• Title/Summary/Keyword: Product of normal variables

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Multivariate SPC Charts for On-line Monitoring the Batch Processes (배치 공정의 온라인 모니터링을 위한 다변량 관리도)

  • Lee Bae Jin;Kang Chang Wook
    • Proceedings of the Society of Korea Industrial and System Engineering Conference
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    • 2002.05a
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    • pp.387-396
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    • 2002
  • Batch processes are a significant class of processes in the process industry and play an important role in the production of high quality speciality materials. Examples include the production of semiconductors, chemicals, pharmaceuticals, and biochemicals. With on-line sensors connected to most batch processes, massive amounts of data are being collected routinely during the batch on easily measured process variables such as temperatures, pressures, and flowrates. In this paper, multivariate SPC charts for on-line monitoring of the progress of new batches are developed which utilize the information in the on-line measurements in real-time. We propose the formation of statistical model which describes the normal operation of a batch at each time interval during the batch operation. An on-line monitoring scheme based on the proposed method can handle both cross-correlation among process variables at any one time and auto-correlation over time. And the control limits for the monitoring charts are established from sound statistical framework unlike previous researches which use the external reference distribution. The proposed charts perform real-time, on-line monitoring to ensure that the batch is progressing in a manner that will lead to a high-quality product or to detect and indicate faults that can be corrected prior to completion of the batch. This approach is capable of tracking the progress of new batch runs, identifying the time periods in which the fault occurred and detecting underlying cause.

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Stability Analysis of Linear Uncertain Differential Equations

  • Chen, Xiaowei;Gao, Jinwu
    • Industrial Engineering and Management Systems
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    • v.12 no.1
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    • pp.2-8
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    • 2013
  • Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

Design of the Robust CV Control Chart using Location Parameter (위치모수를 이용한 로버스트 CV 관리도의 설계)

  • Chun, Dong-Jin;Chung, Young-Bae
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.39 no.1
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    • pp.116-122
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    • 2016
  • Recently, the production cycle in manufacturing process has been getting shorter and different types of product have been produced in the same process line. In this case, the control chart using coefficient of variation would be applicable to the process. The theory that random variables are located in the three times distance of the deviation from mean value is applicable to the control chart that monitor the process in the manufacturing line, when the data of process are changed by the type of normal distribution. It is possible to apply to the control chart of coefficient of variation too. ${\bar{x}}$, s estimates that taken in the coefficient of variation have just used all of the data, but the upper control limit, center line and lower control limit have been settled by the effect of abnormal values, so this control chart could be in trouble of detection ability of the assignable value. The purpose of this study was to present the robust control chart than coefficient of variation control chart in the normal process. To perform this research, the location parameter, ${\bar{x_{\alpha}}}$, $s_{\alpha}$ were used. The robust control chart was named Tim-CV control chart. The result of simulation were summarized as follows; First, P values, the probability to get away from control limit, in Trim-CV control chart were larger than CV control chart in the normal process. Second, ARL values, average run length, in Trim-CV control chart were smaller than CV control chart in the normal process. Particularly, the difference of performance of two control charts was so sure when the change of the process was getting to bigger. Therefore, the Trim-CV control chart proposed in this paper would be more efficient tool than CV control chart in small quantity batch production.

A Study on the Behavior Properties of the High-Strength Lightweight Concrete Beam Using the Industrial By-Products (산업부산물을 활용한 고강도경량 콘크리트보의 거동 특성)

  • Lee Seung Jo;Park Jung Min;Son Young Ho;Kim Wha Jung
    • Proceedings of the Korea Concrete Institute Conference
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    • 2004.05a
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    • pp.188-191
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    • 2004
  • We experimented variables of four kinds(a/d=1.5, 2.5, 3.5, 4.5) of shear span ratio to consider a structural characteristic of high-strength lightweight concrete beam used industrial by-product. Through the research of serials, the more increase of shear span ratio, the more ductility is superior. Rating the capacity of high-strength concrete beam and the capacity of lightweight concrete beam, in existing lightweight concrete beam evaluation formula, if a shear strength formula for normal concrete multiplies 0.85(reduction factor), it is rated as safety side over shear span ratio 2.5, but it is riskful at low shear span ratio. Therefore it is important that these factors are considered as the evaluation.

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Effects of Extruded and Extruded-Pelleted Corn Products Partially Substituted for Unprocessed Corn of the Starter Diet on Growth Performance and Incidence of Diarrhea in Weanling Pigs

