• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.651-656
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• 2006

Wu and Clements-Croome (2005) investigate the optimization problem of PM policies for situations where the quality of PM is a random variable with a certain probability distribution. However, they assume that the cost of preventive maintenance is constant, not depending on the quality of PM. Thus, this paper considers a periodic PM model when PM cost depends on the quality of PM activity. The optimal PM policy are presented for the extended PM model and the numerical examples are presented for illustrative purpose.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.103-114
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• 1994

For a $2 \times 2$ factorial design without the restriction of a linear model or without regard to error terms having homoscedasticity, under the null hypothesis of no interaction we can have the rank transformed F statistic for interaction converge in distribution to a chi-squared random variable with one degree of random if and only if there is only main effect.

• 대한수학회지
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• 제55권2호
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• pp.447-469
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• 2018

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.923-931
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• 2005

The two parameter generalized exponential distribution was recently introduced by Gupta and Kundu (1999). It is observed that the generalized exponential distribution can be used quite effectively to analyze skewed data set. This paper develops the accelerated life test model using generalized exponential distribution and considers maximum likelihood estimation of parameters under the tampered random variable model. To show the performance of proposed maximum likelihood estimates, some simulation will be performed. Using a real data set, an example will be given.

• 대한산업공학회지
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• 제31권3호
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• pp.194-200
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• 2005

A stochastic dynamic lot sizing problem for multi-item is suggested in the case that the distribution of the cumulative demand is known over finite planning horizons and all unsatisfied demand is fully backlogged. Each item is produced simultaneously at a variable ratio of input resources employed whenever setup is incurred. A dynamic programming algorithm is proposed to find the optimal production policy, which resembles the Wagner-Whitin algorithm for the deterministic case problem but with some additional feasibility constraints.

• 한국경영과학회지
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• 제17권2호
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• pp.107-115
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• 1992

Many manufacturing processes involved in the fabrication and assembly of hightech components have highly variable yields that tend to complicate the production control. Under this random yield situation we develop a model to determine optimal input quantity, mean waiting time in the system and variance of waiting time in the system. An example which considers beta distribution as a yield distribution is given.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.21-34
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• 1999

In this paper, conditional expectation of a fuzzy random variable is introduced and its properties are investigated. Using this, we introduce the concept of fuzzy martingales and prove some convergence theorems which generalize te corresponding results for the classical martingales.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.195-204
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• 2006

In this paper, we consider a renewal process in which both the inter-arrival times and rewards are fuzzy random variables. We prove the uniform levelwise convergence of fuzzy renewal and fuzzy renewal rewards. These results improve the result of Popova and Wu[European J. Oper. Research 117(1999), 606-617] and the main result of Hwang [Fuzzy Sets and Systems 116 (2000), 237-244].

• Journal of the Korean Data and Information Science Society
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• 제22권4호
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.219-231
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• 2006

When the correlation of two random variables is weak, the value of one variable can not be used effectively to predict the other. Even when most of the values are overlapped, it is difficult to find a linear relationship. In this paper, we propose two graphical methods of representing the measures of correlation and independence between two random variables. The first method is used to represent their degree of correlation, and the other is used to represent their independence. Both of these methods are based on the cumulative distribution functions defined in this work.