• 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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• 제7권3호
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• pp.773-788
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• 2000

Statistical process control (SPC) and engineering process control (EPC) are based on different strategies for processes quality improvement. SPC reduces process variability by detecting and eliminating special causes of process variation. while EPC reduces process variability by adjusting compensatory variables to keep the quality variable close to target. Recently there has been needs for a process control proceduce which combines the tow strategies. This paper considers a combined scheme which simultaneously applies SPC and EPC techniques to reduce the variation of a process. The process model under consideration is an integrated moving average(IMA) process with a step shift. The EPC part of the scheme adjusts the process back to target at every fixed monitoring intervals, which is referred to a repeated adjustment scheme. The SPC part of the scheme uses an exponentially weighted moving average(EWMA) of observed deviation from target to detect special causes. A Markov chain model is developed to relate the scheme's expected cost per unit time to the design parameters of he combined control scheme. The expected cost per unit time is composed of off-target cost, adjustment cost, monitoring cost, and false alarm 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.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2000년도 추계학술대회
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• pp.387-395
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• 2000

Circular consecutive-k-out-of-n:F system when the failure of component is dependent is studied. We assume that the failure of a component in the system increase the failure rate of the survivor which is working just before the failed component. In this case, a mean time to failure (MTTF), a average failure number of the system, and the expected cost per unit time are obtained. Then the minimum number of consecutive failed components to cause system failure to minimize the expected cost per unit time is determined as searching paths to system failure. And various numerical examples are studied.

• 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.

• International Journal of Reliability and Applications
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• 제3권4호
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• pp.165-171
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• 2002

An optimization of the M/M/1 queue with impatient customers is studied. The impatient customer does not enter the system if his or her virtual waiting time exceeds the threshold K ＞ 0. After assigning three costs to the system, a cost proportional to the virtual waiting time, a penalty to each impatient customer, and also a penalty to each unit of the idle period of the server, we show that there exists a threshold K which minimizes the long-run average cost per unit time.

• 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.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1089-1096
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• 2011

본 논문에서는 댐으로 물이 복합 포아송 과정을 따라 유입되고, 댐 수위가 적정수준 ${\lambda}$를 넘어서게 되면 방출률 M으로 물을 방출하는 무한 댐 모형이 고려된다. 한번 내리는 비의 양이 지수분포를 따르는 경우, 정상상태에서 댐 수위의 확률적 성질들을 구한다. 댐 운영과 관리에 관련된 여러 비용을 고려한 후, 장시간에 걸친 단위시간당 평균 비용을 구하고, 이를 최소화하는 방출률 M과 적정수준${\lambda}$가 유일하게 존재함을 보인다. MATLAB을 이용하여 수치적인 결과도 함께 보인다.

• 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.

• 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.