Search Results (41)

In this paper, a statistical model with three parameters is proposed which is called New Modified Generalized Inverted Exponential Distribution (MGIE). In addition, several statistical characteristics of the MGIE distribution are obtained, including quantile function, median, moments, mode, mean deviation, harmonic mean, reliability, hazard and odds functions and Rényi entropy. Moreover, the estimators of parameters are found using the maximum likelihood estimation method. A simulation study using the Monte Carlo method is performed to assess the behavior of the parameters. Finally, three real data sets are applied to demonstrate the importance of the proposed distribution. Full article

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to ${\mathbb{DC}}_n$, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

This study introduces an innovative analytical solution to the time-fractional Cattaneo heat conduction equation, which models photothermal transport in metallic thin films subjected to short laser pulse irradiation. The model integrates the Caputo fractional derivative of order 0 < p ≤ 1, addressing non-Fourier heat conduction characterized by finite wave speed and memory effects. The equation is nondimensionalized through suitable scaling, incorporating essential elements such as a newly specified laser absorption coefficient and uniform initial and boundary conditions. A hybrid approach utilizing the finite Fourier cosine transform (FFCT) in spatial dimensions and the Laplace transform in temporal dimensions produces a closed-form solution, which is analytically inverted using the two-parameter Mittag–Leffler function. This function inherently emerges from fractional-order systems and generalizes traditional exponential relaxation, providing enhanced understanding of anomalous thermal dynamics. The resultant temperature distribution reflects the spatiotemporal progression of heat from a spatially Gaussian and temporally pulsed laser source. Parametric research indicates that elevating the fractional order and relaxation time amplifies temporal damping and diminishes thermal wave velocity. Dynamic profiles demonstrate the responsiveness of heat transfer to thermal and optical variables. The innovation resides in the meticulous analytical formulation utilizing a realistic laser source, the clear significance of the absorption parameter that enhances the temperature amplitude, the incorporation of the Mittag–Leffler function, and a comprehensive investigation of fractional photothermal effects in metallic nano-systems. This method offers a comprehensive framework for examining intricate thermal dynamics that exceed experimental capabilities, pertinent to ultrafast laser processing and nanoscale heat transfer. Full article

In recent years, the study of model predictive control (MPC) in power electronics has gained significant attention due to its ability to optimize system performance and improve the dynamic control of complex power converters. There are two types of MPC: finite control set (FCS) and continuous control set (CCS). The FCS–MPC has been studied more in regard to these two types of control due to its easy and intuitive implementation. However, FCS–MPC has some drawbacks, such as the exponential growth of the computational burden as the prediction horizon increases and, in some cases, a variable frequency. In contrast, generalized predictive control (GPC), part of CCS–MPC, offers significant advantages. It enables the use of a longer prediction horizon without increasing the computational burden in regard to its implementation, which has practical implications for the efficiency and performance of power converters. This paper presents the design of GPC applied to single-phase multilevel voltage source inverters, highlighting its advantages over FCS–MPC. The controller is optimized offline, significantly reducing the computational cost of implementation. Moreover, the controller is tested in regard to R, RL, and nonlinear loads. Finally, the validation results using a medium-performance controller and a Hardware-in-the-Loop device highlight the improved behavior of the proposed GPC, maintaining a harmonic distortion of less than 1.2% for R and RL loads. Full article

After nearly two decades of development, transient electromagnetic (TEM) 3D forward modeling technology has significantly improved both numerical precision and computational efficiency, primarily through advancements in mesh generation and the optimization of linear equation solvers. However, the dominant approach still relies on direct solvers, which require substantial memory and complicate the modeling of electromagnetic responses in large-scale models. This paper proposes a new method for solving large-scale TEM responses, building on previous studies. The TEM response is expressed as a matrix exponential function with an analytic initial field for a step-off source, which can be efficiently solved using the Shift-and-Invert Krylov (SAI-Krylov) subspace method. The Arnoldi algorithm is used to construct the orthogonal basis for the Krylov subspace, and the preconditioned conjugate gradient (PCG) method is applied to solve large-scale linear equations. The paper further explores how dividing the off-time and optimizing parameters for each time interval can enhance computational efficiency. The numerical results show that this parameter optimization strategy reduces the iteration count of the PCG method, improving efficiency by a factor of 5 compared to conventional iterative methods. Additionally, the proposed method outperforms direct solvers for large-scale model calculations. Conventional approaches require numerous matrix factorizations and thousands of back-substitutions, whereas the proposed method only solves about 300 linear equations. The accuracy of the approach is validated using 1D and 3D models, and the propagation characteristics of the TEM field are studied in large-scale models. Full article

