The reliability of software has a tremendous influence on the reliability of systems. Software dependability models are frequently utilized to statistically analyze the reliability of software. Numerous reliability models are based on the nonhomogeneous Poisson method (NHPP). In this respect, in the current study, a novel NHPP model established on the basis of the new power function distribution is suggested. The mathematical formulas for its reliability measurements were found and are visually illustrated. The parameters of the suggested model are assessed utilizing the weighted nonlinear least-squares, maximum-likelihood, and nonlinear least-squares estimation techniques. The model is subsequently verified using a variety of reliability datasets. Four separate criteria were used to assess and compare the estimating techniques. Additionally, the effectiveness of the novel model is assessed and evaluated with two foundation models both objectively and subjectively. The implementation results reveal that our novel model performed well in the failure data that we examined.

This article presents the magnetohydrodynamic (MHD) flow of a nanoliquid due to a rotating sphere at a stagnation point. The flow is considered to be influenced by the magnetic field, dissipative, thermally radiative, and chemically reactive. Also, the thermophoretic and Brownian motion influences are taken into consideration. Some restrictions in the present analysis are taken: like there is no-slip and convective conditions, joule heating, Hall effects and buoyancy-driven. The solution of the present analysis is derived through the homotopy analysis method (HAM). The significance of several physical parameters on velocities, thermal and concentration profiles are shown with the help of Figures. Also, the significance of different physical factors on skin frictions, local Nusselt number and Sherwood number are demonstrated with the help of Tables. The outcomes show that the Nusselt number is lower for the larger Brownian motion parameter, Eckert number, and thermophoretic parameter, while the increment in the thermal radiation parameter augmented the Nusselt number. It is established that the increasing rotation, magnetic and positive constant parameters have increased the velocity profiles along the x-direction while reducing the velocity profiles along the z-direction of the nanoliquid flow. The increasing positive constant parameter reduces the thermal graph of the nanoliquid flow. Furthermore, the intensifying Eckert number, thermophoresis, Brownian motion, and thermal radiation factor have escalated the thermal profiles of the nanoliquid flow.

In this paper, 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.

This research article addresses an efficient separate and combined class of estimators for the population mean estimation based on stratified random sampling (StRS). The first order approximated expressions of bias and mean square error of the proposed separate and combined class of estimators are obtained. A comparative study is conducted to determine the efficiency conditions in which the suggested class of estimators outperforms the contemporary estimators. These efficiency conditions are examined through an extensive simulation study by employing a hypothetically drawn symmetrical and asymmetrical populations. The simulation results have shown that the suggested class of estimators is more effective than the other available estimators. In addition, an application of the proposed methods is also presented by examining a real data set.

The stress-strength reliability (SSRe) model is widely investigated in reliability engineering to determine the probability of the strength component overcomes the stress imposed on it. In this paper, we studied the estimation of SSRe model based on the Burr III distribution under the improved adaptive progressive type-II censoring scheme (IAPrgCS-II). Estimation methods of the SSRe parameters are developed using frequentist and Bayesian approaches. The point and interval estimations using the maximum likelihood are considered to estimate the parameters. Two approximations are applied to compute the Bayes estimates. A simulation study is conducted for the comparison of the methods of estimation. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, the droplet splashing (DrS) data under two wettabilities are proposed as an application of the considered SSRe model and methods. The results show us that the reliability model can be used to amend the quality of coatings.

A control chart is the most well-known statistical monitoring tecnique to address unfavourable process parameter (s) changes. Quality practitioners always desire a charting device that promptly identifies the undesired changes in the process. This study intends to design a sensitive homogeneously weighted moving average chart using two supplementary variables (hereafter, TAHWMA). The two supplementary variables are correlated with the study variable in the form of a regression estimator, which is an efficient and unbiased estimator for the process mean. The suggested TAHWMA charting structure is checked out and compared in terms of appearance and non-appearance of multicollinearity amidst the two additional variables. Average run length-related measures are taken as performance measures. It is observed that the proposed TAHWMA scheme performs effectively when the two supplementary variables have no collinearity. A comprehensive comparison between the proposed TAHWMA and existing charts is also carried out, showing the proposed’s supremacy over existing counterparts. For execution purposes, two illustrative examples, one belonging to carbon fibre manufacturing-related data and the other using a simulated dataset and where our simulated dataset belongs to symmetrical distribution, are also presented for the application of the recommended TAHWMA chart.