• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.547-562
• /
• 2005

The distribution of products of random variables is of interest in many areas of the sciences, engineering and medicine. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, the distribution of the product | XY | is derived when X and Y are Student's t and Bessel function random variables distributed independently of each other.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.339-353
• /
• 2008

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Pearson type VII random variables.

• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.441-452
• /
• 2007

The exact distributions of X + Y, XY and X/(X + Y) are derived when X and Y are independent generalized Planck random variables.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.28 no.3
• /
• pp.49-60
• /
• 2003

In this paper, we study the joint design of sampling inspections and service capacities for multi-products. Products of different defect rates which are either deterministic or random variables are supplied in batches after sampling inspection and rework. When supplied, all defective products that have not been inspected in batches are uncovered through total inspection and returned to service. We identify the optimal inspection policies and service capacities for multi-products reflecting the relationships between inspection rework costs and service provision costs. We also develope a marginal allocation algorithm for the optimal allocation of the limited total service capacity to products as well as inspection quantities.

• Journal of Korean Society for Quality Management
• /
• v.49 no.3
• /
• pp.421-431
• /
• 2021

Purpose: For improving outgoing quality, this study presents a novel sampling framework based on predictive analytics. Methods: The proposed framework is composed of three steps. The first step is the variable selection. The knowledge-based and data-driven approaches are employed to select important variables. The second step is the model learning. In this step, we consider the supervised classification methods, the anomaly detection methods, and the rule-based methods. The applying model is the third step. This step includes the all processes to be enabled on real-time prediction. Each prediction model classifies a product as a target sample or random sample. Thereafter intensive quality inspections are executed on the specified target samples. Results: The inspection data of three Samsung products (mobile, TV, refrigerator) are used to check functional defects in the product by utilizing the proposed method. The results demonstrate that using target sampling is more effective and efficient than random sampling. Conclusion: The results of this paper show that the proposed method can efficiently detect products that have the possibilities of user's defect in the lot. Additionally our study can guide practitioners on how to easily detect defective products using stratified sampling

• Communications for Statistical Applications and Methods
• /
• v.25 no.2
• /
• pp.217-234
• /
• 2018

Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.

• Communications for Statistical Applications and Methods
• /
• v.18 no.3
• /
• pp.277-286
• /
• 2011

Global companies can sell their products with dierent warranty periods based on location and times. Customers can select the length of warranty on their own if they pay an additional fee. In this paper, we consider the warranty period and the repair time limit as random variables. A two-dimensional warranty policy is considered with repair times and failure times. The repair times are considered within the repair time limit and the failure times are considered within the warranty period. Under the non-renewable warranty policy, we obtain the expected number of warranty services and their variances in the censored area by warranty period and repair time limit to conduct a warranty cost analysis. Numerical examples are discussed to demonstrate the applicability of the methodologies and results using field data based on the proposed approach in the paper.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.22 no.3
• /
• pp.75-87
• /
• 1980