In this paper, inference under dependent competing risk data is considered with multiple causes of failure. We discuss both classical and Bayesian methods for estimating model parameters under the assumption that data are observed under generalized progressive hybrid censoring. The maximum likelihood estimators of model parameters are obtained when occurrences of latent failure follow a bivariate inverted exponentiated Pareto distribution. The associated existence and uniqueness properties of these estimators are established. The asymptotic interval estimators are also constructed. Further, Bayes estimates and highest posterior density intervals are derived using flexible priors. A Monte Carlo sampling algorithm is proposed for posterior computations. The performance of all proposed methods is evaluated through extensive simulations. Moreover, a real-life example is also presented to illustrate the practical applications of our inferential procedures. Full article

The inevitability of faults arises due to prolonged exposure of photovoltaic (PV) power plants to intricate environmental conditions. Therefore, fault diagnosis of PV power plants is crucial to ensure the continuity and reliability of power generation. This paper proposes a fault diagnosis method that integrates PV power prediction and an exponentially weighted moving average (EWMA) control chart. This method predicts the PV power based on meteorological factors using the adaptive particle swarm algorithm-back propagation neural network (APSO-BPNN) model and takes its error from the actual value as a control quantity for the EWMA control chart. The EWMA control chart then monitors the error values to identify fault types. Finally, it is verified by comparison with the discrete rate (DR) analysis method. The results showed that the coefficient of determination of the prediction model of the proposed method reached 0.98. Although the DR analysis can evaluate the overall performance of the inverter and identify the faults, it often fails to point out the specific location of the faults accurately. In contrast, the EWMA control chart can monitor abnormal states such as open and short circuits and accurately locate the string where the fault occurs. Full article

To ensure the efficient functioning of solar energy generation systems, it is crucial to have dependable designs and regular maintenance. However, when these systems or their components operate at multiple working levels, optimizing reliability becomes a complex task for models and analyses. In the context of reliability modeling in solar energy generation systems, researchers often assume that random variables follow an exponential distribution (binary-state representation) as a simplification, although this may not always hold true for real-world engineering systems. In the present paper, a multi-state solar energy generating system with inverters in series configuration is investigated, in which unreliable by-pass changeover switches, common cause failures (CCFs), and multiple repairman vacations are also considered. Furthermore, the arrivals of CCFs and the repair processes of the failed system due to CCFs are governed by different Markovian arrival processes (MAPs), and the lifetimes and repair times of inverters and by-pass changeover switches and the repairman vacation time in the system have different phase-type (PH) distributions. Therefore, the behavior of the system is represented using a Markov process methodology, and reliability measures for the proposed system are derived utilizing aggregated stochastic process theory. Finally, a numerical example and a comparison analysis are presented to demonstrate the findings. Full article

This article discusses different methods for estimating the shape and scale parameters of the generalized inverted exponential distribution (GIED) and the acceleration factor in constant stress partially accelerated life test (CSPALT) with general progressively Type-II censored samples. We obtain the maximum likelihood estimates for the three parameters and calculate correlated approximate confidence intervals. Bayesian point estimates and credible intervals are also determined using the importance sampling method. Monte-Carlo simulation studies are conducted to demonstrate and compare the effectiveness of the proposed parameter estimation techniques. Additionally, a real-life dataset is examined to highlight the practical utility of these methodologies. Our findings indicate that the GIED provides an appropriate and flexible model for the real lifetime data, and the Bayesian approach offers better estimation than classical methods under most scenarios, in terms of using generally progressively Type-II censored samples under CSPALT. Full article

A new Type-II generalized progressively hybrid censoring strategy, in which the experiment is ensured to stop at a specified time, is explored when the lifetime model of the test subjects follows a two-parameter alpha-power inverted exponential (Alpha-PIE) distribution. Alpha-PIE’s parameters and reliability indices, such as reliability and hazard rate functions, are estimated via maximum likelihood and Bayes estimation methodologies in the presence of the proposed censored data. The estimated confidence intervals of the unknown quantities are created using the normal approximation of the acquired classical estimators. The Bayesian estimators are also produced using independent gamma density priors under symmetrical (squared-error) loss. The Bayes’ estimators and their associated highest posterior density intervals cannot be calculated theoretically since the joint likelihood function is derived in a complicated form, but they can potentially be assessed using Monte Carlo Markov-chain algorithms. We next go through four optimality criteria for identifying the best progressive design. The effectiveness of the suggested estimation procedures is assessed using Monte Carlo comparisons, and certain recommendations are offered. Ultimately, two different applications, one focused on the failure times of electronic tubes and the other on vinyl chloride, are analyzed to illustrate the effectiveness of the proposed techniques that may be employed in real-world scenarios. Full article

