• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.75-78
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• 2002

A simplified methodology is presented to predict fatigue life and residual strength of composite structures. To avoid excessive amount of tests that are required for model characterization, strength degradation parameter is assumed as function of fatigue life. S-N curve is used to extract fatigue life that is required to characterize the stress levels comprising a randomly-ordered load spectrum. And different stress ratios are handled with Goodman correction approach(fatigue envelope). It is assumed that the residual strength is a function of the number of loading cycles and applied fatigue stress amplitude. And the residual strength distribution after an arbitrary load cycles is represented by two parameter Weibull functions.

• Composites Research
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• v.16 no.1
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• pp.13-18
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• 2003

Prediction of composite fatigue life is not a straightforward matter, depending on various failure modes and their interactions. In this paper, a methodology is presented to predict fatigue life and residual strength of composite materials based on Phenomenological Model(non-linear fatigue damage model). It is assumed that the residual strength is a monotonically decreasing function of the number of loading cycles and applied fatigue stress ratio and the model parameters(strength degradation parameter and fatigue shape parameter) are assumed as function of fatigue life. Then S-N curve is used to extract model parameters that are required to characterize the stress levels comprising a randomly-ordered load spectrum. Different stress ratios (${\sigma}_{min}/{\;}{\sigma}_{max}$) are handled with Goodman correction approach(fatigue envelope) and the residual strength after an arbitrary load cycles is represented by two parameter weibull functions.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.177-186
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• 2006

Typical confidence intervals for a mean or mean residual life (MRL) are centered about the mean or mean residual life. We discuss novel confidence intervals that produce statements like "we are 95% confident that the MRL function, e(t), is greater than a prespecified $\mu_o$ for all t in the interval [0, $\hat{\theta})$)" where $\hat{\theta}$ is determined from the sample data, confidence level, and $\mu_o$. Also, we can have statements like 'we are 95% confident that the MRL of population 1, namely $e_1$(t), is greater than the MRL of population 2, $e_2$(t), for all t in the interval [0, $\hat{\theta}$)" where $\hat{\theta}$ is determined from the sample data and confidence level. We illustrate these one and two sample confidence intervals on internal bonds (tensile strengths) for an important modem engineered wood product, called medium density fiberboard (MDF), used internationally.

• Journal of the Korean Data and Information Science Society
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• v.22 no.1
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• pp.89-97
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• 2011

The aims of this study were to propose a method of estimation for mean residual life function (MRLF) from conditional survival function using the Buckley and James's (1979) pseudo random variables, and then to assess the performance of the proposed method through the simulation studies. The mean squared error (MSE) of proposed method were less than those of the Cox's proportional hazard model (PHM) and Beran's nonparametric method for non-PHM case. Futhermore in the case of PHM, the MSE's of proposed method were similar to those of Cox's PHM. Finally, to evaluate the appropriateness of practical use, we applied the proposed method to the gastric cancer data. The data set consist of the 1, 192 patients with gastric cancer underwent surgery at the Department of Surgery, K-University Hospital.

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

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.191-202
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• 2004

The paper considers nonparametric empirical Bayes estimation of residual survival function at age t using a Dirichlet process prior V(a). Empirical Bayes estimators are proposed for the case where both the function ${\alpha}$(0, $\chi$] and the size a(R$\^$+/) are unknown. It is shown that the proposed empirical Bayes estimators are asymptotically optimal at a rate n$\^$-1/, where n is the number of past data available for the present estimation problem. Therefore, the result of Lahiri and Park (1988) in which a(R$\^$+/) is assumed to be known and a rate n$\^$-1/ is achieved, is extended to a(R$\^$+/) unknown case.

• Journal of Applied Reliability
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• v.18 no.3
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• pp.220-228
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• 2018

Purpose: The purpose of this study is to investigate the tail behavior of the life distribution which exhibits an increasing failure rate or other positive aging effects after a certain time point. Methods: We characterize the tail behavior of the life distribution with regard to certain reliability measures such as failure rate, mean residual life and reliability function and derive several stochastic properties regarding such life distributions. Also, utilizing an L-statistic and its asymptotic normality, we propose new nonparametric testing procedures which verify if the life distribution has an increasing tail failure rate. Results: We propose the IFR-Tail (Increasing Failure Rate in Tail), DMRL-Tail (Decreasing Mean Residual Life in Tail) and NBU-Tail (New Better than Used in Tail) classes, all of which represent the tail behavior of the life distribution. And we discuss some stochastic properties of these proposed classes. Also, we develop a new nonparametric test procedure for detecting the IFR-Tail class and discuss its relative efficiency to explore the power of the test. Conclusion: The results of our research could be utilized in the study of wide range of applications including the maintenance and warranty policy of the second-hand system.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.3
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• pp.305-313
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• 2009

This paper provides a method for evaluating a residual life of water mains using a proportional hazard model(PHM). The survival time of individual pipe is defined as the elapsed time since installation until a break rate of individual pipe exceeds the Threshold Break Rate. A break rate of an individual pipe is estimated by using the General Pipe Break Model(GPBM). In order to use the GPBM effectively, improvement of the GPBM is presented in this paper by utilizing additional break data that is the cumulative number of pipe break of 0 for the time of installation and adjusting a value of weighting factor(WF). The residual lives and hazard ratios of the case study pipes of which the cumulative number of pipe breaks is more than one is estimated by using the estimated survival function. It is found that the average residual lives of the steel and cast iron pipes are about 25.1 and 21 years, respectively. The hazard rate of the cast iron pipes is found to be higher than the steel pipes until 20 years since installation. However, the hazard rate of the cast iron pipes become lower than the hazard rates of the steel pipes after 20 years since installation.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.152-161
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• 1994

In this paper we develop a test for alternatives representing decreasing mean residual life. The test statistic for decreasing mean residual life, $K_{1n}$, is a modified version of Hollander and Proschan's test $V^*$ and critical constants and large sample approximation are shown to make the test readily applicable. Consistency is also shown for the tests based on $K_{1n}$. And small sample powers for four alernatives are obtained.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.