• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.395-406
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• 2003

In this thesis, we propose a test statistic for testing exponentiality against NBU alternatives. Our test statistics is based on a linear function of the order statistics and is readily applied in the case of small sample as well as large sample. The exact and asymptotic distribution of the test statistics is derived and asymptotic efficiencies are studied. Our new test is easier to compute and performs better for several alternatives than test of Hollander and Proschan(1972).

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.167-175
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• 2004

A nonparametric procedure is proposed to test the exponentiality against the hypothesis that one life distribution has a greater residual life times than the other life distribution. Such a hypothesis turns out to be equivalent to the one that one failure rate is greater than the other and so the proposed test works as a competitor to more IFR tests by Kochar (1979, 1981) and Cheng (1985). Our test statistic utilizes the U-statistics theory and a large sample nonpara metric test is established. The power of the proposed test is discussed by calculating the Pitman asymptotic relative efficiencies against several alter native hypotheses. A numerical example is presented to exemplify the proposed test.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.6
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• pp.140-145
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• 2011

An anisotropic beam model is proposed by employing an asymptotic expansion method for thermo-mechanical multiphysics environment. An asymptotic method based on virtual work is introduced first, and then the variables of mechanical displacement and temperature rise are asymptotically expanded by taking advantage of geometrical slenderness of elastic bodies. Subsequently substituting these expansions into the virtual work principle allows us to asymptotically expand the virtual work. This will yield a set of recursive virtual works from which two-dimensional microscopic and one-dimensional macroscopic equations are systematically derived at each order. In this way, homogenized stiffnesses and thermomechanical coupling coefficients are derived. To demonstrate the validity and efficiency of the proposed approach, composite beams are taken as a test-bed example. The results obtained herein are compared to those of three-dimensional finite element analysis.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.101-116
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• 1997

This is primarily an expository paper that presents several nonparametric procedures for testing exponentiality against certain monotonicity properties of the mean residual life function, tests against the trend change in such function attract a great deal of attention of late in reliability analysis. In this note, we present some of the known testing procedures regarding the behavior of mean residual life function. These tests are also compared in terms of asymptotic relative efficiency and empirical power against a few alternatives. The tests based on incomplete data are also briefly discussed.

• International Journal of Reliability and Applications
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• v.9 no.2
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• pp.125-140
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• 2008

The new better than used failure rate (NBUFR), Abouammoh and Ahmed (1988), and new better than average failure rate (NBAFR) Loh (1984) classes of life distributions, have been considered in the literature as natural weakenings of NBU (NWU) property. The paper considers testing exponentiality against strictly NBUFR (NBAFR) alternatives, or their duals, based on goodness of fit approach that is possible in life testing problems and that it results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. The asymptotic normality are proved. Powers, Pitman asymptotic efficiency and critical points are computed. Dealing with censored data case also studied. Practical applications of our tests in the medical sciences are present.

• International Journal of Reliability and Applications
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• v.15 no.2
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• pp.99-110
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• 2014

Based on the kernel function, a new test is presented, testing $H_0:\bar{F}$ is exponential against $H_1:\bar{F}$ is UBACT and not exponential is given in section 2. Monte Carlos null distribution critical points for sample sizes n = 5(5)100 is investigated in section 3. The Pitman asymptotic efficiency for common alternatives is obtained in section 4. In section 5 we propose a test statistic for censored data. Finally, a numerical examples in medical science for complete and censored data using real data is presented in section 6.

• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.1-11
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• 2006

The better mean residual life at $t_0\;(BMRL-t_0)$ class of life distribution is introduced by Kulasekara and Park (1987). They proved that the $BMRL-t_0$ class contains the DMRL class, but it is a proper subclass of the NBUE class. In this paper we develop a new family of tests for testing exponentiality against the $BMRL-t_0\;(WMRL-t_0)$ alternatives based on the goodness of fit approach. It is shown that the suggested test is better than the one introduced by Kulasekara and Park (1987) in the sense of Pitman asymptotic efficiency values.

• Journal of Power System Engineering
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• v.19 no.3
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.177-196
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• 1997

In this paper, statistically optimal accelerated life test(ALT) plans considering statistical efficiency only and new compromise ALT plans to sacrifice some statistical efficiency in return for improved overall properties including estimobility probability and robustness for the model assumptions are developed under the assumptions of constant stress, intermittent inspection, Type I censoring and lognormal failure distribution which has been one of the popular choices of failure distributions in the extensive engineering applications of ALT. Computational experiments are conducted to compare with four ALT plans including two proposed ones under continuous and intermittent inspections over a range of parameter values in terms of asymptotic variance, sensitivities for guessed input values, and proportion of estimable samples, etc. The small and moderate sample properties for the proposed ALT plans designed under asymptotic criterion are also investigated by Monte Carlo simulation.