• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.11a
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• pp.263-266
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• 2003

This paper is intended to compare between the Bayesian estimates of hazard rate and the hazard rates of mixed distributions. In estimating hazard rates, especially when the MLE method is used, such difficulties as a lack of data and the existence of censored data make it difficult to estimate the rates. For this reason, the estimates of hazard rate based on the Bayesian approach are introduced. For the simplicity, the exponential and gamma distributions are adopted as a sampling distribution and its natural conjugate prior distribution, respectively.

• Proceedings of the Korean Reliability Society Conference
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• 2005.06a
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• pp.121-129
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• 2005

In this paper, we consider a periodic preventive maintenance(PM) policy in which each PM reduces the hazard rate of amount proportional to the failure intensity, which increases since the last PM and slows down the wear-out speed to that of new one. And the proportion of reduction in hazard rate decreases with the number of PMs. Our model is similar to $ARI_1$ proposed by Doyen and Gaudoin(2004) in the sense of reduction of hazard rate. Our model has totally different wear-out pattern of hazard rate after PM's, however, and the proportion of reduction depends on the number of PM's. Assuming that the system undergoes only minimal repairs at failures between PM's, the expected cost rate per unit time is obtained. The optimal number N of PM and the optimal period x, which minimize the expected cost rate per unit time are discussed. Explicit solutions for the optimal periodic PM are given for the Weibull distribution case.

• Journal of Labour Economics
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• v.26 no.1
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• pp.111-151
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• 2003

This study attempted to analize the hazard rate from unemployment and the influncing factors on the rate by regions. The data this study uses is Korea Labor Institute Panal Study(1998-2001) and the models are hazard analysis and Cox model. The results of hazard analysis are as follow. In capital and it's vicinity, the duration of unemployment is shorter than other regions even if the unemployment rate is higher. The labor market segmentation is confirmed between capital and it's vicinity region and other regions. Kyungsang region is higher in the unemployment hazard rate than Chunla or Chungchung regions. The duration of unemployment in capital and it's vicinity is 9.29 months comparing 11.86 months in the other region. The difference is statistically significant by the significance level 0.001. The duration of unemployment in Kyungsang is 6.96 months comparing 10.95 months in Chunla region. The Cox results which indicate the influncing factors on the hazard rate are as follow. In the regions like non-metro cities and non-capital and vicinitiy, the factors such as female, tenure, wage earners, manufacturing, wholesale and retale decrease the hazard rate. The results indicate that active labor market policies region by region are needed in Korea, especially for the marginal unemployed workes from non flourishing sectors.

• 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 on Water Environment
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• v.23 no.1
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• pp.87-96
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• 2007

In this paper a methodology of identifying individual pipes according to the internal and external characteristics of pipe is developed, and the methodology is applied to a case study water distribution pipe break database. Using the newly defined individual pipes the hazard rates of the cast iron 6 inch pipes are modeled by implementing the proportional hazards modeling approach for consecutive pipe failures. The covariates to be considered in the modeling procedures are selected by considering the general availability of the data and the practical applicability of the modeling results. The individual cast iron 6 inch pipes are categorized into seven ordered survival time groups according to the total number of breaks recorded in a pipe to construct distinct proportional hazard model (PHM) for each survival time group (STG). The modeling results show that all of the PHMs have the hazard rate forms of the Weibull distribution. In addition, the estimated baseline survivor functions show that the survival probabilities of the STGs generally decrease as the number of break increases. It is found that STG I has an increasing hazard rate whereas the other STGs have decreasing hazard rates. Regarding the first failure the hazard ratio of spun-rigid and spun-flex cast iron pipes to pit cast iron pipes is estimated as 1.8 and 6.3, respectively. For the second or more failures the relative effects of pipe material/joint type on failure were not conclusive. The degree of land development affected pipe failure for STGs I, II, and V, and the average hazard ratio was estimated as 1.8. The effects of length on failure decreased as more breaks occur and the population in a GRID affected the hazard rate of the first pipe failure.

• International Journal of Reliability and Applications
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• v.2 no.1
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• pp.49-56
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• 2001

In this paper we consider empirical Bayes estimation of the hazard rate and survival probabilities with right censored data under the assumption that the hazard function is constant over the period of observation and the prior distribution is gamma. We provide an estimator of the first derivative of the prior moment generating function that converges at each point to the true value in $L_2$ and use it to obtain, easy to compute, asymptotically optimal estimators under the squared error loss function.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.133-143
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• 2000

Data from weighted distributions appear, among other situations, when some of the data are missing or are damaged, a case that is important in reliability and life testing. The kernel method for hazard rate estimation is discussed for these data where the basic large sample properties are given. As a by product, the basic properties of the kernel estimate of the distribution function for data from weighted distribution are presented.

• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.359-370
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• 1999

We considered a change-point hazard rate model generalizing constant hazard rate model. This type of model is very popular in the sense that the Weibull and exponential distributions formulating survival time data are the special cases of it. Maximum likelihood estimation and the asymptotic properties such as the consistency and its limiting distribution of the change-point estimator were discussed. A parametric bootstrap method for finding confidence intervals of the unknown change-point was also suggested and the proposed method is explained through a practical example.

• Proceedings of the KIEE Conference
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• 2003.04a
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• pp.438-440
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• 2003

It is very important to ensure system safety during the process of developing a system. Railway system is also devoting a great portion for the safety. Nowadays many countries leading railway industry have their own system assessment process according to the situation of their train control system. In this Paper, several methods to derive Tolerable Hazard Rate are represented in the railway signalling system the characteristics of those methods are also considered respectively.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.491-496
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• 1997

For the survival data analysis of no covariate the discount survival model is proposed to estimate the time-varying hazard rate and the survival function recursively. In comparison with the covariate case it provide the distributionally explicit evolution of hazard rate between time intervals under the assumption of a conjugate gamma distribution. Also forecasting of the hazard rate in the next time interval is suggested, which leads to the forcecasted survival function.