• 응용통계연구
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• 제20권2호
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• pp.333-343
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• 2007

고객의 도착간격시간과 서비스시간 중 어느 하나가 지수분포가 아닌 큐를 분석할 때 중요하게 등장하는 함수가 보조재생함수(auxiliar renewal function)이다. 재생함수와 마찬가지로 보조재생함수도 이론적으로는 정의할 수 있으나 함수값을 실제로 계산하기에는 어려움이 많아 근사값을 구하는 연구가 필요하다. 본 논문에서는 보조재생함수의 값을 근사적으로 계산하는 두 가지 방법을 보여주고 부분적으로 알려져 있는 보조재생 함수의 참값과의 비교를 통하여 두 방법을 서로 비교한다.

• International Journal of Reliability and Applications
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• 제1권1호
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• pp.81-87
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• 2000

One of the most important quantities in reliability theory is the expected number of renewals of a system during a given interval. This quantity, the renewal function, is used to determine the optimal preventive maintenance policy and to estimate the cost of a warranty. In this paper we study a parametric approach for a renewal function. The simulation study is presented to compare the relative performance of the introduced estimators of a renewal function. And we show that the proposed parametric estimator performs well.

• 대한수학회보
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• 제48권2호
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• pp.325-334
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• 2011

In this paper we consider the discrete time delayed renewal risk model. We investigate what will happen when the distribution function of the discounted proper deficit is asymptotic in the initial surplus. In doing this we establish several lemmas regarding some related ruin quantities in the discrete time delayed renewal risk model, which are of significance on their own right.

• 품질경영학회지
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• 제34권1호
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• pp.34-39
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• 2006

This paper applies approximation of the renewal function for Hjorth model and Dhillon model which show the trend change in its aging properties. We obtain the renewal function for Hjorth model and Dhillon model by a numerical solution of an approximate integral. We observe the influence of each parameter in these models. The results of the computation are described and their corresponding graphs are provided.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.607-625
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• 2015

Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.153-159
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• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.125-128
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• 2002

In this paper, we define an availability of network, when the states of links are modeled by alternating renewal processes. The actual availabilities of some simple networks are obtained and compared to each other.

• 한국군사과학기술학회지
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• 제9권2호
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• pp.51-59
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• 2006

The purpose of this paper is to present reliability analysis procedures for repairable systems and apply the procedures for assessing the reliabilities of two subsystems of a specific group of military equipment based on field failure data. The mean cumulative function, M(t), the average repair rate, ARR(t), and analytic test methods are used to determine whether a failure process follows a renewal or non-renewal process. For subsystem A, the failure process turns out to follow a homogeneous Poisson process, and subsequently, its mean time between failures, availability, and the necessary number of spares are estimated. For subsystem B, the corresponding M(t) plot shows an increasing trend, indicating that its failure process follows a non-renewal process. Therefore, its M(t) is modeled as a power function of t, and a preventive maintenance policy is proposed based on the annual mean repair cost.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• 품질경영학회지
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• 제25권4호
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• pp.99-105
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• 1997

We consider a nonparametric estimation of the renewal function. In this paper, we suggest modified methods for Frees's estimator to enhance the efficiency. The methods are based on a piecewise linearization and on the fact that the bounded monotonic functions converging pointwise to the bounded monotonic continuous function converge uniformly. In a simulation study, we show that the modified methods have the better efficiency than that introduced by Frees.