• Journal of the Korean Statistical Society
• /
• v.28 no.2
• /
• pp.235-251
• /
• 1999

In this paper we examine extremal behavior of a $textsc{k}$th-order stationary Markov chain {X\ulcorner} by considering excesses over a high level which typically appear in clusters. Excesses over a high level within a cluster define a cluster damage, i.e., a normalized sum of all excesses within a cluster, and all excesses define a damage point process. Under some distributional assumptions for {X\ulcorner}, we prove convergence in distribution of the cluster damage and obtain a representation for the limiting cluster damage distribution which is well suited for simulation. We also derive formulas for the mean and the variance of the limiting cluster damage distribution. These results guarantee a compound Poisson limit for the damage point process, provided that it is strongly mixing.

• Journal of the Semiconductor & Display Technology
• /
• v.17 no.4
• /
• pp.42-45
• /
• 2018

As The semiconductor decrease from 10 nanometer to 7 nanometer, It is suggested that "More than Moore" is needed to follow Moore's Law, which has been a guide for the semiconductor industry. Fan-Out Wafer Level Package(FOWLP) is considered as the key to "More than Moore" to lead the next generation in semiconductors, and the reasons are as follows. the fan-out WLP does not require a substrate, unlike conventional wire bonding and flip-chip bonding packages. As a result, the thickness of the package reduces, and the interconnection becomes shorter. It is easy to increase the number of I / Os and apply it to the multi-layered 3D package. However, FOWLP has many issues that need to be resolved in order for mass production to become feasible. One of the most critical problem is the warpage problem in a process. Due to the nature of the FOWLP structure, the RDL is wired to multiple layers. The warpage problem arises when a new RDL layer is created. It occurs because the solder ball reflow process is exposed to high temperatures for long periods of time, which may cause cracks inside the package. For this reason, we have studied warpage in the FOWLP structure using commercial simulation software through the implementation of the reflow process. Simulation was performed to reproduce the experiment of products of molding compound company. Young's modulus and poisson's ratio were found to be influenced by the order of influence of the factors affecting the distortion. We confirmed that the lower young's modulus and poisson's ratio, the lower warpage.

• IE interfaces
• /
• v.11 no.3
• /
• pp.55-63
• /
• 1998

In this study we consider a CONWIP system in which the processing times at each station follow an exponential distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied instantaneously are assumed to be lost. We assume that the lot size at each station is greater than one. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts at each station, average number of parts at each station and the proportion of lost demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a closed queueing network with a synchronization station and analyze the closed queueing network using a product form approximation method. A recursive technique is used to solve the subnetwork in the application of the product-form approximation method. To test the accuracy of the approximation method, the results obtained from the approximation method were compared with those obtained by simulation. Comparisons with simulation have shown that the accuracy of the approximate method is acceptable.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.27 no.2
• /
• pp.111-121
• /
• 2002

In this paper, we analyze an M$^{x}$ /G/1 with three types of vacation periods including setup time. Three types of vacations are : N-policy, single vacation, and multiple vacation. We consider compound poisson arrival process and general service time, where the server starts his service when a setup is completed. We find the PGF of the number of customers in system and LST of waiting time, with welch we obtain their means. A decomposition property for the system sloe and waiting time is described also.

• Journal of the Korean Statistical Society
• /
• v.31 no.4
• /
• pp.491-507
• /
• 2002

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

• The Korean Journal of Applied Statistics
• /
• v.25 no.1
• /
• pp.81-87
• /
• 2012

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below ${\tau}$(0 < ${\tau}$ < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.27 no.4
• /
• pp.246-257
• /
• 2015

The progressive degradation paths of structures have quantitatively been tracked by using stochastic processes, such as Wiener process, gamma process and compound Poisson process, in order to consider both the sampling uncertainty due to the usual lack of damage data and the temporal uncertainty associated with the deterioration evolution. Several important features of stochastic processes which should carefully be considered in application of the stochastic processes to practical problems have been figured out through assessing cumulative damage and lifetime distribution as a function of time. Especially, the Wiener process and the gamma process have straightforwardly been applied to armors of rubble-mound breakwaters by the aid of a sample path method based on Melby's formula which can estimate cumulative damage levels of armors over time. The sample path method have been developed to calibrate the related-parameters required in the stochastic modelling of armors of rubble-mound breakwaters. From the analyses, it is found that cumulative damage levels of armors have surely been saturated with time. Also, the exponent of power law in time, that plays a significant role in predicting the cumulative damage levels over time, can easily be determined, which makes the stochastic models possible to track the cumulative damage levels of armors of rubble-mound breakwaters over time. Finally, failure probabilities with respect to various critical limits have been analyzed throughout its anticipated service life.