• International Journal of Reliability and Applications
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• 제1권1호
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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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• 제21권2호
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• pp.299-302
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• 1981

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권3호
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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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• 제3권4호
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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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• 제34권3_4호
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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.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2002년도 정기학술대회
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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.

• 대한수학회지
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• 제32권2호
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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.

• 한국통신학회논문지
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• 제18권1호
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• pp.110-122
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• 1993

음성이 패킷망을 통해 전송될때 각각의 call들에 의해서 발생되는 패킷들은 statistical multiplexer에 의해 다중화 되는데 이때 overload control이 필요하다. Overload control 방식은 음성 traffic을 coding하는 방식과 밀접한 관계가 있으며 그동안 많은 연구가 진행되어 왔다. CCITT에서는 최근에 packetized voice protocol에 대한 권고안 초안인 G.764를 작성하였는데 여기에서 embedded coding을 사용하는 경우에 bit dropping 방식을 사용하면 매우 훌륭하게 overload control을 할 수 있다는 사실을 언급하였다. 이에 따라 본 논문에서는 음성을 embedded ADPCM으로 coding하여 CCITT권고안 G.764에 따라 전송하는 경우에, bit dropping 방식에 따른 overload control 방식을 사용하는 패킷 multiplexer의 성능을 분석하고자 한다. 성능 분석을 위해서는 먼저 multiplexer에 도착하는 중첩된 packet arrival process에서 패킷들의 interarrival time들 간에 존재하는 큰 correlation을 정확히 나타낼 수 있는 수학적인 model이 필요하다. 본 논문에서는 Poisson process나 birth-and-death process에 비해 이들 packet arrival process를 상대적으로 정확히 표현할 수 있는 Makov-modulated Poisson Process(MMPP)를 사용하여 모델링을 하였다.따라서 성능분석은 MMPP/G/1 queueing system에 대한 분석과 비슷하다. 다만 서비스 시간의 분포가 시스템의 상태에 따라 달라지는데 이러한 경우에 대해서는 기존의 논문에서 분석되지 않았다. 성능분석을 통하여 queue에서 서비스를 기다리는 패킷의 수에 대한 분포의 Z-transform을 구하고 이를 이용하여 임의의 시간에서의 queue length와 waiting time의 평균과 표준편차를 구하였다. 이를 통하여 bit dropping 방식에 의한 overload control이 음성의 질을 많이 저하시키지 않으면서도 overload control을 하지 않을 때에 비해 statistical multiplexer에서 훨씬 많은 수의 call을 수용할 수 있도록 하는 효과를 가진다는 사실을 확인 하였다. 또한 패킷이 queue에서 떠난 직후와 임의의 시간에서 구한 queue length와 waiting time의 평균과 표준편차가 매우 비슷하다는 사실을 알 수 있었다. 본 논문에서와 마찬가지로 임의의 시간에서의 분석은 매우 복잡한 경우가 대부분이므로 이러한 사실을 이용하면 매우 간단히 성능분석을 할 수 있을 것이다.

• 대한산업공학회지
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• 제20권4호
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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.

• 대한수학회보
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• 제52권3호
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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.