• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.429-437
• /
• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Proceedings of the KSR Conference
• /
• 2011.10a
• /
• pp.717-723
• /
• 2011

When the Balise(the device to transmit information between the on-board equipment and the wayside equipment) failure occurs, it may not be able to transmit data(Telegram) required for the train running. And in some cases, it may be able to cause an accident. Therefore, both the Balise failure affecting train safety running and the hazard in accordance with Balise failure require some activities to establish them. General failure mode & hazard analysis associated with the Balise are described in UNISIG SUBSET-036 spec & UNISIG SUBSET-088 spec. And, with reference to these specifications, safety activities are being performed. In recent domestic railway, the train control system applying ETCS(European Train Control System) Level 1, 2 is being serviced and is being planned, and as part of this system, the Balise is being applied. The design-method of the Balise device for each manufacturer are different, therefore the Balise failure mode & failure rate are different, either. But the functionalities & transmission-data format(Telegram) of the Balise in ETCS Level 1, 2 application for each manufacturer are identical. Accordingly, the hazard caused by function-fail can be identical, either. In order to establish these hazard, in this paper, we analyzed the detailed functions of the Balise. And we analyzed the Balise failure types & failure effects in accordance with the detailed functions.

• The Korean Journal of Applied Statistics
• /
• v.11 no.1
• /
• pp.163-175
• /
• 1998

The change of hazard rates at some unknown time point has been the interest of many statisticians. But it was restricted to the constant hazard rates which correspond to the exponential distribution. In this paper we generalize the change-point model in which any specific functional forms of hazard rates are net assumed. The assumed model includes various types of changes before and after the unknown time point. The Nelson estimator of cumulative hazard function is introduced. We estimate the change-point maximizing slope changes of Nelson estimator. Consistency and asymptotic distribution of bootstrap estimator are obtained using the martingale theory. Through a Monte Carlo study we check the performance of the proposed method. We also explain the proposed method using the Stanford Heart Transplant Data set.

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

• Structural Engineering and Mechanics
• /
• v.29 no.6
• /
• pp.689-707
• /
• 2008

This study presents a method to evaluate the seismic risk of an extradosed bridge with seismic isolators of lead rubber bearings (LRBs), and also to show the effectiveness of the LRB isolators on the extradosed bridge, which is one of the relatively flexible and lightly damped structures in terms of seismic risk. Initially, the seismic vulnerability of a structure is evaluated, and then the seismic hazard of a specific site is rated using an earthquake data set and seismic hazard maps in Korea. Then, the seismic risk of the structure is assessed. The nonlinear seismic analyses are carried out to consider plastic deformation of bridge columns and the nonlinear characteristics of soil foundation. To describe the nonlinear behaviour of a column, the ductility demand is adopted, and the moment-curvature relation of a column is assumed to be bilinear hysteretic. The fragility curves are represented as a log-normal distribution function for column damage, movement of superstructure, and cable yielding. And the seismic hazard at a specific site is estimated using the available seismic hazard maps. The results show that in seismically-isolated extradosed bridges under earthquakes, the effectiveness of the isolators is much more noticeable in the columns than the cables and girders.

• Geomechanics and Engineering
• /
• v.37 no.6
• /
• pp.565-576
• /
• 2024

In this study, the earthquake risk assessment of single-story RC precast buildings in Turkey was carried out using loss curves. In this regard, Kocaeli, a seismically active city in the Marmara region, and this building class, which is preferred intensively, were considered. Quality and period parameters were defined based on structural and geometric properties. Depending on these parameters, nine main sub-classes were defined to represent the building stock in the region. First, considering the mean fragility curves and four different central damage ratio models, vulnerability curves for each sub-class were computed as a function of spectral acceleration. Then, probabilistic seismic hazard analyses were performed for stiff and soft soil conditions for different earthquake probabilities of exceedance in 50 years. In the last step, 90 loss curves were derived based on vulnerability and hazard results. Within the scope of the study, the comparative parametric evaluations for three different earthquake intensity levels showed that the structural damage ratio values for nine sub-classes changed significantly. In addition, the quality parameter was found to be more effective on a structure's damage state than the period parameter. It is evident that since loss curves allow direct loss ratio calculation for any hazard level without needing seismic hazard and damage analysis, they are considered essential tools in rapid earthquake risk estimation and mitigation initiatives.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.4
• /
• pp.1171-1177
• /
• 2007

We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.227-235
• /
• 1998

In this paper, we consider a hierarchical Bayes estimation of the parameter, the reliability and hazard rate function based on type-II censored samples from a Rayleigh failure model. Bayes calculations can be implemented easily by means of the Gibbs sampler. A numerical study is provided.

• Communications for Statistical Applications and Methods
• /
• v.5 no.3
• /
• pp.723-731
• /
• 1998

In this paper, we consider a hierarchical Bayes estimation of the parameter, the reliability and hazard rate function based on samples from a Burr type X failure model. Bayes calculations can be implemented by means of the Gibbs sampler and a numerical study us provided.

• Journal of the Korea Safety Management & Science
• /
• v.2 no.2
• /
• pp.71-83
• /
• 2000

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, $S_j$, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, ,$theta_j$, is the random variable of environments and the function of probabilistic stress. Also it is assumed that the general stress distribution is uniform, the life distribution for the given hazard rate, $\theta$, is exponential and inverse power law model holds. In this paper, we obtained maximum likelihood estimators of model parameters and the mean life in use stress condition.