• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.623-632
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• 2014

We shall consider the estimation for the parameter and the right tail probability in a general exponential distribution. We also shall consider the estimation of the reliability P(X < Y ) and the skewness trends of the density function of the ratio X=(X+Y) for two independent general exponential variables each having different shape parameters and known scale parameter. We then shall consider the estimation of the failure rate average and the hazard function for a general exponential variable having the density function with the unknown shape and known scale parameters, and for a bivariate density induced by the general exponential density.

• 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 the Korean Data and Information Science Society
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• v.15 no.2
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• pp.405-411
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• 2004

In the analysis of cancer data, it is important to make inferences of survival function and to assess the effects of covariates. Cox's proportional hazard model(PHM) and Beran's nonparametric method are generally used to estimate the survival function with covariates. We adjusted the incomplete survival time using the Buckley and James's(1979) pseudo random variables, and then proposed the estimator for the conditional survival function. Also, we carried out the simulation studies to compare the performances of the proposed method.

• Journal of the Korea Safety Management & Science
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• v.4 no.3
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• pp.59-66
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• 2002

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, S, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, $\theta$ is a random variable of environments and a function of probabilistic stress. In detail, it is assumed that the hazard rate is linear function of the stress, the general stress distribution is a gamma distribution and the life distribution for the given hazard rate, $\theta$is an exponential distribution. Maximum likelihood estimators of model parameters are obtained, and the mean life in use stress condition is estimated. A hypothetical example is given to show its applicability.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1225-1238
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• 2015

In this research, we fit various survival models and conduct tests and estimation for the hazard change-point with the rectal cancer data. By the log-rank tests, at significance level ${\alpha}=0.10$, survival functions are significantly different according to the uniporter of glucose (GLUT1), clinical stage (cstage) and pathologic stage (ypstage). From the Cox proportional hazard model, the most significant covariates are GLUT1 and ypstage. Assuming that the rectal cancer data follows the exponential distribution, we estimate one hazard change-point using Matthews and Farewell (1982), Henderson (1990) and Loader (1991) methods.

• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.15-26
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• 2000

This paper considers an aperiodic preventive maintenance (PM) model for repairable systems, in which the time intervals between two consecutive preventive maintenances are unequal. To propose such an aperiodic PM model, we assume that each PM reduces the current hazard rate by a certain amount which depends on the number of PMs performed previously. If the system fails between PMs, the minimal repair is performed and the hazard rate remains unchanged after the repair. We give the exact expressions for the hazard rate function for the aperiodic PM model. Based on the proposed aperiodic PM model, we suggest the maximum likelihood method to estimate the parameters characterizing the model and apply the method to the case of Weibull distribution. Numerical examples for estimating the parameters are presented for the purpose of illustration.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.793-800
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• 2023

In this paper, we propose a generalization of Lindley distribution (GLD) via a special structure that is concern with progressively Type-II right censoring and time failure data. We study the modern properties that we have built by such combination, for example, survival function, hazard function, moments, and estimation by non-Bayesian methods. Application on some selected data related to Lindley distribution (LD) and (ED) have been employed to find out the best distribution that can fit data comparing with the GLD.

• 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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.40 no.4
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• pp.201-209
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• 2007

Line transect sampling in a sighting survey is one of most widely used methods for assessing animal abundance. This study applied distance data, collected from three sighting surveys using line transects for finless porpoise that were conducted in 2004 and 2005 off the west coast of Korea, to four models (hazard-rate, uniform, half-normal and exponential) that can use a variety of detection functions, g (x). The hazard-rate model, a derived model for the detection function, should have a shoulder condition chosen using the AIC (Akaike Information Criterion), as the most suitable model. However, it did not describe a shoulder shape for the value of g(x) near the track tine and underestimated g (x), just as the exponential model did. The hazard-rate model showed a bias toward overestimating the densities of finless porpoises with a higher coefficient of variation (CV) than the other models did. The uniform model underestimated the densities of finless porpoise but had the lowest CV. The half-normal model described a detection function with a shape similar to that of the uniform model. The half-normal model was robust for finless porpoise data and should be able to avoid density underestimation. The estimated abundance of finless porpoise was 3,602 individuals (95% CI=1,251-10,371) inshore in 2005 and 33,045 individuals (95% CI=24,274-44,985) offshore in 2004.

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