• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.123-128
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• 2004

A finite dam under $P_{\lambda,;,T}^M-policy$ is considered, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. Explicit expression is deduced for the stationary distribution of the level of water. And the long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty which is a function of the level of water in the reservoir.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.159-167
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• 2004

We present a simple approach to finding the stationary workload of M/G/1 queues having generalized vacations and exhaustive service discipline. The approach is based on the level crossing technique. According to the approach, all that we need is the workload at the beginning of a busy period. An example system to which we apply the approach is the M/G/1 queue with both multiple vacations and D-policy.

• Journal of Korean Institute of Industrial Engineers
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• v.16 no.1
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• pp.107-114
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• 1990

A queueing system with compound Poisson arrival and server vacation is analyzed by including supplementary variables. We consider a vacation system in which the server leaves for a vacation as soon as the system empties. When he returns, if no customer is waiting for service, he waits until a group of customers arrive and then begins to serve. We obtain the system size distribution and the waiting time distribution. Additional performance measures will be also considered.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.205-218
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• 1996

본 연구는 써버의 고장을 허용하는 단수써버 Queueing 시스템의 확률적 모델을 제시한 것으로, 써버는 N 제어 정책에 의하여 작동되며, 도착은 Stationary compound poisson에 의하여 이루어지고, 서비스 시간에 대한 분포는 Erlang에 의하여 발생하며, 수리시간에 대한 분포는 평균이 일정한 분포에 의하여 생성되는 경우를 고려하였다. 또한 고장간격 시간은 일정한 평균을 가진 임의의 분포를 가진 Renewal process에 의한다고 가정하였고, 완료 시간의 개념은 재생과정의 적용방법에 의하여 유도할 수 있으며, 시스템 크기의 확율 생성 함수의 값이 구해진다는 것을 제시하였다.

• 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 Operations Research and Management Science Society
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• v.17 no.3
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• pp.27-46
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• 1992

This paper considers an (r, Q) policy for operation of a multipurpose facility. It is assumed that whenever the inventory level falls below r, the model starts to produce the fixed amount of Q. The facility can be utilized for extra production during idle periods, that is, when the inventory level is still greater than r right after a main production operation is terminated or an extra production operation is finished. But, whenever the facility is in operation for an extra production, the operation can not be terminated for the main production even though the inventory level falls below r. In the model, the demand for the product is assumed to arrive according to a compound Poisson process and the processing time required to produce a product is assumed to follow an arbitary distribution. Similarly, the orders for the extra production is assumed to accur in a Poisson process are the extra production processing time is assumed to follow an arbitrary distribution. It is further assumed that unsatisfied demands are backordered and the expected comulative amount of demands is less than that of production during each production period. Under a cost structure which includes a setup/ production cost, a linear holding cost, a linear backorder cost, a linear extra production lost sale cost, and a linear extra production profit, an expression for the expected cost per unit time for a given (r, Q) policy is obtained, and using a convex property of the cost function, a procedure to find the optimal (r, Q) policy is presented.

• Journal of the Korean Society of Industry Convergence
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• v.23 no.6_2
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• pp.1103-1110
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• 2020

In this study, a segmented model with Upside-Down bathtub shaped failure intensity for a repairable system are proposed under the assumption that the occurrences of the failures of a repairable system follow the Non-Homogeneous Poisson Process. The proposed segmented model is the compound model of S-PLP and LIP (Segmented Power Law Process and Logistic Intensity Process), that fits the separate failure intensity functions on each segment of time interval. The maximum likelihood estimation is used for estimating the parameters of the S-PLP and LIP model. The case study of system A shows that the S-PLP and LIP model fits better than the other models when compared by AICc (Akaike Information Criterion corrected) and MSE (Mean Squared Error). And it also implies that the S-PLP and LIP model can be useful for explaining the failure intensities of similar systems.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.937-942
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• 2009

In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

• Explosives and Blasting
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• v.27 no.1
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• pp.32-37
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• 2009

To look over the effect of mixed proportion of cement, sand and water on strength, 162 tests were made for 9 mix proportions. It was observed that strength increased as water in the mixture is reduced. As a result of the control of sand ratio by 50%, the execution strength increased when the sand ratio is raised. Strength was consistent during curing period on each mix proportion, but there were sections where it suddenly increased. Poisson's ratio widely ranged from 0.13 to 0.27, and Young's modulus also broadly ranged from 13.79MPa to 33.25MPa. Poisson's ratio had nothing to do with uniaxial compressive strength, wheras Young's modulus was concerned with it. Young's modulus from theory and experiment showed similar outcome on the 3rd curing day, however, the strength from theory was higher than that from test after 3rd day. In consequence, there was a great change of strength between 3rd and 7th curing day. In addition, it is more efficient to use field strength value between the 3rd and 7th day and to apply Young's modulus on it for determining the exact time.

• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.591-610
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• 2017

This paper is concerned with the static analysis of variable thickness of two directional functionally graded porous materials (FGPM) circular plate resting on a gradient hybrid foundation (Horvath-Colasanti type) with friction force and subjected to compound mechanical loads (e.g., transverse, in-plane shear traction and concentrated force at the center of the plate).The governing state equations are derived in terms of displacements based on the 3D theory of elasticity, assuming the elastic coefficients of the plate material except the Poisson's ratio varying continuously throughout the thickness and radial directions according to an exponential function. These equations are solved semi-analytically by employing the state space method (SSM) and one-dimensional differential quadrature (DQ) rule to obtain the displacements and stress components of the FGPM plate. The effect of concentrated force at the center of the plate is approximated with the shear force, uniformly distributed over the inner boundary of a FGPM annular plate. In addition to verification study and convergence analysis, numerical results are displayed to show the effect of material heterogeneity indices, foundation stiffness coefficients, foundation gradient indices, loads ratio, thickness to radius ratio, compressibility, porosity and friction coefficient of the foundation on the static behavior of the plate. Finally, the responses of FG and FG porous material circular plates to compound mechanical loads are compared.