• Journal of Korean Institute of Industrial Engineers
• /
• v.21 no.3
• /
• pp.371-385
• /
• 1995

The yield of semiconductor chips is dependent not only on the average defect density but also on the distribution of defects over a wafer. The distribution of defects leads to consider a cluster index. This paper briefly reviews the existing yield prediction models ad proposes a new cluster index, which utilizes the information about the defect location on a wafer in terms of the coefficient of variation. An extensive simulation is performed under a variety of defect distributions and a yield prediction model is derived through the regression analysis to relate the yield with the proposed cluster index and the average number of defects per chip. The performance of the proposed simulation-based yield prediction model is compared with that of the well-known negative binomial model.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.24 no.3
• /
• pp.109-123
• /
• 1999

Fleet sizing and empty equipment redistribution are two of the most critical problems in managing a fleet of equipment over a transportation network. Where the demand pattern followed the compound Poisson process(CPP) which can be generated one or more at a time under homogeneous Poisson process(HPP), this paper presented a mathematical model to determine control parameters of a decentralized distribution policy and fleet size in case of the pure hub-and-spoke system, a popular form of a logistics system. and validated this model by simulation. That is, where the number of demanded equipments followed geometric and binomial distributions, respectively, cost models on the pure hub-and-spoke logistics system with deterministic trans-portation times, which could be solved analytically, were established and analyzed. We also compared the deterministic case with stochastic one that the transportation time follows some probability distributions.

• Communications for Statistical Applications and Methods
• /
• v.6 no.2
• /
• pp.523-532
• /
• 1999

Generalized linear models have various applications for data arising from many kinds of statistical studies. Although the response variable is generally assumed to be generated from a wide class of probability distributions we focus on count data that are most often analyzed using binomial models for proportions or poisson models for rates. The methods and results presented here also apply to many other categorical data models in general due to the relationship between multinomial and poisson sampling. The novelty of the approach suggested here is that all conditional distribution s can be specified directly so that staraightforward Gibbs sampling is possible. The prior distribution consists of two stages. We rely on a normal nonconjugate prior at the first stage and a vague prior for hyperparameters at the second stage. The methods are demonstrated with an illustrative example using data collected by Rosenkranz and raftery(1994) concerning the number of hospital admissions due to back pain in Washington state.

• The Transactions of the Korea Information Processing Society
• /
• v.7 no.4
• /
• pp.1103-1111
• /
• 2000

The hyper-geometric distribution software reliability growth model (HGDM) usually assumes that all the software faults detected are perfectly removed without introducing new faults. However, since new faults can be introduced during the test-and-debug phase, the perfect debugging assumption should be relaxed. In this context, Hou, Kuo and Chang [7] developed a modified HGDM for imperfect debugging environment, assuming tat the learning factor is constant. In this paper we extend the existing imperfect debugging HGDM for tow respects: introduction of random sensitivity factor and allowance of variable learning factor. Then the statistical characteristics of he suggested model are studied and its applications to two real data sets are demonstrated.

• Journal of Environmental Impact Assessment
• /
• v.6 no.1
• /
• pp.111-119
• /
• 1997

This study was carried out to suggest the best statistical test which may be used to quantify the change of water quality between two groups. Traditional t-test may not be used in cases where the normality of underlying population distribution is not assured. Three non-parametric tests which are based on the relative order of the measurements, were studied to find out the applicability in water quality data analysis. The sign test is based on the sign of the deviation of the measurement from the median value, and the binomial distribution table is used. The signed rank test utilizes not only the sign but also the magnitude of the deviation. The Wilcoxon rank-sum test which is basically same as Mann-Whitney test, tests the mean difference between two independent samples which may have missing data. Among the three non-parametric tests studied, the singed rank test was found out to be applicable in the quantification of the change of water quality between two samples.

• Nuclear Engineering and Technology
• /
• v.44 no.4
• /
• pp.405-414
• /
• 2012

In this paper, we propose a reliability estimation method for DI&C systems. At the system level, a fault tree model is suggested and Boolean algebra is used to obtain the minimal cut sets. At the component level, an exponential distribution is used to model hardware failures, and Bayesian estimation is suggested to estimate the failure rate. Additionally, a binomial distribution is used to model software failures, and a recently developed software reliability estimation method is suggested to estimate the software failure rate. The overall system reliability is then estimated based on minimal cut sets, hardware failure rates and software failure rates.

