• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.725-741
• /
• 1997

This paper considers the problem of deriving exponential probability inequalities for product symmetric Poisson processes. As an application they are used to show the existence of regular version of some product process derived from L$\acute{e}$vy process.

• Communications of the Korean Mathematical Society
• /
• v.10 no.1
• /
• pp.195-205
• /
• 1995

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.2
• /
• pp.387-394
• /
• 2004

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.6 no.2
• /
• pp.51-55
• /
• 1981

In both continuous-review and periodic-review non-stationary inventory systems, the non-stationary Poisson demand process and the associated inventory position processes were proved being mutually independent of each other, which lead to the probability distribution of the corresponding net inventory position process in the form of a finite product sum of those two process distributions. It is also discussed how these results can correspond to analytical stochastic inventory cost function formulations in terms of the probability distributions of the processes.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.3
• /
• pp.153-168
• /
• 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 backordered. 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, the proportion of backordered demands, the average number of backordered demands and the mean waiting time of a backordered demand. 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 matrix geometric method 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 approximate method provides fairly good results.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.221-231
• /
• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Journal of Korean Institute of Industrial Engineers
• /
• v.39 no.3
• /
• pp.172-182
• /
• 2013

In this study we consider a flow line CONWIP system in which two types of product are produced. The processing times of each product type at each station follow an independent exponential distribution and the demands for the finished products of each type arrive according to a Poisson process. The demands that are not satisfied instantaneously are either backordered or lost according to the number of unsatisfied demands that exist at their arrival instants. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts of each product type at each station, mean waiting times of backordered demands and the proportion of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a two class closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method for multiple classes developed by Baynat and Dallery. In the approximation method, each subsystem is analyzed using a matrix geometric method. Comparisons with simulation show that the approximation method provides fairly good results for all performance measures.

• Journal of Korea Society of Digital Industry and Information Management
• /
• v.10 no.2
• /
• pp.1-11
• /
• 2014

Software reliability in the software development process is an important issue. Software process improvement helps in finishing with reliable software product. In this field, SPC (Statistical process control) is a method of process management through application of statistical analysis, which involves and includes the defining, measuring, controlling, and improving of the processes. The proposed process involves evaluation of the parameter of the mean value function and hence the values of the mean value function at various inter failure times to develop relevant time control chart. In this paper, was proposed a control mechanism, based on time between failures observations using Rayleigh and Burr distribution property, which is based on Non Homogeneous Poisson Process (NHPP). In this study, the proposed model is reliable in terms of hazard function, because it is more efficient in this area can be used as an alternative to the existing model. Through this study, software developers are considered by the various intended functions, prior knowledge of the software to identify failure modes to feed to some extent shall be able to help.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.17 no.3
• /
• pp.27-46
• /
• 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 Operations Research and Management Science Society
• /
• v.31 no.3
• /
• pp.63-79
• /
• 2006

In this study we consider a CONWIP system in which the processing times at each station follow a Coxian distribution and the demands for the finished products arrive according to a compound Poisson process. The demands that are not satisfied immediately are either backordered or lost according to the number of demands that exist at their arrival Instants. For this system we develop an approximation method to calculate performance measures such as steady state probabilities of the number of parts at each station, proportion of lost demands and the mean number of backordered 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 are compared with those obtained by simulation. Comparisons with simulation show that the approximation method provides fairly good results.