Analysis of incorporating modified Weibull model fault detection rate function into software reliability modeling.

When software systems are introduced, they are typically deployed in field environments similar to those used during development and testing. However, these systems may also be used in various other locations with different environmental conditions, making it challenging to improve software reliability. Factors such as the specific operating environment and the location of bugs in the code contribute to this difficulty. In this paper, we propose a new software reliability model that accounts for the uncertainty of operating environments. We present the explicit closed-form mean value function solution for the proposed model. The model's goodness of fit is demonstrated by comparing it to the nonhomogeneous Poisson process (NHPP) model based on Weibull model, using four sets of failure data sets from software applications. The proposed model performs well under various estimation techniques, making it a versatile tool for practitioners and researchers alike. The proposed model outperforms other existing NHPP Weibull based in terms of fitting accuracy under two different methods of estimation and provides a more detailed and precise evaluation of software reliability. Additionally, sensitivity analysis shows that the parameters of the suggested distribution significantly impact the mean value function.

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling.

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference.

Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.

A novel extended model with versatile shaped failure rate: Statistical inference with Covid -19 applications.

Statistical models perform an essential role in data analysis, and statisticians are constantly looking for novel or pretty recent statistical models to fit data sets across a broad variety of fields. In this study, we used modified Kies generalized transformation and the new power function to suggest an unique statistical model. We present and discuss a linear illustration of the density function. Theoretically, quantile function, characteristic function, stochastic ordering, mean, and moments are just a few of the structure properties we discuss. By defining an ideal statistical distribution for assessing the COVID-19 mortality rate, an attempt is performed to determine the model of COVID-19 spread in different nations like the United Kingdom and Italy. In some countries, the novel distribution have been shown to be more appropriate than existing competing models when fitted to COVID-19.

A new modified Kies Fréchet distribution: Applications of mortality rate of Covid-19.

The purpose of this paper is to identify an effective statistical distribution for examining COVID-19 mortality rates in Canada and Netherlands in order to model the distribution of COVID-19. The modified Kies Frechet (MKIF) model is an advanced three parameter lifetime distribution that was developed by incorporating the Frechet and modified Kies families. In particular with respect to current distributions, the latest one has very versatile probability functions: increasing, decreasing, and inverted U shapes are observed for the hazard rate functions, indicating that the capability of adaptability of the model. A straight forward linear representation of PDF, moment generating functions, Probability weighted moments and hazard rate functions are among the enticing features of this novel distribution. We used three different estimation methodologies to estimate the pertinent parameters of MKIF model like least squares estimators (LSEs), maximum likelihood estimators (MLEs) and weighted least squares estimators (WLSEs). The efficiency of these estimators is assessed using a thorough Monte Carlo simulation analysis. We evaluated the newest model for a variety of data sets to examine how effectively it handled data modeling. The real implementation demonstrates that the proposed model outperforms competing models and can be selected as a superior model for developing a statistical model for COVID-19 data and other similar data sets.

Estimation of unsteady hydromagnetic Williamson fluid flow in a radiative surface through numerical and artificial neural network modeling.

In current investigation, a novel implementation of intelligent numerical computing solver based on multi-layer perceptron (MLP) feed-forward back-propagation artificial neural networks (ANN) with the Levenberg-Marquard algorithm is provided to interpret heat generation/absorption and radiation phenomenon in unsteady electrically conducting Williamson liquid flow along porous stretching surface. Heat phenomenon is investigated by taking convective boundary condition along with both velocity and thermal slip phenomena. The original nonlinear coupled PDEs representing the fluidic model are transformed to an analogous nonlinear ODEs system via incorporating appropriate transformations. A data set for proposed MLP-ANN is generated for various scenarios of fluidic model by variation of involved pertinent parameters via Galerkin weighted residual method (GWRM). In order to predict the (MLP) values, a multi-layer perceptron (MLP) artificial neural network (ANN) has been developed. There are 10 neurons in hidden layer of feed forward (FF) back propagation (BP) network model. The predictive performance of ANN model has been analyzed by comparing the results obtained from the ANN model using Levenberg-Marquard algorithm as the training algorithm with the target values. When the obtained Mean Square Error (MSE), Coefficient of Determination (R) and error rate values have been analyzed, it has been concluded that the ANN model can predict SFC and NN values with high accuracy. According to the findings of current analysis, ANN approach is accurate, effective and conveniently applicable for simulating the slip flow of Williamson fluid towards the stretching plate with heat generation/absorption. The obtained results showed that ANNs are an ideal tool that can be used to predict Skin Friction Coefficients and Nusselt Number values.

