• Journal of the Korean Data and Information Science Society
• /
• v.15 no.4
• /
• pp.965-971
• /
• 2004

In this paper we consider several nonparametric estimators for the mean residual life by using the partial moment approximation under the proportional hazard model. Also we compare the magnitude of mean square error of the proposed nonparametric estimators for mean residual life under the proportional hazard model.

• Journal of Korean Society for Quality Management
• /
• v.22 no.3
• /
• pp.111-118
• /
• 1994

In this paper we propose a parametric and a nonparametric small sample estimators for the mean residual life (MRL) under the random censorship model using the partial moment approximation. We also compare the proposed nonparametric estimator with the well-known nonparametric MRL estimator based on Kaplan-Meier estimator of the survival function, and present the efficiency of the nonparametric method relative to the Weibull model for small samples.

• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.467-484
• /
• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• Structural Engineering and Mechanics
• /
• v.56 no.4
• /
• pp.549-567
• /
• 2015

A first-order moment method (FORM) reliability analysis is commonly used for structural stability analysis. It requires the values and partial derivatives of the performance to function with respect to the random variables for the design. These calculations can be cumbersome when the performance functions are implicit. A Gaussian process (GP)-based response surface is adopted in this study to approximate the limit state function. By using a trained GP model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis with a FORM, thereby reducing the number of stability analysis calculations. This dynamic renewed knowledge source can provide great assistance in improving the predictive capacity of GP during the iterative process, particularly from the view of machine learning. An iterative algorithm is therefore proposed to improve the precision of GP approximation around the design point by constantly adding new design points to the initial training set. Examples are provided to illustrate the GP-based response surface for both structural and non-structural reliability analyses. The results show that the proposed approach is applicable to structural reliability analyses that involve implicit performance functions and structural response evaluations that entail time-consuming finite element analyses.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.6
• /
• pp.1997-2003
• /
• 2010

Mean Residual Life (MRL) function plays a very important role in the area of engineering, medical science, survival studies, social sciences, and many other fields. Specially, in the reliability study of technical systems, the MRL estimation of a component is very important because the sudden stop of a system brings a serious problem. So, many simulation studies of MRL estimation have been done considering various situation variables. In this paper, four estimators of MRL are proposed under random censoring and their performances re compared through bias and Mean Square Error (MSE) by Monte Carlo simulation.

• Structural Engineering and Mechanics
• /
• v.17 no.1
• /
• pp.1-14
• /
• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.