• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2003년도 추계학술대회 및 정기총회
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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.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.327-336
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• 2000

We are mainly interested in hazard rate changes which are usually occur in survival times of manufactured products or patients. We may expect early failures with one hazard rate and next another hazard rate. For this type of data we apply a hazard rate change-point model and estimate the unkown time point to improve the model adequacy. We introduce change-point logistic model to the discrete time hazard rates. The MLEs are obtained routinely and we also explain the suggested model through a dataset of survival times.

• 응용통계연구
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• 제11권1호
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• pp.163-175
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• 1998

위험률 변화점모형에서 특별한 함수형이나 분포함수에 대한 가정을 하지 않는 일반적인 모형을 고려하였다. 이러한 모형은 지금까지 주로 다루어 왔던 상수항 위험률의 변화점모형뿐만 아니라 여러 유형의 변화점모형을 내포한다. 중도절단된 자료하에서 위험률 변화점에 관한 모수적 모형을 가정하지 않고 변화점 이전과 이후의 넬슨(Nelson) 누적위험함수 추정량의 기울기 차를 이용하여 추정량을 제안하고, 그의 점근적 성질을 규명한다. 붓스트랩 추정량의 일치성과 점근분포를 유도하고, 몇가지 분포함수의 경우에 몬테칼로 모의실험을 통해 제안된 방법의 경험적 성질을 살펴보았다. 또한, 심장병 이석환자의 생존시간 자료를 통해 변화점을 추정하고 추정량의 붓스트랩 분포를 구하였다.

• 한국철도학회논문집
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• 제16권2호
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• pp.104-109
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• 2013

The paper will outline how hazard identification and risk evaluation can effectively be performed to obtain Tolerable Hazard Rates (THR). As a target group manufacturers are addressed, who face the situation, that for a generic application THRs are needed for compliance with EN 50129 [1]. Focusing on functional hazards this paper shows a possible hazard log and the relevant analysis methods. The terms safety barrier and barrier function will be introduced and used instead of the term "safety function". As functional hazards and barrier functions depend on each other, emphasis will be put on a comprehensive and detailed definition of barrier functions and the usage of function lists. By using detailed and complete hazard and barrier function definitions THRs can be obtained while at the same time the approach becomes clear how the hazard rates (HR) will be established.

• International Journal of Reliability and Applications
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• 제2권1호
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• pp.1-26
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• 2001

The purpose of this paper is to introduce a proportional reversed hazard rate model, in contrast to the celebrated proportional hazard model, and study some of its structural properties. Some criteria of ageing are presented and the inheritance of the ageing notions (of the base line distribution) by the proposed model are studied. Two important data sets are analyzed: one uncensored and the other having some censored observations. In both cases, the confidence bands for the failure rate and survival function are investigated. In one case the failure rate is bathtub shaped and in the other it is upside bath tub shaped and thus the failure rates are non-monotonic even though the baseline failure rate is monotonic. In addition, the estimates of the turning points of the failure rates are provided.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2002년도 춘계 학술발표회 논문집
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• pp.28-35
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• 2002

The probabilistic seismic hazard analysis for engineering needs several active fault parameters as input data. Fault slip rates, the segmentation model for each fault, and the date of the most recent large earthquake in seismic hazard analysis are the critical pieces of information required to characterize behavior of the faults. Slip rates provide a basis for calculating earthquake recurrence intervals. Segmentation models define potential rupture lengths and are inputs to earthquake magnitude. The most recent event is used in time-dependent probability calculations. These data were assembled by expert source-characterization groups consisting of geologists, geophysicists, and seismologists evaluating the information available for earth fault. The procedures to prepare inputs for seismic hazard are illustrated with possible segmentation scenarios of capable fault models and the seismic hazards are evaluated to see the implication of considering capable faults models.

• 한국물환경학회지
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• 제23권1호
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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.

• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.481-498
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• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

• Asian Pacific Journal of Cancer Prevention
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• 제13권4호
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• pp.1533-1537
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• 2012

In general, breast cancer is the most common malignancy among women in developed as well as some developing countries, often being the second leading cause of cancer mortality after lung cancer. Using a parametric log-logistic model to consider the effects of prognostic factors, the present study focused on the 5-year survival of women with the diagnosis of breast cancer in Southern Iran. A total of 1,148 women who were diagnosed with primary invasive breast cancer from January 2001 to January 2005 were included and divided into three prognosis groups: poor, medium, and good. The survival times as well as the hazard rates of the three different groups were compared. The log-logistic model was employed as the best parametric model which could explain survival times. The hazard rates of the poor and the medium prognosis groups were respectively 13 and 3 times greater than in the good prognosis group. Also, the difference between the overall survival rates of the poor and the medium prognosis groups was highly significant in comparison to the good prognosis group. Use of the parametric log-logistic model - also a proportional odds model - allowed assessment of the natural process of the disease based on hazard and identification of trends.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.445-455
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• 1999

We modify the Gompertz regression model for estimation of cure rates from pediatric clinical trials by assuming different hazard rates on the different periods. A treatment period may be divided by the stages of treatments under the different treatment arms. The piecewise Gompertz models provide an efficient method for estimation of the cure rates and a method for testing the difference of the treatment effects in the given interval.