• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.49-64
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• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.

• Kyungpook Mathematical Journal
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• v.21 no.2
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• pp.299-302
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• 1981

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.3
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• pp.219-223
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• 2009

Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables and provided fuzzy random renewal reward theorem on the limit value of the long run expected reward per unit time in the fuzzy random renewal reward process. In this note, we simplify the proofs of two main results of the paper.

• International Journal of Reliability and Applications
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• v.3 no.4
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• pp.185-198
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• 2002

In the traditional life testing model, it is assumed that a certain number of identical items are tested under identical condition. This is due to statistical rather than practical considerations. The proportional hazards model can be used to develop a realistic approach to determine the performance of an item. That is also capable of modeling the failure rates of accelerated life testing when the covariates are applied stresses. The proportional hazards model is typically applied for a group of items to assess the importance of factors that may influence the reliability of an item. In this paper we considered the interarrival times of an item rather than the time to first failure for grouped items and provided the availability estimation for the determination of maintenance policy and overhaul time. In order to demonstrate the proposed approach, an example is presented.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.355-357
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• 2016

Recently, some results of Blackwell's Theorem in which interarrival times are characterized as fuzzy variables under t-norm-based fuzzy operations are discussed by Hong. However, these results are invalid. In this note, we give counter examples of these results.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.415-415
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• 2002

Proportional hazards model can be used to develop a realistic approach to determine the performance of a system. The proportional hazards model is typically applied for a group of equipments to assess the importance of factors that may influence the reliability of a system. In this paper we considered the interarrival times of a maintained system for the analysis of reliability, maintainability and availability. In order to demonstrate the proposed approach, an example is presented.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-236
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• 1995

The purpose of this paper is to provide a transient diffusion approximation of queue size distribution for M/G/m/N system. The M/G/m/N system can be expressed as follows. The interarrival times of customers are exponential and the service times of customers have general distribution. The system can hold at most a total of N customers (including the customers in service) and any further arriving customers will be refused entry to the system and will depart immediately without service. The queueing system with finite capacity is more practical model than queueing system with infinite capacity. For example, in the design of a computer system one of the important problems is how much capacity is required for a buffer memory. It its capacity is too little, then overflow of customers (jobs) occurs frequently in heavy traffic and the performance of system deteriorates rapidly. On the other hand, if its capacity is too large, then most buffer memories remain unused.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.1
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• pp.110-122
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• 1993

When voice is transmitted through packet switching network, there needs a overload control, that is, a control for the congestion which lasts short periods and occurrs in local extents. In this thesis, we analyzed the performance of the statistical packet voice multiplexer using the overload control strategy by bit dropping. We assume that the voice is coded accordng to (4,2) embedded ADPCM and that the voice packet is generated and transmitted according to the procedures in the CCITT recomendation G. 764. For the performance analysis, we must model the superposed packet arrival process to the multiplexer as exactly as possible. It is well known that interarrival times of the packets are highly correlated and for this reason MMPP is more suited for the modelling in the viewpoint of accuracy. Hence the packet arrival process in modeled as MMPP and the matrix geometric method is used for the performance analysis. Performance analysis is similar to the MMPP IG II queueing system. But the overload control makes the service time distribution G dependent on system status or queue length in the multiplexer. Through the performance analysis we derived the probability generating function for the queue length and using this we derived the mean and standard deviation of the queue length and waiting time. The numerical results are verified through the simulation and the results show that the values embedded in the departure times and that in the arbitrary times are almost the same. Results also show bit dropping reduces the mean and the variation of the queue length and those of the waiting time.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.4
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• pp.37-50
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• 1994

The efficiency of production system is mainly considered in the viewpoints of reducing the average flow time of products and increasing the throughput rate. The performance in these viewpoints is very depending on job dispatching of each machine in real time operation, in the case jobs are released dynamically. In this research, a heuristic dynamic dispatching method is suggested for a flow shop case where new jobs with random process times are released by an interarrival time distribution and the number of waiting jobs between each pair of machines are limited. The proposed method has been compared with some priority rule-based dispatching methods by simulation and found to be superior to them.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.895-906
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• 2015

Recently, Li [12] gave an asymptotic formula for the ultimate ruin probability in a delayed-claim risk model with constant force of interest and pairwise quasi-asymptotically independent and extended-regularly-varying-tailed claims. This paper extends Li's result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.