Generalized progressively Type-II hybrid strategy has been suggested to save both the duration and cost of a life test when the experimenter aims to score a fixed number of failed units. In this paper, using this mechanism, the maximum likelihood and Bayes inferential problems for unknown model parameters, in addition to both reliability, and hazard functions of the inverted exponentiated Rayleigh model, are acquired. Applying the observed Fisher data and delta method, the normality characteristic of the classical estimates is taken into account to derive confidence intervals for unknown parameters and several indice functions. In Bayes’ viewpoint, through independent gamma priors against both symmetrical and asymmetrical loss functions, the Bayes estimators of the unknown quantities are developed. Because the Bayes estimators are acquired in complicated forms, a hybrid Monte-Carlo Markov-chain technique is offered to carry out the Bayes estimates as well as to create the related highest posterior density interval estimates. The precise behavior of the suggested estimation approaches is assessed using wide Monte Carlo simulation experiments. Two actual applications based on actual data sets from the mechanical and chemical domains are examined to show how the offered methodologies may be used in real current events. Full article

Microgrid systems may employ various combinations of system designs to connect generating units, and the number of different system designs increases exponentially upon adding different brands of inverters to a system. Each of the different microgrid system designs must be set up in a way that it works in balance. An example of an unbalanced microgrid system is given in this paper, with the main issue being the non-predictive excess power, which causes a frequency rise and faulty conditions in the microgrid system. There are many simple options for controlling excess power in a microgrid system; however, none of these options solve the issue permanently while ensuring excess power control without affecting the system’s accumulated energy—the battery state-of-charge (SOC) level. Therefore, there is a need to create a variable average power load (VAPL) device to utilize the excess power at a rate it is changing to avoid a reduction in accumulated energy. The main goal of this study is to review average power control methods for the VAPL device and provide guidance to researchers in selecting the most suitable method for controlling excess power. A key finding of the paper is a suggested optimal average power control method ensuring that the VAPL device is versatile to implement, economically attractive, and not harmful to other devices in a microgrid system. Full article

This paper deals with the statistical inference of the unknown parameter and some life parameters of inverse Lindley distribution under the assumption that the data are adaptive Type-II progressively censored. The maximum likelihood method is considered to acquire the point and interval estimates of the distribution parameter, reliability, and hazard rate functions. The approximate confidence intervals are also addressed. The delta method is taken into consideration to approximate the variances of the estimators of the reliability and hazard rate functions to get the required intervals. Based on the assumption of gamma prior, we further consider Bayesian estimation of the different parameters. The Bayes estimates are obtained by considering squared error and general entropy loss functions. The Bayes estimates and highest posterior density credible intervals are obtained by employing the Markov chain Monte Carlo procedure. An exhaustive numerical study is conducted to compare the offered estimates with regard to their root means squared error, relative absolute biases, confidence lengths, and coverage probabilities. To explain the suggested methods, two applications are investigated. The numerical findings show that the Bayes estimates perform better than those obtained based on the maximum likelihood method. The Bayesian estimations using the asymmetric loss function give more efficient estimates than the symmetric loss. Finally, the inverse Lindley distribution is recommended to be used as a suitable model to fit airborne communication transceiver and wooden toys data sets when compared with some competitive models including inverse Weibull, inverse gamma and alpha power inverted exponential. Full article

It is generally assumed that the larger the bottle volume, the longer the duration of phytoplankton microcosm experiments. We hypothesize that volume and duration are independent, as volume does not regulate the extension of the exponential growth phase. We conducted two microcosm experiments using 1, 2, and 8 L bottles, inoculated with phytoplankton collected in the Ria Formosa lagoon (SE Portugal) and incubated for 1, 2, 4, and 8 days. Phytoplankton net growth rates were estimated using chlorophyll a concentration and cell abundance, determined with epifluorescence and inverted microscopy. Results show that the experimental duration significantly affected net growth rates, independently of volume, with decreasing net growth rates with time. Regarding volume, we found significant, but weak, differences in net growth rates, and significant two-way interactions only for the larger-sized cells. No significant differences in net growth rates across the different volumes were detected for the smaller, most abundant taxa and for the whole assemblage. We conclude that duration, not volume, is the main factor to consider in microcosm experiments, and it should allow the measurement of responses during the exponential growth phase, which can be detected through daily sampling throughout the duration of the experiment. Full article

This article considers a new improved balanced joint progressive type-II censoring scheme based on two different populations, where the lifetime distributions of two populations follow the generalized inverted exponential distribution with different shape parameters but a common scale parameter. The maximum likelihood estimates of all unknown parameters are obtained and their asymptotic confidence intervals are constructed by the observed Fisher information matrix. Furthermore, the existence and uniqueness of solutions are proved. In the Bayesian framework, the common scale parameter follows an independent Gamma prior and the different shape parameters jointly follow a Beta-Gamma prior. Based on whether the order restriction is imposed on the shape parameters, the Bayesian estimates of all parameters concerning the squared error loss function along with the associated highest posterior density credible intervals are derived by using the importance sampling technique. Then, we use Monte Carlo simulations to study the performance of the various estimators and a real dataset is discussed to illustrate all of the estimation techniques. Finally, we seek an optimum censoring scheme through different optimality criteria. Full article