• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.11-19
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• 2015

A certain number of products are transported to be sold each month and some of them are returned for repair. In this study we first assume that the transported products are the ones that have been sold, Then nonparametric approach is applied to the warranty returns data to see how the reliability decreases over time. Parametric approach such as Weibull distribution is applied to the same data and the results for both nonparametric and parametric approaches are compared. Next we assume that there is a time lag between shipment and sale. Then both nonparametric and parametric approaches are applied to the time-lag data and the results are compared.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.567-573
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• 2011

This study develops a predictive model for household water end-uses based on data that have measured household characteristics, housing characteristics and other items, surveyed over 3 years in Korea. However, the measured data was left-skewed and it was not fitted to normal distribution. The parameter estimate were biased when using a multiple regression model. In addition, the results of the testing for the model were usually of significance due to the tiny residual from a large number of observations. In order to solve the problem, we suggested log-normal regression model and Weibull regression model as alternatives. The results of this study can be utilized in the planning stages of water and waste water facilities.

• Journal of Preventive Medicine and Public Health
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• v.35 no.1
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• pp.65-71
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• 2002

Objective : To estimate the status of HIV infection and AIDS incidence using a back-calculation model in Korea. Methods : Back-calculation is a method for estimating the past infection rate using AIDS incidence data. The method has been useful for obtaining short-term projections of AIDS incidence and estimating previous HIV prevalence. If the density of the incubation periods is known, together with the AIDS incidence, we can estimate historical HIV infections and forecast AIDS incidence in any time period up to time t. In this paper, we estimated the number of HIV infections and AIDS incidence according to the distribution of various incubation periods Results : The cumulative numbers of HIV infection from 1991 to 1996 were $708{\sim}1,426$ in Weibull distribution and $918{\sim}1,980$ in Gamma distribution. The projected AIDS incidence in 1997 was $16{\sim}25$ in Weibull distribution and $13{\sim}26$ in Gamma distribution. Conclusions : The estimated cumulative HIV infections from 1991 to 1996 were $1.4{\sim}4.0$ times more than notified cumulative HIV infections. Additionally, the projected AIDS incidence in 1997 was less than the notified AIDS cases. The reason for this underestimation derives from the very low level of HIV prevalence in Korea, further research is required for the distribution of the incubation period of HIV infection in Korea, particularly for the effects of combination treatments.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.1-12
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• 2017

Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.8 no.5
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• pp.339-344
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• 2015

NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, infinite failures NHPP models that repairing software failure point in time reflects the situation, was presented for comparing property. Commonly used in the field of software reliability based on Weibull extension distribution software reliability of infinite failures was presented for comparison problem. The result is that a relatively large shape parameter was effectively. The parameters estimation using maximum likelihood estimation was conducted and Model selection was performed using the mean square error and the coefficient of determination. In this research, software developers to identify software failure property follows shape parameter, some extent be able to help is considered.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.8
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• pp.1903-1910
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• 2009

In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used the Weibull distribution which has the efficient various property which has the place efficient quality. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

• The Korean Journal of Applied Statistics
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• v.32 no.1
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• pp.129-138
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• 2019

Ammunition is an integral element of a weapon systems and in calculating fighting strength. The Korea Army utilizes the basic load (B/L) concept to supply ammunition smoothly. The required supply rate (RSR) is the basis of a B/L that is estimated from real combat data that includes a troop's mission and operation terrain. The current RSR is based on Korean War data and the sample mean has some problems in applications to modern combat. Therefore, this study used Korea Combat Training Center (KCTC) data that is similar to real combat to estimate rifle ammunition RSR. We used a quantile of truncated Weibull distribution to estimate rifle ammunition RSR considering that rifle ammunition consumption data in KCTC is truncated. As a result, we obtained a rifle ammunition RSR which covers most ammunition consumption by reflecting the individual consumption of rifle ammunition.

• Journal of Power System Engineering
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• v.4 no.2
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• pp.40-45
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• 2000

Some engineering materials are often known to have considerable spatial variation in their resisting strength and other properties. The objective of this study is to investigate the averaging effect and the applicability of extremal statistic for the statistical size effect. In the present study, it is assumed that the material property is a stationary random process in space. The theoretical autocorrelation function of the material strength are discussed for several correlation lengths. And, in order to investigate the statistical size effect, the material properties was simulated by using the non-Gaussian random process method. The material properties were plotted on the Weibull probability papers. The main results are summarized as follows: The autocorrelation function of the material properties are almost independent of the averaging length. The variance decreases with increasing the averaging length. As correlation length is smaller, the slope is larger. And also, it was found that Weibull statistics based on the weakest-link model could not explain the spatial variation of material properties with respect to the size effect satisfactory.

• Journal of the Korean Ceramic Society
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• v.21 no.1
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• pp.27-32
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• 1984

During the last decade there have been many studies on the new ceramics especially engineering ceramics. Sintered silicon carbide is one of the main materials in engineering ceramics. This study shows the effects of surface treatment and microstructure especially the abnormal grain growth on the strength of sintered SiC. Surface of sintered SiC and treated with 400, 800 and 1200 grit diamond wheel. Grain growth is introduced by increasing the sintering times at 205$0^{\circ}C$. The $\beta$longrightarrow$\alpha$ transformation occurs during the sintering of $\beta$-starting materials and is often accompanied by abnormal grain growth. The overall strength distribution are estimated using the Weibull statistics. The results show that the strength of sintered SiC is limited by extrinsic surface flaws in normal-sintered specimens. And it is sound that the finer the surface finishing and the grain size the higher the strength results. But the strength of abnormal sintering specimens is limited by the abnormally-grown large tabular grains. The Weibull modulus increases with the decreasing grain size and the decreasing grit size of grinding.