• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.189-201
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• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• Journal of Applied Reliability
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• v.18 no.2
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• pp.104-113
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• 2018

Purpose: This paper proposes the non-periodic preventive maintenance policy based on the level of cumulative hazard intensity. We aim to construct a cost-effectiveness on the proposed model with relaxing the constraint on reliability. Methods: We use the level of cumulative hazard intensity as a condition variable, instead of reliability. Such a level of cumulative hazard intensity can derive the reliability which decreases as the frequency of preventive maintenance action increases. We also model the imperfect preventive maintenance action using the proportional age setback model. Conclusion: We provide a numerical example to illustrate the proposed model. We also analyze how the parameters of our model affect the optimal preventive maintenance policy. The results show that as long as high reliability is guaranteed, the inefficient preventive maintenance action is performed reducing the system operation time. Moreover, the optimal value of the proposed model is sensitive to changes in preventive maintenance cost and replacement cost.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.623-633
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• 2019

This paper proposes two distance measures between two cumulative hazard functions that can be obtained by comparing their difference and ratio, respectively. Then we estimate the measures and present goodness of t test statistics. Since the proposed test statistics are expressed in terms of the cumulative hazard functions, we can easily give more weights on earlier (or later) departures in cumulative hazards if we like to place an emphasis on earlier (or later) departures. We also show that these test statistics present comparable performances with other well-known test statistics based on the empirical distribution function for an exponential null distribution. The proposed test statistic is an omnibus test which is applicable to other lots of distributions than an exponential distribution.

• 대한예방의학회:학술대회논문집
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• 1994.02a
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• pp.651-657
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• 1994

To assess quantitatively the association between benzene exposure and leukemia, we examined the mortality rate of a cohort with occupational exposure to benzene. Cumulative exposure for each cohort member was estimated from historical air-sampling data and, when no sampling data existed, from interpolation on the basis of existing data. The overall standardized mortality ratio (a measure of relative risk multiplied by 100) for leukemia was 337 (95 percent confidence interval, 154 to 641), and that for multiple myeloma was 409 (95 percent confidence interval, 110 to 1047). With stratification according to levels of cumulative exposure, the standardized mortality ratios for leukemia increased from 109 to 322, 1186, and 6637 with increases in cumulative benzene exposure from less than 40 parts per million-years (ppm-years), to 40 to 199, 200 to 399, and 400 or more. respectively. A cumulative benzene exposure of 400 ppm years is equivalent to a mean annual exposure of 10 ppm over a 40-year working lifetime; 10 ppm is the currently enforceable standard in the United States for occupational exposure to benzene. To examine the shape of the exposure-response relation, we performed a conditional logistic-regression analysis, in which 10 controls were matched to each cohort member with leukemia. From this model, it can be calculated that protection from benzene induced leukemia would increase exponentially with any reduction in the permissible exposure limit.

• Journal of the Korean Statistical Society
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• v.30 no.3
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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.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.2
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• pp.90-96
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• 2000

The technology of preventive maintenance and corrective maintenance is widely applied to ships in order to maintain the good voyageable condition. One of the most important fields of marine engineering is to seek the maximum availability and to solve the stochastic maintenance problem such that the cost for corrective maintenance is minimized. Accordingly, for the purpose of making the most suitable maintenance schedule which minimizes the expected cost function, this paper suggests the method to grasp the failure characteristics by the ship's maintenance data that are collected from the past. And, suggests the method to estimate the optimal maintenance interval by using the dynamic programming and the cumulative hazard rate function attained from the maintenance data.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.45-58
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• 2017

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.357-371
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• 2007

For the time-to-failure data with competing risks, cumulative incidence functions (CIFs) are commonly estimated using nonparametric methods. If the cases of events due to the cause of primary interest are infrequent relative to other cause of failure, nonparametric methods may result in rather imprecise estimates for CIF. In such cases, Bryant et al. (2004) suggested to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimator. We represented the semiparametric cumulative incidence estimator and extended to the model of Weibull and log-normal distribution. We also conducted simulations to access the performance of the semiparametric cumulative incidence estimators and to investigate the impact of model misspecification in log-normal cause-specific hazard model.

• 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 Gastric Cancer
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• v.12 no.2
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• pp.88-98
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• 2012

Purpose: Local recurrence, due to residual tumor, may occur after endoscopic resection for early gastric cancer. The aims of this study are to evaluate the predictive factors for local recurrence, and suggest an appropriate follow-up biopsy strategy. Materials and Methods: We retrospectively reviewed 396 early gastric cancers from 372 consecutive patients, who underwent endoscopic resection between January 2002 and April 2008. Cumulative recurrence rates were determined by the Kaplan-Meier method, and Cox proportional hazard analysis was used to determine the risk factors for local recurrence. Results: Local recurrence at the endoscopic resection site was found in 17 cases, among the total 396 lesions, during a median follow-up period of 48 months. The 5-year cumulative local recurrence rate was 4.8%. Multivariate analyses determined that tumor involvement at the lateral resection margin [hazard ratio: 35.9; P<0.001], uncheckable lateral resection margin [hazard ratio: 16.8; P<0.001], uncheckable or involved deep resection margin [hazard ratio: 3.76; P=0.047], and piecemeal resection [hazard ratio: 3.95; P=0.007] were associated with local recurrence. If a lesion was positive for any of these risk factors, the 5-year cumulative recurrence rate was 27.0%, while local recurrence was not found in any lesion that lacked these risk factors. Most episodes of recurrence were found during the first or second follow-up endoscopic biopsy at the ulcer scar. Conclusions: Routine follow-up biopsies at the endoscopic resection site might be unnecessary in cases where an early gastric cancer lesion was endoscopically resected en bloc with tumor-free lateral and deep margins.