• Journal of the military operations research society of Korea
• /
• v.23 no.1
• /
• pp.63-75
• /
• 1997

This study is concerned with a few models for optimal requirement level of CSP by improving and adjusting the existing models to determine CSP items and quantity as follows. First, by building a model with a objective function of the operating level and constrains of budget, quantity and items of CSP are simultaneously determined. Second, we removed some steps to improve initial solution by using a constraint of usable budget level. Third, we demonstrated a model to be applied with real operating situation by combining two models of Lee(1994) and above. Lastly, by assuming a failure probability distribution is a binomial distribution, the better solution can be obtained. Some facts with necessity of policy improvement were raised as follows: (1) necessity of improvement of the CSP acquisition system, (2) in case of the same kind, permission of diversion in order to execute budget effectively, (3) getting accurate failure rate.

• Communications for Statistical Applications and Methods
• /
• v.11 no.3
• /
• pp.619-629
• /
• 2004

Binomial group testing or composite sampling is often used to estimate the proportion, p, of positive(infects, defectives) in a population when that proportion is known to be small; the potential benefits of group testing over one-at-a-time testing are well documented. The literature has focused on maximum likelihood estimation. We provide two Bayes estimators and compare them with the MLE. The first of our Bayes estimators uses an uninformative Uniform (0, 1) prior on p; the properties of this estimator are poor. Our second Bayes estimator uses a much more informative prior that recognizes and takes into account key aspects of the group testing context. This estimator compares very favorably with the MSE, having substantially lower mean squared errors in all of the wide range of cases we considered. The priors uses a Beta distribution, Beta ($\alpha$, $\beta$), and some advice is provided for choosing the parameter a and $\beta$ for that distribution.

• The Korean Journal of Applied Statistics
• /
• v.23 no.1
• /
• pp.189-196
• /
• 2010

It is never an easy task to physically randomize the sequence of cards. For instance, US 1970 draft lottery resulted in a social turmoil since the outcome sequence of 366 birthday numbers showed a significant relationship with the input order (Wikipedia, "Draft Lottery 1969", Retrieved 2009/05/01). We are motivated by Laplace's 1825 book titled Philosophical Essay on Probabilities that says "Suppose that the numbers 1, 2, ..., 100 are placed, according to their natural ordering, in an urn, and suppose further that, after having shaken the urn, to shuffle the numbers, one draws one number. It is clear that if the shuffling has been properly done, each number will have the same chance of being drawn. But if we fear that there are small differences between them depending on the order in which the numbers were put into the urn, we can decrease these differences considerably by placing these numbers in a second urn in the order in which they are drawn from the first urn, and then shaking the second urn to shuffle the numbers. These differences, already imperceptible in the second urn, would be diminished more and more by using a third urn, a fourth urn, &c." (translated by Andrew 1. Dale, 1995, Springer. pp. 35-36). Laplace foresaw what would happen to us in 150 years later, and, even more, suggested the possible tool to handle the problem. But he did omit the detailed arguments for the solution. Thus we would like to write the supplement in modern terms for Laplace in this research note. We formulate the problem with a lottery box model, to which Markov chain theory can be applied. By applying Markov chains repeatedly, one expects the uniform distribution on k states as stationary distribution. Additionally, we show that the probability of even-number of successes in binomial distribution with trials and the success probability $\theta$ approaches to 0.5, as n increases to infinity. Our theory is illustrated to the cases of truncated geometric distribution and the US 1970 draft lottery.

• Journal of Korean Society for Quality Management
• /
• v.27 no.4
• /
• pp.143-152
• /
• 1999

In Shewhart control chart, the average run length(ARL) is calculated using the mean of a conventional geometric distribution(CGD) assuming a sequence of identical and independent Bernoulli trials. In this, the success probability of CGB is the probability that any point exceeds the control limits. When the process is in-control state, there is no problem in the above assumption since the probability that any point exceeds the control limits does not change if the in-control state continues. However, if the out-of-control state begins and continues during the process, the probability of exceeding the control limits may take two forms. First, once the out-of-control state begins with exceeding probability p, it continues with the same exceeding probability p. Second, after the out-of-control state begins, the exceeding probabilities may very according to some pattern. In the first case, ARL is the mean of CGD with success probability p as usual. But in the second case, the assumption of a sequence of identical and independent Bernoulli trials is invalid and we can not use the mean of CGD as ARL. This paper concentrate on that point. By adopting one generalized binomial distribution(GBD) model that allows correlated Bernoulli trials, generalized geometric distribution(GGD) is defined and its mean is derived to find an alternative ARL when the process is in out-of-control state and the exceeding probabilities take the second form mentioned in the above. Small-scale simulation is performed to show how an alternative ARL works.