• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.723-731
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• 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
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• v.2 no.2
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• pp.71-83
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• 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.

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

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.11
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• pp.5643-5646
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• 2012

Background and Objectives: Increase of mortality rates of gastric cancer in Iran and the world in recent years reveal necessity of studies on this disease. Here, hazard function for gastric cancer patients was estimated using Wavelet and Kernel methods and some related factors were assessed. Materials and Methods: Ninety-five gastric cancer patients in Fayazbakhsh Hospital between 1996 and 2003 were studied. The effects of age of patients, gender, stage of disease and treatment method on patient's lifetime were assessed. For data analyses, survival analyses using Wavelet method and Log-rank test in R software were used. Results: Nearly 25.3% of patients were female. Fourteen percent had surgery treatment and the rest had treatment without surgery. Three fourths died and the rest were censored. Almost 9.5% of patients were in early stages of the disease, 53.7% in locally advance stage and 36.8% in metastatic stage. Hazard function estimation with the wavelet method showed significant difference for stages of disease (P<0.001) and did not reveal any significant difference for age, gender and treatment method. Conclusion: Only stage of disease had effects on hazard and most patients were diagnosed in late stages of disease, which is possibly one of the most reasons for high hazard rate and low survival. Therefore, it seems to be necessary a public education about symptoms of disease by media and regular tests and screening for early diagnosis.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1171-1177
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• 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 Statistical Society
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• v.36 no.1
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• pp.93-109
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• 2007

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

• Structural Engineering and Mechanics
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• v.69 no.3
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• pp.317-326
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• 2019

This research aims to assess the tight seismic risk curve of the intake tower at Geumgwang reservoir by considering the recorded historical earthquake data in the Korean Peninsula. The seismic fragility, a significant part of risk assessment, is updated by using Bayesian inference to consider the uncertainties and computational efficiency. The reservoir is one of the largest reservoirs in Korea for the supply of agricultural water. The intake tower controls the release of water from the reservoir. The seismic risk assessment of the intake tower plays an important role in the risk management of the reservoir. Site-specific seismic hazard is computed based on the four different seismic source maps of Korea. Probabilistic Seismic Hazard Analysis (PSHA) method is used to estimate the annual exceedance rate of hazard for corresponding Peak Ground Acceleration (PGA). Hazard deaggregation is shown at two customary hazard levels. Multiple dynamic analyses and a nonlinear static pushover analysis are performed for deriving fragility parameters. Thereafter, Bayesian inference with Markov Chain Monte Carlo (MCMC) is used to update the fragility parameters by integrating the results of the analyses. This study proves to reduce the uncertainties associated with fragility and risk curve, and to increase significant statistical and computational efficiency. The range of seismic risk curve of the intake tower is extracted for the reservoir site by considering four different source models and updated fragility function, which can be effectively used for the risk management and mitigation of reservoir.

• International Journal of Reliability and Applications
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• v.13 no.2
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• pp.91-104
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• 2012

Sarhan and Kundu (2009) introduced a new distribution named as the generalized linear failure rate distribution. This distribution generalizes several well known distributions. The probability density function of the generalized linear failure rate distribution can be right skewed or unimodal and its hazard function can be increasing, decreasing or bathtub shaped. This distribution can be used quite effectively to analyze lifetime data in place of linear failure rate, generalized exponential and generalized Rayleigh distributions. In this paper, we apply the simulated annealing algorithm to obtain the maximum likelihood point estimates of the parameters of the generalized linear failure rate distribution. Simulated annealing algorithm can not only find the global optimum; it is also less likely to fail because it is a very robust algorithm. The estimators obtained using simulated annealing algorithm have been compared with the corresponding traditional maximum likelihood estimators for their risks.

• Journal of the military operations research society of Korea
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• v.35 no.2
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• pp.33-49
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• 2009

The objective of this study is as follows. First, the hazard function on the failure probability density function of the K-1 tracked vehicles can be occurred in the form of the bathtub curve. Second, the failure mode may be different under two different operational situations. The research result shows that the bathtub curve can be fitted in the Weibull distribution, that assumes different shapes according to the specific stage of the system's life cycle. The K-1 tracked vehicle has a relatively high hazard(failure) rate at the time of its first service. The failure rate starts decreasing for a time immediately after it goes into service. After the break-in period, the surviving components have a fairly constant hazard rate. As the K-1 system ages, deterioration of its various parts takes place and the hazard rate starts Increasing. Second, the result shows the failure rate in the harsh operational environment is higher than that in the mild operational environment. In conclusion, the bathtub curve can be logically appropriate in establishing the depot overhaul cycle. Moreover, it is necessary for determining the right time of the depot overhaul to consider not only the age of defense equipment but also the different operational environment.

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