• International Journal of Highway Engineering
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• v.16 no.1
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• pp.49-56
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• 2014

PURPOSES : This study was done to model the headway distribution of rural two lane roads. METHODS : Time headway data for the various level of traffic volumes was measured in twelve sites. Based on the time headway data, existing seven mathematical models were evaluated and selected by comparing graphically the measured and theoretical distributions and conducting the Chi-square test. RESULTS : The results show that both the Schul model and Composite Model were the most appropriate models of the models. Based on the measured time-headway distributions, this study proposed a new headway distribution model by the shift of the Schul model. CONCLUSIONS : The shifted Schul model has the ability to describe time headway distirbutons for random, intermediate, and constant-headway states.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.268-275
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• 2003

We consider the Bayesian accelerated failure time model. The error distribution is assigned a skewed normal distribution which is including normal distribution. For noninformative priors of regression coefficients, we show the propriety of posterior distribution. A Markov Chain Monte Carlo algorithm(i.e., Gibbs Sampler) is used to obtain a predictive distribution for a future observation and Bayes estimates of regression coefficients.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.325-334
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• 2011

In this paper we consider the discrete time delayed renewal risk model. We investigate what will happen when the distribution function of the discounted proper deficit is asymptotic in the initial surplus. In doing this we establish several lemmas regarding some related ruin quantities in the discrete time delayed renewal risk model, which are of significance on their own right.

• 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 Safety Management & Science
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• v.13 no.1
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• pp.195-202
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• 2011

The study interprets each of three classification models based on Bath-Tub Failure Rate (BTFR), Extreme Value Distribution (EVD) and Conjugate Bayesian Distribution (CBD). The classification model based on BTFR is analyzed by three failure patterns of decreasing, constant, or increasing which utilize systematic management strategies for reliability of time. Distribution model based on BTFR is identified using individual factors for each of three corresponding cases. First, in case of using shape parameter, the distribution based on BTFR is analyzed with a factor of component or part number. In case of using scale parameter, the distribution model based on BTFR is analyzed with a factor of time precision. Meanwhile, in case of using location parameter, the distribution model based on BTFR is analyzed with a factor of guarantee time. The classification model based on EVD is assorted into long-tailed distribution, medium-tailed distribution, and short-tailed distribution by the length of right-tail in distribution, and depended on asymptotic reliability property which signifies skewness and kurtosis of distribution curve. Furthermore, the classification model based on CBD is relied upon conjugate distribution relations between prior function, likelihood function and posterior function for dimension reduction and easy tractability under the occasion of Bayesian posterior updating.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.42
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• pp.31-38
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• 1997

The main objective of this research is to develop a model to select the optimal input service level for a distribution center - multi branch inventory distribution system. With the continuous review policy, the distribution center places an order for specific order quantity to an outside supplier, and the order quantity is replenished after a certain lead time. Also, each branch places an order for particular order quantity to the distribution center to satisfy the customer demands, and receives the replenishment after a lead time. When an out of stock condition occurs during an order cycle, a backorder is placed to the upper level to fill the unfilled demands. With these situation, variable demand and variable lead time are used for better industrial practice. Further, actual lead times with a generic lead time distribution are used in developing the control model. Under the actual lead time model, the customer service measures actually attained for the distribution center and each branch are explained as the effective customer service measures. Thus, throughout the optimal control (using computer search procedures), we can select the optimal input service levels for the distribution center and each branch to attain the effective service level for each branch which is consistent with the goal level of service for each branch. At the same time, the entire distribution system keeps minimum inventories.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.2
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• pp.102-113
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• 2004

This paper addresses the transportation planning that is based on genetic algorithm for determining transportation time and transportation amount of minimizing cost of distribution system. The vehicle routing of minimizing the transportation distance of vehicle is determined. A distribution system is consisted of a distribution center and many retailers. The model is assumed that the time horizon is discrete and finite, and the demand of retailers is dynamic and deterministic. Products are transported from distribution center to retailers according to transportation planning. Cost factors are the transportation cost and the inventory cost, which transportation cost is proportional to transportation distance of vehicle when products are transported from distribution center to retailers, and inventory cost is proportional to inventory amounts of retailers. Transportation time to retailers is represented as a genetic string. The encoding of the solutions into binary strings is presented, as well as the genetic operators used by the algorithm. A mathematical model is developed. Genetic algorithm procedure is suggested, and a illustrative example is shown to explain the procedure.

• Journal of the Korea Safety Management & Science
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• v.3 no.3
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• pp.55-64
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• 2001

The main objective of this research is to develop a model to select the optimal input service level for a distribution center-multi branch inventory distribution system. With the continuous review policy, the distribution center places an order for specific order quantity to an outside supplier, and the order quantity is replenished after a certain lead time Also, each branch places an order for particular order quantity to the distribution center to satisfy the customer demands, and receives the replenishment after a lead time. When an out of stock condition occurs during an order cycle, a backorder is placed to the upper level to fill the unfilled demands. With these situation, variable demand and variable lead time are used for better industrial practice. Further, actual lead times with a generic lead time distribution are used in developing the control model. Under the actual lead time model, the customer service measures actually attained for the distribution center and each branch are explained as the effective customer service measures. Thus, throughout the optimal control (using computer search procedures), we can select the optimal input service levels for the distribution center and each branch to attain the effective service levels for each branch which is consistent with the goal level of service for each branch. At the same time, the entire distribution system keeps minimum inventories.

• Proceedings of the Korea Society for Simulation Conference
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• 2000.11a
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• pp.165-173
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• 2000

Analytic models have been developed to solve integrated production-distribution problems in supply chain management (SCM). As one of major constraints in analytic models, capacity, which is the total operation time in this paper has mostly been known or disregarded assuming infinite capacity. Also, as major factors, machine processing time to fabricate or assemble a part or product at a certain machine center in production system and vehicle processing time to deliver a product to a customer by a certain vehicle in distribution system have been fixed and regarded as a static factor, But in the real systems significant differences exit between capacity and the required time to achieve the production-distribution plan and between processing time and consumed time to process a part or product. In this paper, capacity and processing times in the analytic model are considered as dynamic factors and adjusted by the results from independently developed simulation model, which includes general production-distribution characteristics. Through experiments, we obtain the more realistic solutions reflecting stochastic natures by performing the iterative analytic-simulation procedure.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.6
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• pp.645-650
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• 2018

Software stability is the possibility of operating without any malfunction in the operating environment over time. In a finite failure NHPP for software failure analysis, the failure occurrence rate may be constant, monotonically increasing, or monotonically decreasing. In this study, based on the NHPP model and based on the software failure time data, we compared and analyzed the attributes of the software development cost model using the exponential distribution Rayleigh distribution and inverse exponential distribution considering the shape parameter of the Weibull distribution as the life distribution. The results of this study show that the Rayleigh model is the fastest release time and has the economic cost compared to the inverse-exponential model and the Goel-Okumoto model. Using the results of this study, it can be expected that software developers and operators will be able to predict the optimal release time and economic development cost.