Statistical modeling for bioconvective tangent hyperbolic nanofluid towards stretching surface with zero mass flux condition.

This article presents the implementation of a numerical solution of bioconvective nanofluid flow. The boundary layer flow (BLF) towards a vertical exponentially stretching plate with combination of heat and mass transfer rate in tangent hyperbolic nanofluid containing microorganisms. We have introduced zero mass flux condition to achieve physically realistic outcomes. Analysis is conducted with magnetic field phenomenon. By using similarity variables, the partial differential equation which governs the said model was converted into a nonlinear ordinary differential equation, and numerical results are achieved by applying the shooting technique. The paper describes and addresses all numerical outcomes, such as for the Skin friction coefficients (SFC), local density of motile microorganisams (LDMM) and the local number Nusselt (LNN). Furthermore, the effects of the buoyancy force number, bioconvection Lewis parameter, bioconvection Rayleigh number, bioconvection Pecelt parameter, thermophoresis and Brownian motion are discussed. The outcomes of the study ensure that the stretched surface has a unique solution: as Nr (Lb) and Rb (Pe) increase, the drag force (mass transfer rate) increases respectively. Furthermore, for least values of Nb and all the values of Nt under consideration the rate of heat transfer upsurges. The data of SFC, LNN, and LDMM have been tested utilizing various statistical models, and it is noted that data sets for SFC and LDMM fit the Weibull model for different values of Nr and Lb respectively. On the other hand, Frechet distribution fits well for LNN data set for various values of Nt.

A sensitivity study on carbon nanotubes significance in Darcy-Forchheimer flow towards a rotating disk by response surface methodology.

The current research explores incremental effect of thermal radiation on heat transfer improvement corresponds to Darcy-Forchheimer (DF) flow of carbon nanotubes along a stretched rotating surface using RSM. Casson carbon nanotubes' constructed model in boundary layer flow is being investigated with implications of both single-walled CNTs and multi-walled CNTs. Water and Ethylene glycol are considered a basic fluid. The heat transfer rate is scrutinized via convective condition. Outcomes are observed and evaluated for both SWCNTs and MWCNTs. The Runge-Kutta Fehlberg technique of shooting is utilized to numerically solve transformed nonlinear ordinary differential system. The output parameters of interest are presumed to depend on governing input variables. In addition, sensitivity study is incorporated. It is noted that sensitivity of SFC via SWCNT-Water becomes higher by increasing values of permeability number. Additionaly, sensitivity of SFC via SWCNT-water towards the permeability number is higher than the solid volume fraction for medium and higher permeability levels. It is also noted that sensitivity of SFC (SWCNT-Ethylene-glycol) towards volume fraction is higher for increasing permeability as well as inertia coefficient. Additionally, the sensitivity of LNN towards the Solid volume fraction is higher than the radiation and Biot number for all levels of Biot number. The findings will provide initial direction for future device manufacturing.

On the analysis of number of deaths due to Covid -19 outbreak data using a new class of distributions.

In this article, we develop a generator to suggest a generalization of the Gumbel type-II model known as generalized log-exponential transformation of Gumbel Type-II (GLET-GTII), which extends a more flexible model for modeling life data. Owing to basic transformation containing an extra parameter, every existing lifetime model can be made more flexible with suggested development. Some specific statistical attributes of the GLET-GTII are investigated, such as quantiles, uncertainty measures, survival function, moments, reliability, and hazard function etc. We describe two methods of parametric estimations of GLET-GTII discussed by using maximum likelihood estimators and Bayesian paradigm. The Monte Carlo simulation analysis shows that estimators are consistent. Two real life implementations are performed to scrutinize the suitability of our current strategy. These real life data is related to Infectious diseases (COVID-19). These applications identify that by using the current approach, our proposed model outperforms than other well known existing models available in the literature.