• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.243-252
• /
• 2001

The points of failure of a decomposition process are defined to be the union of the points of failure from two component point processes for software reliability systems. Because sampling from the likelihood function of the decomposition model is difficulty, Gibbs Sampler can be applied in a straightforward manner. A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For model determination, we explored the prequential conditional predictive ordinate criterion that selects the best model with the largest posterior likelihood among models using all possible subsets of the component intensity functions. A numerical example with a simulated data set is given.

• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.519-530
• /
• 2001

A two commodity continuous review inventory system with independent Poisson processes for the demands is considered in this paper. The maximum inventory level for the i-th commodity fixed as $S_i$(i = 1,2). The net inventory level at time t for the i-th commodity is denoted by $I_i(t),\;i\;=\;1,2$. If the total net inventory level $I(t)\;=\;I_1(t)+I_2(t)$ drops to a prefixed level s $[{\leq}\;\frac{({S_1}-2}{2}\;or\;\frac{({S_2}-2}{2}]$, an order will be placed for $(S_{i}-s)$ units of i-th commodity(i=1,2). The probability distribution for inventory level and mean reorders and shortage rates in the steady state are computed. Numerical illustrations of the results are also provided.

• 한국경영과학회지
• /
• 제29권3호
• /
• pp.63-78
• /
• 2004

This paper deals with a supplier-managed inventory(SMI) control for a two-echelon supply chain model with a service facility and a single supplier. The service facility is allocated to customers and provides a service using items of inventory that are purchased from the supplier, Assuming that the supplier knows the information of customer queue length as well as inventory position in the service facility at the time when it makes a replenishment decision, we identify an optimal replenishment policy which minimizes the total supply chain costs by reflecting these information into the replenishment decision. Numerical analysis demonstrates that the SMI strategy can be more cost-effective when the information of both customer queue length and inventory position is shared than when the information of inventory position only is shared.

• Journal of applied mathematics & informatics
• /
• 제6권2호
• /
• pp.553-568
• /
• 1999

This paper is of concern to queueing analysis of the dynamic rate leaky bucket(LB) scheme in which the token generation interval changes according to the buffer state at a token generation epoch. Cell arrivals are assumed to follow a Markovian arrival process (MAP) which is weakly dense in the class of the stationary point processes. By using the embedded Markov chain method we obtain the probability distribution of the system state at a token generation epoch and an arbitrary time. Some simple numerical examples also are provided to show the effects of the proposed LB scheme.

• 대한수학회보
• /
• 제46권4호
• /
• pp.673-689
• /
• 2009

We analyze $MAP_1,\;MAP_2$/G/1 finite queues with service scheduling function dependent upon queue lengths. The customers are classified into two types. The arrivals of customers are assumed to be the Markovian Arrival Processes (MAPs). The service order of customers in each buffer is determined by a service scheduling function dependent upon queue lengths. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, the performance measures such as loss probability and mean waiting time are derived. Some numerical examples also are given with applications in telecommunication networks.

• 대한수학회지
• /
• 제36권1호
• /
• pp.139-157
• /
• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• 응용통계연구
• /
• 제21권5호
• /
• pp.835-843
• /
• 2008

In this paper, we investigate a Bayesian inference for software reliability models based on mean value functions which take the form of the mixture of beta distribution functions. The posterior simulation via the Markov chain Monte Carlo approach is used to produce estimates of posterior properties. Its applicability is illustrated with two real data sets. We compute the predictive distribution and the marginal likelihood of various models to compare the performance of them. The model comparison results show that the model based on the beta-mixture performs better than other models.

• Journal of the Korean Data and Information Science Society
• /
• 제18권2호
• /
• pp.553-560
• /
• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.157-172
• /
• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• 대한수학회지
• /
• 제50권6호
• /
• pp.1165-1181
• /
• 2013

In this paper, we consider a class of periodic It$\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\hat{o}$ et al. [6], Bainov et al. [1] and Xu et al. [15]. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al. [7].