• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.65-71
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• 2003

We consider the finite dam with compound Poisson inputs which is called M/G/1 finite dam. We assign some costs related to operating the dam and calculate the long-run average cost per unit time. Then, we find the optimal dam capacity under which the average costs is minimized.

• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.147-154
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• 1997

An infinite dam with a compound Poisson input having exponential jumps is considered. As an output policy, we adopt the $P_{\lambda}$$^{M}$ Policy. After assigning costs to the dam we obtain the long-rum average cost per unit time of operating the dam and find the optimal values of .lambda. and M which minimize the long-run average cost.t.

• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.91-97
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• 2018

In this paper, we show that there exists an optimal investment policy for the surplus in a risk model, in which the surplus is continuously invested to other business at a constant rate a > 0, whenever the level of the surplus exceeds a given threshold V > 0. We assign, to the risk model, two costs, the penalty per unit time while the level of the surplus being under V > 0 and the opportunity cost per unit time by keeping a unit amount of the surplus. After calculating the long-run average cost per unit time, we show that there exists an optimal investment rate $a^*$>0 which minimizes the long-run average cost per unit time, when the claim amount follows an exponential distribution.

• Communications for Statistical Applications and Methods
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• 제11권3호
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• pp.631-641
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• 2004

In this paper, a model for an inventory whose stock decreases with time is considered. When a deliveryman arrives, if the level of the inventory exceeds a threshold $\alpha$, no stock is delivered, otherwise a delivery is made. It is assumed that the size of a delivery is a random variable Y which is exponentially distributed. After assigning various costs to the model, we calculate the long-run average cost and show that there exist unique value of arrival rate of deliveryman $\alpha$, unique value of threshold $\alpha$ and unique value of average delivery m which minimize the long-run average cost.

• Journal of the Korean Data and Information Science Society
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• 제15권4호
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• pp.773-782
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2004년도 추계학술대회
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• pp.33-42
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• 2004

In this paper, a random shock model for a system is considered. Each shock arriving according to a Poisson process decreases the state of the system by a random amount. A repairman arriving according to another Poisson process of rate $\lambda$ repairs the system only if the state of the system is below a threshold $\alpha$. After assigning various costs to the system, we calculate the long-run average cost and show that there exist a unique value of arrival rate $\lambda$ and a unique value of threshold $\alpha$ which minimize the long-run average cost per unit time.

• International Journal of Reliability and Applications
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• 제4권2호
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• pp.51-56
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• 2003

A k-out-of-n system with n identical and independent components is considered in which the components takes two types of function: 0 (open-circuit) or 1 (closed) on command (e.g. electromagnetic relays and solid state switches). Components are subject to two types of failure on command: failure to close or failure to open. In our k-out-of-n system, failure of (n-k)＋1 or more components to close causes to the close failure of the system, or failure of k or more components to open causes the open failure of the system. The long-run average cost rate is obtained. We find the optimal k minimizing the long run average cost rate for given n. A numerical example is presented.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1345-1352
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• 2008

An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.85-89
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• 1997

In this paper, we consider a random replacement model with minimal repair, which is a generalization of the random replacement model introduced Lee and Lee(1994). It is assumed that a system is minimally repaired when it fails and replaced only when the accumulated operating time of the system exceeds a threshold time by a supervisor who arrives at the system for inspection according to Poisson process. Assigning the corresponding cost to the system, we obtain the expected long-run average cost per unit time and find the optimum values of the threshold time and the supervisor's inspection rate which minimize the average cost.

• 응용통계연구
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• 제29권7호
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• pp.1165-1172
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• 2016

보험 상품의 잉여금은 보험료 수입에 의해 증가하며 고객이 보험료를 청구할 때 감소한다. 보험회사는 잉여금이 충분히 많아지면 잉여금의 일부를 재투자하는 것을 통해 이익을 창출한다. 본 연구에서는 보험료 수입과 청구를 고려하여 잉여금의 수준을 나타낸 기존의 잉여금 모형을 소개하고 기존의 모형에 재투자의 개념과 운용비용을 도입하여 장시간에 걸친 단위시간당 평균비용을 구하고, 이를 최소화하는 재투자 수준과 목표 잉여금을 구한다.