• Communications for Statistical Applications and Methods
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• v.25 no.1
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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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• v.7 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1165-1172
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• 2016

In this paper, a surplus process with investments is introduced. Whenever the level of the surplus reaches a target value V > 0, amount S($0{\leq}S{\leq}V$) is invested into other business. After assigning three costs to the surplus process, a reward per unit amount of the investment, a penalty of the surplus being empty and the keeping (opportunity) cost per unit amount of the surplus per unit time, we obtain the long-run average cost per unit time to manage the surplus. We prove that there exists a unique value of S minimizing the long-run average cost per unit time for a given value of V, and also that there exists a unique value of V minimizing the long-run average cost per unit time for a given value of S. These two facts show that an optimal investment policy of the surplus exists when we manage the surplus in the long-run.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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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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• v.32 no.1
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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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• v.3 no.4
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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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• v.26 no.1
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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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• v.22 no.6
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• pp.1089-1096
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• 2011

We consider an infinite dam with inputs formed by a compound Poisson process and adopt a $P^M_{\lambda}$-policy to control the level of water, where the water is released at rate M when the level of water exceeds threshold ${\lambda}$. We obtain interesting stationary properties of the level of water, when the amount of each input independently follows an exponential distribution. After assigning several managing costs to the dam, we derive the long-run average cost per unit time and show that there exist unique values of releasing rate M and threshold ${\lambda}$ which minimize the long-run average cost per unit time. Numerical results are also illustrated by using MATLAB.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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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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• v.19 no.4
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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.