume fraction of nanoparticles in industrial, mechanical, and biological domains, with an emphasis on water conveying 47 nm nanoparticles of alumina nanoparticles. We explored the impact of the volume fraction and rotation parameter on water conveying 47 nm of alumina nanoparticles across a uniform surface in this study. The Levenberg–Marquardt backpropagated neural network (LMB-NN) architecture was used to examine the transport phenomena of 47 nm conveying nanoparticles. The partial differential equations (PDEs) are converted into a system of Ordinary Differential Equations (ODEs). To assess our soft-computing process, we used the RK4 method to acquire reference solutions. The problem is investigated using two situations, each with three sub-cases for the change of the rotation parameter K and the volume fraction ϕ. Our simulation results are compared to the reference solutions. It has been proven that our technique is superior to the current state-of-the-art. For further explanation, error histograms, regression graphs, and fitness values are graphically displayed