Most hydro]ogic phenomena are the complex and organic products of multiple causations like climatic and hydro-geological factors. A certain significant correlation on the run-off in river basin would be expected and foreseen in advance, and the effect of each these causual and associated factors (independant variables; present-month rainfall, previous-month run-off, evapotranspiration and relative humidity etc.) upon present-month run-off(dependent variable) may be determined by multiple regression analysis. Functions between independant and dependant variables should be treated repeatedly until satisfactory and optimal combination of independant variables can be obtained. Reliability of the estimated function should be tested according to the result of statistical criterion such as analysis of variance, coefficient of determination and significance-test of regression coefficients before first estimated multiple regression model in historical sequence is determined. But some error between observed and estimated run-off is still there. The error arises because the model used is an inadequate description of the system and because the data constituting the record represent only a sample from a population of monthly discharge observation, so that estimates of model parameter will be subject to sampling errors. Since this error which is a deviation from multiple regression plane cannot be explained by first estimated multiple regression equation, it can be considered as a random error governed by law of chance in nature. This unexplained variance by multiple regression equation can be solved by stochastic approach, that is, random error can be stochastically simulated by multiplying random normal variate to standard error of estimate. Finally hybrid model on estimation of monthly run-off in nonhistorical sequence can be determined by combining the determistic component of multiple regression equation and the stochastic component of random errors. Monthly run-off in Naju station in Yong-San river basin is estimated by multiple regression model and hybrid model. And some comparisons between observed and estimated run-off and between multiple regression model and already-existing estimation methods such as Gajiyama formula, tank model and Thomas-Fiering model are done. The results are as follows. (1) The optimal function to estimate monthly run-off in historical sequence is multiple linear regression equation in overall-month unit, that is; Qn=0.788Pn+0.130Qn-1-0.273En-0.1 About 85% of total variance of monthly runoff can be explained by multiple linear regression equation and its coefficient of determination (R2) is 0.843. This means we can estimate monthly runoff in historical sequence highly significantly with short data of observation by above mentioned equation. (2) The optimal function to estimate monthly runoff in nonhistorical sequence is hybrid model combined with multiple linear regression equation in overall-month unit and stochastic component, that is; Qn=0. 788Pn+0. l30Qn-1-0. 273En-0. 10+Sy.t The rest 15% of unexplained variance of monthly runoff can be explained by addition of stochastic process and a bit more reliable results of statistical characteristics of monthly runoff in non-historical sequence are derived. This estimated monthly runoff in non-historical sequence shows up the extraordinary value (maximum, minimum value) which is not appeared in the observed runoff as a random component. (3) "Frequency best fit coefficient" (R2f) of multiple linear regression equation is 0.847 which is the same value as Gaijyama's one. This implies that multiple linear regression equation and Gajiyama formula are theoretically rather reasonable functions.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.44 no.4
• /
• pp.12-22
• /
• 2021

This article suggests the machine learning model, i.e., classifier, for predicting the production quality of free-machining 303-series stainless steel(STS303) small rolling wire rods according to the operating condition of the manufacturing process. For the development of the classifier, manufacturing data for 37 operating variables were collected from the manufacturing execution system(MES) of Company S, and the 12 types of derived variables were generated based on literature review and interviews with field experts. This research was performed with data preprocessing, exploratory data analysis, feature selection, machine learning modeling, and the evaluation of alternative models. In the preprocessing stage, missing values and outliers are removed, and oversampling using SMOTE(Synthetic oversampling technique) to resolve data imbalance. Features are selected by variable importance of LASSO(Least absolute shrinkage and selection operator) regression, extreme gradient boosting(XGBoost), and random forest models. Finally, logistic regression, support vector machine(SVM), random forest, and XGBoost are developed as a classifier to predict the adequate or defective products with new operating conditions. The optimal hyper-parameters for each model are investigated by the grid search and random search methods based on k-fold cross-validation. As a result of the experiment, XGBoost showed relatively high predictive performance compared to other models with an accuracy of 0.9929, specificity of 0.9372, F₁-score of 0.9963, and logarithmic loss of 0.0209. The classifier developed in this study is expected to improve productivity by enabling effective management of the manufacturing process for the STS303 small rolling wire rods.

• The Journal of Information Systems
• /
• v.32 no.3
• /
• pp.133-150
• /
• 2023

Purpose This study aims to develop classification models using a decision tree algorithm to identify core keywords and rules influencing online consumer review evaluations for the robot vacuum cleaner on Amazon.com. The difference from previous studies is that we analyze core keywords that affect the evaluation results by dividing the subjects that evaluate online consumer reviews into self-evaluation (star ratings) and peer evaluation (helpfulness votes). We investigate whether the core keywords influencing star ratings and helpfulness votes vary across different products and whether there is a similarity in the core keywords related to star ratings or helpfulness votes across all products. Design/methodology/approach We used random under-sampling to balance the dataset. We progressively removed independent variables based on decreasing importance through backwards elimination to evaluate the classification model's performance. As a result, we identified classification models that best predict star ratings and helpfulness votes for each product's online consumer reviews. Findings We have identified that the core keywords influencing self-evaluation and peer evaluation vary across different products, and even for the same model or features, the core keywords are not consistent. Therefore, companies' producers and marketing managers need to analyze the core keywords of each product to highlight the advantages and prepare customized strategies that compensate for the shortcomings.