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

• Ocean and Polar Research
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• v.39 no.2
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• pp.73-84
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• 2017

The probability distribution of ichthyoplankton is important for enhancing the precision of sampling while reducing unnecessary surveys. To estimate the ichthyoplankton detection proportion (IDP) and its margin of error (ME), the monitoring information of the chub mackerel's (Scomber japonicus) ichthyoplankton presence-absence sampling data has been were collected over approximately 30 years (from 1982 to 2011) in the Korean coastal seas. Based on the computed spatial distributions of the mackerel's IDP and ME, the confidence interval (CI) range, defined as 2 ME, decreases from approximately 80% to 40% as the sample size n increases from 4 to 24 and the ME is approximately 40% in the typical (seasonal survey) case n = 4 per year. The IDP and ME off Jeju Island are relatively high at the 0.5-degree smoothing level. After increasing the spatial smoothing level to 1.0-degree, the ME decreased, and the spatial distribution pattern also changed due to the over-smoothing effects. In this study, the 0.5-degree smoothing is more suitable for the distribution pattern than the 1.0-degree smoothing level. The area of the high IDP and the low ME on the mackerel's ichthyoplankton was similar to the estimated spawning ground in the Korean peninsula. This information could contribute to enhancing for the spawning ecology surveys.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.177-193
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• 2010

The purpose of this study is to explore normal distribution in probability distributions of the area of statistics in high school mathematics. To do this these contents such as approximation of normal distribution from binomial distribution, investigation of normal distribution curve and the area under its curve through the method of Monte Carlo, linear transformations of normal distribution curve, and various types of normal distribution curves are explored with CAS calculator. It will not be ablt to be attained for the objectives suggested the area of probability distribution in a paper-and-pencil classroom environment from the perspectives of tools of CAS calculator such as trivialization, experimentation, visualization, and concentration. Thus, this study is to explore various properties of normal distribution curve with CAS calculator and derive from pedagogical implications of teaching and learning normal distribution curve.

• Korean Journal of Agricultural Science
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• v.47 no.3
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• pp.615-624
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• 2020

An effective sampling method is necessary to monitor potato tuber moths (Phthorimaea operculella) because they are the biggest concern in potato-cultivating areas. In this study, a sequential sampling method was developed based on the results of field surveys of potato tuber moths in South Korea. Potato tuber moths were collected in fields cultivating potatoes at six sites, and their spatial distribution was investigated using the Taylor power law. The optimal sampling size and cumulative number of potato tuber moths in traps to stop sampling were determined based on the spatial distribution pattern and mean density of the collected potato tuber moths. Finally, the developed sampling method was applied to propose a control action, and its sampling efficiency was compared with that of the traditional sampling method using a binomial distribution. The potato tuber moths tended to aggregate; the optimal number was approximately 5 - 16 traps for sampling, and the number varied with the mean density of potato tuber moths according to the sampling sites. In addition, one, two, and three sites might require the following actions: Continued sampling, control, and no control, respectively. Sampling with the binomial distribution showed the minimum sample size was 12 when considering the economic threshold level. Here, we propose an effective sampling method that can be applied for future monitoring and field surveys of potato tuber moths in South Korea.

• The Mathematical Education
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• v.59 no.1
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• pp.47-62
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• 2020

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.197-207
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• 2015

In baseball game, the hitting ability of batter is frequently assessed by a batting average, a run batted in, a home run, a run scored, an on-base percentage, etc. Recently, more comprehensive indicators such as OPS, ISO, SECA, TA, RC and XR are often used. But, these measures generally shows large deviations since they are calculated from the data for a certain period of time, and they are not an estimate of a population parameter, either. In this paper, we will presume the pure hitting ability of the korea professional baseball players as a parameter which is depend upon at bat. We will estimate the parameter by using the Bayesian method.

• Fisheries and Aquatic Sciences
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• v.23 no.7
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• pp.19.1-19.14
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• 2020

Three generalized additive models were applied to the distribution of anchovy eggs and oceanographic factors to determine the occurrence of anchovy spawning grounds in Korean waters and to identify the indicators of their occurrence using survey data from the spring and summer of 1985, 1995, and 2002. Binomial and Gaussian types of generalized additive models (GAM) and quantile generalized additive models (QGAM) revealed that egg density was influenced mostly by ocean temperature and salinity in spring, and the vertical structure of temperature, salinity, dissolved oxygen, and zooplankton biomass during summer in the upper quantiles of egg density. The GAM and QGAM model deviance explained 18.5-63.2% of the egg distribution in summer in the East and West Sea. For the principle component analysis-based GAMs, the variance explained by the final regression model was 27.3-67.0%, higher than the regular models and QGAMs for egg density in the East and West Sea. By analyzing the distribution of anchovy eggs off the Korean coast, our results revealed the optimal temperature and salinity conditions, in addition to high production and high vertical mixing, as the key indicators of the major spawning grounds of anchovies.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.37 no.4
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• pp.24-34
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• 2014

In order to manage essential parts that are required for the repairable parts services performed at the military maintenance depots, the United States Air Force developed the Repairability Forecasting Model (RFM). In the RFM, if the requirements of the parts are assumed to follow the normal probability distribution after applying means from the past data to the replacement rate and lead times, the chance of the AWP (Awaiting Parts) occurring is 50%. In this study, to counter the uncertainties of requirements and lead times from the RFM, the safety level concept is considered. To obtain the safety level for requirements, the binomial probability distribution is applied, while the safety level for lead time is obtained by applying the normal probability distribution. After adding this concept, the improved RFM is renamed as the ARFM (Advanced RFM), and by conducting the numerical stimulation, the effectiveness of the ARFM, minimizing the occurrence of the AWP, is shown by increasing the efficiency of the maintenance process and the operating rate of the weapon system.

• Journal of agricultural medicine and community health
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• v.14 no.1
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• pp.44-53
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• 1989

The distribution pattern of Clonorchis sinensis metacercaria in Pseudorasvora parva population and correlation between P. parva and metacercaria of C. sinensis were studied. The surveved areas were Chomanpo and Bulamdong, Kim-Hae Gun which were endemic area of clonorchiasis, and wansa, Sa-Chon Gun, Souh Kyong-Sang Do. The results are as follows: 1) The areas of Chornanpo and Wansa showed high infectivity in 99-100% of infection rate and 282-308 of average infection number per-fish. But the area of Bulamdong showed relatively. low infectivity in 95.8% of infection rate and 44 of average infection number. 2) The distribution patterns of C. sinensis metacercaria in P. parva population which were collected in Chomanpo and Wansa were shown Poisson distribution and the distribution pattern in Bulamdong showed mid-pattern of shifting over from Poisson distribution to Negative binomial distribution. 3) The correlation between P. parva length and average number of C. sinensis metacercaria in the present studied areas represented as direct proportion relationship.

• Research in Plant Disease
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• v.21 no.4
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• pp.268-272
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• 2015

Bacterial leaf blight caused by Pseudomonas syringae pv. porri is one of the major bacterial diseases of garlic (Allium sativum). In South Korea, the disease has only been observed in garlic-growing regions of Jeju island. The spatial distribution pattern of the disease was analyzed by binary power law, in which the natural logarithm of the observed variance is regressed on the natural logarithm of the binomial variance. The estimated slope (b=1.361) of the regression was greater than 1 which meant that the diseased plants were aggregated. The sequential sampling plans were developed for estimating the mean incidence rate ($p_m$) and classifying the mean incidence as being below or above the critical incidence rate ($p_t$). These results could be used on more efficient and higher precisive sampling for bacterial blight of garlic compared to fixed sample sized sampling.