Statistical analysis of the /() system with dependent competing failure components influenced by Gumbel-Hougarrd Copula and progressively hybrid censored data.

Consider a system, in which the system components are composed of multiple dependent failure mechanisms, and the dependence between the mechanisms is connected by the Gumbel-Hougarrd (GH) Copula. This paper presents a progressively hybrid censored test based on the system. Based on the censored test, the IFM(Marginal inference) method is used to estimate the model parameters and system reliability.

Reliability analysis of inverse Gaussian processes with two-stage degenerate paths.

For randomly degraded products undergoing a two-stage degradation process, traditional random effects models assume that the degradation rate follows a symmetrically normal distribution. However, certain products exhibit asymmetric degradation rates. In light of this, this paper proposes an approach for reliability analysis based on the inverse Gaussian (IG) degeneration process, which considers both asymmetric random effects and the two-stage nature simultaneously.

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment.

The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method.

E-Bayesian and H-Bayesian Inferences for a Simple Step-Stress Model with Competing Failure Model under Progressively Type-II Censoring.

In this paper, we discuss the statistical analysis of a simple step-stress accelerated competing failure model under progressively Type-II censoring. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows exponential distribution. The distribution functions under different stress levels are connected through the cumulative exposure model.

Multicomponent Stress-Strength Model Based on Generalized Progressive Hybrid Censoring Scheme: A Statistical Analysis.

The statistical inference of the reliability and parameters of the stress-strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress-strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton-Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI).

A new exponential ratio-type estimator with linear combination of two auxiliary variables.

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al.

Random search algorithm for solving the nonlinear Fredholm integral equations of the second kind.

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by considering some conditions on the kernel of the integral equation. And then we convert the problem to an optimal control problem by introducing an artificial control function.

A class of ratio estimators of a finite population mean using two auxiliary variables.

In sample surveys, it is usual to increase the efficiency of the estimators by the use of the auxiliary information. We propose a class of ratio estimators of a finite population mean using two auxiliary variables and obtain mean square error (MSE) equations for the class of proposed estimators. We find theoretical conditions that make proposed family estimators more efficient than the traditional ratio estimator and the estimators proposed by Abu-Dayeh et al.