• Journal of Korean Society for Quality Management
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• v.26 no.3
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• pp.31-45
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• 1998

This paper proposes a method of designing one-sided cumulative scored control charts to control the process mean with a normally distributed quality characteristic. The average run length(ARL) is obtained from the average sample number of sequential probability ratio test(SPRT) on trinomial distribution. Using the analogy between cumulative scored control chart and SPRT for trinomial observations, a procedure is presented to determine three control chart parameters; lower and u, pp.r scoring boundaries and action limit. The parameters are determined by minimizing the ARL when the process is out of control with prespecified ARL when the process is in control.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.135-148
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• 1989

Cumulative sum schemes based on a weighted score are considered for controlling the mean of a continuous production process; in which both the one-sided and two-sided schemes are proposed. The average run lengths and the run length distributions for the proposed schemes are obtained by the Markov chain approach. Comparisons by the average run length show that the proposed schemes perform nearly as well as the standard cumulative sum schemes in detecting changes in the process mean. Comparisons of the one-sided schemes by the run length distribution are also presented.

• 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 Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.15-21
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• 1993

This paper considers the optimal design of accelerated life test in which the stress is linearly increased. It discusses the special case when the life distribution under constant stress follows an exponential distribution and the accelerated equation satisfies the inverse power law. It is assumed that cumulative damage is linear, that is, the remaining life of test units depends only on the current cumulative fraction failed and current stress(cumulative exposure model). The optimization criterion is the asymptotic variance of the maximum likelihood estimator of the log mean life at a design stress. The optimal increasing rate is obtained to minimize the asymptotic variance. Table of sensitivity analysis is given for the prior estimators of model parameters.

• Journal of the Korean Solar Energy Society
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• v.28 no.6
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• pp.78-86
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• 2008

The aim of this paper is to show the daylight environment of a light pipe system according to sun movement. A light pipe system has been mounted on the roof of the windowless full scale model: the solar spot has diameter of 0.65m and is 1.3m long, giving an aspect ratio of 1:2. The full scale model was installed on the rooftop of the SHINAN apartment in Yongin city that has no obstructions against sunlight. The test room is equipped with sensors for the measurements of the internal illuminance and has an area of 6m(W)$\times$6m(D)$\times$4m(H). The system has been monitored with a data-logger to evaluate the cumulative distribution of illuminance on a floor-plane from 16th, April to 29th, May, 2008 over one month and selected clear sky condition. For the daylight performance of floor area, the totally 49 measuring points has been used to determine the internal illuminance and an HP datalogger(HP34970A) records the measurements for one consecutive month. The horizontal external illuminance has been measured with two outdoor sensors. This paper presents the results of monitoring light pipe system with internal/external illuminance ratio and cumulative frequency distribution of floor-plane illuminance are discussed The results show that lightpipe is proficient device for introducing daylight into the building. However It provided different daylight indoor environment with wide or narrow Interquatile range of illuminance, internal/external illuminance ratio and cumulative frequency distribution according to solar positions under suuny sky condition. For more achieving the improvement of lightpipes also include energy savings, user visual comfort with various indicators; seasonal solar height, room and lightpipes geometries.

• Journal of the Korea Society for Simulation
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• v.29 no.3
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• pp.41-48
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• 2020

In this paper, a dynamic prediction algorithm using the cumulative distribution function for traffic volume is presented as a new method for predicting highway traffic rate more accurately, where an approximation function of the cumulative distribution function is obtained through numerical methods such as natural cubic spline interpolation and Levenberg-Marquardt method. This algorithm is a new structure of random number generation algorithm using the cumulative distribution function used in financial mathematics to be suitable for predicting traffic flow. It can be confirmed that if the highway traffic rate is simulated with this algorithm, the result is very similar to the actual traffic volume. Therefore, this algorithm is a new one that can be used in a variety of areas that require traffic forecasting as well as highways.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.621-632
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• 2012

Recurrent event data can be easily found in longitudinal studies such as clinical trials, reliability fields, and the social sciences; however, there are a few observations that disappear temporarily in sight during the follow-up and then suddenly reappear without notice like the Young Traffic Offenders Program(YTOP) data collected by Farmer et al. (2000). In this article we focused on inference for a cumulative mean function of the recurrent event data with these incomplete observation gaps. Defining a corresponding risk set would be easily accomplished if we know the exact intervals where the observation gaps occur. However, when they are incomplete (if their starting times are known but their terminating times are unknown) we need to estimate a distribution function for the terminating times of the observation gaps. To accomplish this, we treated them as interval-censored and then estimated their distribution using the EM algorithm proposed by Turnbull (1976). We proposed a nonparametric estimator for the cumulative mean function and also a nonparametric test to compare the cumulative mean functions of two groups. Through simulation we investigated the finite-sample performance of the proposed estimator and proposed test. Finally, we applied the proposed methods to YTOP data.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.65-85
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• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• 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.