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

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.2
• /
• pp.99-106
• /
• 1999

In this paper, the spline hazard rate model to the randomly censored data is introduced. The unknown hazard rate function is expressed as a linear combination of B-splines which is constrained to be linear(or constant) in tails. We determine the coefficients of the linear combination by maximizing the likelihood function. The number of knots are determined by Bayesian Information Criterion. Examples using simulated data are used to illustrate the performance of this method under presenting the random censoring.

• Journal of the Korean Data and Information Science Society
• /
• v.10 no.2
• /
• pp.437-444
• /
• 1999

We propose control charts for constant hazard rate by using the number of failures based on the non-placement(replacement) life test. Also we study the sensitivity of the control chart from the operating characteristic curve.

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

• Journal of Korea Society of Digital Industry and Information Management
• /
• v.7 no.4
• /
• pp.7-14
• /
• 2011

Infinite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rate per fault (hazard function). This infinite non-homogeneous Poisson process is model which reflects the possibility of introducing new faults when correcting or modifying the software. In this paper, polynomial hazard function have been proposed, which can efficiency application for software reliability. Algorithm for estimating the parameters used to maximum likelihood estimator and bisection method. Model selection based on mean square error and the coefficient of determination for the sake of efficient model were employed. In numerical example, log power time model of the existing model in this area and the polynomial hazard function model were compared using failure interval time. Because polynomial hazard function model is more efficient in terms of reliability, polynomial hazard function model as an alternative to the existing model also were able to confirm that can use in this area.

• Earthquakes and Structures
• /
• v.24 no.4
• /
• pp.303-316
• /
• 2023

Rapid post-earthquake damage estimation of subway stations is particularly necessary to improve short-term crisis management and safety measures of urban subway systems after a destructive earthquake. The conventional Performance-Based Earthquake Engineering (PBEE) framework with constant earthquake occurrence rate is invalid to estimate the aftershock risk because of the time-varying rate of aftershocks and the uncertainty of mainshock-damaged state before the occurrence of aftershocks. This study presents a time-varying probabilistic seismic risk assessment framework for underground structures considering mainshock and aftershock hazards. A discrete non-omogeneous Markov process is adopted to quantify the time-varying nature of aftershock hazard and the uncertainties of structural damage states following mainshock. The time-varying seismic risk of a typical rectangular frame subway station is assessed under mainshock-only (MS) hazard and mainshock-aftershock (MSAS) hazard. The results show that the probabilities of exceeding same limit states over the service life under MSAS hazard are larger than the values under MS hazard. For the same probability of exceedance, the higher response demands are found when aftershocks are considered. As the severity of damage state for the station structure increases, the difference of the probability of exceedance increases when aftershocks are considered. PSDR=1.0% is used as the collapse prevention performance criteria for the subway station is reasonable for both the MS hazard and MSAS hazard. However, if the effect of aftershock hazard is neglected, it can significantly underestimate the response demands and the uncertainties of potential damage states for the subway station over the service life.

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

• Communications for Statistical Applications and Methods
• /
• v.27 no.1
• /
• pp.37-46
• /
• 2020

Recurrent event data frequently occur in clinical studies, demography, engineering reliability and so on (Cook and Lawless, The Statistical Analysis of Recurrent Events, Springer, 2007). Sometimes, two or more different but related type of recurrent events may occur simultaneously. In this study, our interest is to estimate the covariate effect on bivariate recurrent event times with zero inflations. Such zero inflation can be related with susceptibility. In the context of bivariate recurrent event data, furthermore, such susceptibilities may be different according to the type of event. We propose a joint model including both two intensity functions and two cure rate functions. Bivariate frailty effects are adopted to model the correlation between recurrent events. Parameter estimates are obtained by maximizing the likelihood derived under a piecewise constant hazard assumption. According to simulation results, the proposed method brings unbiased estimates while the model ignoring cure rate models gives underestimated covariate effects and overestimated variance estimates. We apply the proposed method to a set of bivariate recurrent infection data in a study of child patients with leukemia.

• Journal of the Korean Society of Hazard Mitigation
• /
• v.8 no.1
• /
• pp.145-151
• /
• 2008

A novel method was suggested for the estimation of design population and design wastewater flow rate in fishing and agrarian village. Even though the population was decreasing continuously in this area, the design population was considered as constant with the passage of the time in conventional methods. And although the portion of groundwater uses was pretty high, the design wastewater flow rate was determined by the supply amount of tap water. Consequently, the design population and the design wastewater flow rate were overestimated. To prevent these overestimates, the design population was predicted to decrease gradually using the population trends from Korea National Statistical Office, and the design wastewater flow rate was determined using the way that the supply amount of tap water was applied in developed areas and the supply amount of groundwater was used in undeveloped areas.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.9 no.3
• /
• pp.278-284
• /
• 2016

Software reliability in the software development process is an important issue. In infinite failure NHPP software reliability models, the fault occurrence rates may have constant, monotonic increasing or monotonic decreasing pattern. In this paper, infinite failures NHPP models that the situation was reflected for the fault occurs in the repair time, were presented about comparing property. Commonly, the software model of the infinite failures using the linear hazard rate distribution software reliability based on intercept parameter was used in business economics and actuarial modeling, was presented for comparison problem. The result is that a relatively large intercept parameter was appeared effectively form. The parameters estimation using maximum likelihood estimation was conducted and model selection was performed using the mean square error and the coefficient of determination. The linear hazard rate distribution model is also efficient in terms of reliability because it (the coefficient of determination is 90% or more) in the field of the conventional model can be used as an alternative model could be confirmed. From this paper, the software developers have to consider intercept parameter of life distribution by prior knowledge of the software to identify failure modes which can be able to help.