  • Park, Byung-Chul;Han, Jeong-Cheol;Ko, Young-Hyun;Ha, Duck-Min;Kim, Doo-Hwan;Jang, Insurk;Lee, C. Young
    • Journal of Animal Science and Technology
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    • v.55 no.2
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    • pp.109-113
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    • 2013
  • The aim of the present study was to investigate the effects of partial substitution of an extruded or extruded-pelleted corn product for unprocessed corn of the starter diet on growth performance and incidence of diarrhea in weanling pigs. Seventy-two 21-day-old weanling pigs were allotted to 24 pens and provided ad libitum with one of the four experimental diets for 3 wk in two serial feeding trials during summer beginning from late June. The treatments were a milk product-soy-corn-based control diet containing 25% unprocessed corn and the other three diets only substituted with 12.5% extruded corn Suprex$^{(R)}$, Optigrain$^{(R)}$, an extruded mixture of wheat, rye and durum, or extruded-pelleted corn for an equal percentage of unprocessed corn of the control diet. All diets were supplemented with 100 ppm sulfathiazone, 50 ppm penicillin, and 100 ppm chlortetracycline for preventive medication. The initial and final weights as well as gain : feed were less in the second trial than in the first one (P<0.05). However, effects of the dietary treatments were not detected in any of the performance variables including final weight, ADG, ADFI, and gain : feed, nor were there any interactions between the trial and dietary treatment. In addition, almost all pigs exhibited normal firm feces in both trials and therefore there was no main effect in the fecal consistency score. Results suggest that partial substitution of the thermally processed corn for unprocessed corn of the milk product-corn-soy-based and medicated starter diet has no effect on growth performance or incidence of diarrhea in weanling pigs.

Optimum time-censored ramp soak-stress ALT plan for the Burr type XII distribution

  • Srivastava, P.W.;Gupta, T.
    • International Journal of Reliability and Applications
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    • v.15 no.2
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    • pp.125-150
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    • 2014
  • Accelerated life tests (ALTs) are extensively used to determine the reliability of a product in a short period of time. Test units are subject to elevated stresses which yield quick failures. ALT can be carried out using constant-stress, step-stress, progressive-stress, cyclic-stress or random-stress loading and their various combinations. An ALT with linearly increasing stress is ramp-stress test. Much of the previous work on planning ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations where the stress is generally increased. This paper presents an optimal design of ramp soak-stress ALT model which is based on the principle of Thermal cycling. Thermal cycling involves applying high and low temperatures repeatedly over time. The optimal plan consists in finding out relevant experimental variables, namely, stress rates and stress rate change points, by minimizing variance of reliability function with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out.

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Correlation among Ownership of Home Appliances Using Multivariate Probit Model (다변량 프로빗 모형을 이용한 가전제품 구매의 상관관계 분석)

  • Kim, Chang-Seob;Shin, Jung-Woo;Lee, Mi-Suk;Lee, Jong-Su
    • Journal of Global Scholars of Marketing Science
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    • v.19 no.2
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    • pp.17-26
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    • 2009
  • As the lifestyle of consumers changes and the need for various products increases, new products are being developed in the market. Each household owns various home appliances which are purchased through the choice of a decision maker. These appliances include not only large-sized products such as TV, refrigerator, and washing machine, but also small-sized products such as microwave oven and air cleaner. There exists latent correlation among possession of home appliances, even though they are purchased independently. The purpose of this research is to analyze the effect of demographic factors on the purchase and possession of each home appliances, and to derive some relationships among various appliances. To achieve this purpose, the present status on the possession of each home appliances are investigated through consumer survey data on the electric and energy product. And a multivariate probit(MVP) model is applied for the empirical analysis. From the estimation results, some appliances show a substitutive or complementary pattern as expected, while others which look apparently unrelated have correlation by co-incidence. This research has several advantages compared to previous literatures on home appliances. First, this research focuses on the various products which are purchased by each household, while previous researches such as Matsukawa and Ito(1998) and Yoon(2007) focus just on a particular product. Second, the methodology of this research can consider a choice process of each product and correlation among products simultaneously. Lastly, this research can analyze not only a substitutive or complementary relationship in the same category, but also the correlation among products in the different categories. As the data on the possession of home appliances in each household has a characteristic of multiple choice, not a single choice, a MVP model are used for the empirical analysis. A MVP model is derived from a random utility model, and has an advantage compared to a multinomial logit model in that correlation among error terms can be derive(Manchanda et al., 1999; Edwards and Allenby, 2003). It is assumed that the error term has a normal distribution with zero mean and variance-covariance matrix ${\Omega}$. Hence, the sign and value of correlation coefficients means the relationship between two alternatives(Manchanda et al., 1999). This research uses the data of 'TEMEP Household ICT/Energy Survey (THIES) 2008' which is conducted by Technology Management, Economics and Policy Program in Seoul National University. The empirical analysis of this research is accomplished in two steps. First, a MVP model with demographic variables is estimated to analyze the effect of the characteristics of household on the purchase of each home appliances. In this research, some variables such as education level, region, size of family, average income, type of house are considered. Second, a MVP model excluding demographic variables is estimated to analyze the correlation among each home appliances. According to the estimation results of variance-covariance matrix, each households tend to own some appliances such as washing machine-refrigerator-cleaner-microwave oven, and air conditioner-dish washer-washing machine and so on. On the other hand, several products such as analog braun tube TV-digital braun tube TV and desktop PC-portable PC show a substitutive pattern. Lastly, the correlation map of home appliances are derived using multi-dimensional scaling(MDS) method based on the result of variance-covariance matrix. This research can provide significant implications for the firm's marketing strategies such as bundling, pricing, display and so on. In addition, this research can provide significant information for the development of convergence products and related technologies. A convergence product can decrease its market uncertainty, if two products which consumers tend to purchase together are integrated into it. The results of this research are more meaningful because it is based on the possession status of each household through the survey data.

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A Study of Possibilities on Developing of Traditional Convenience Foods for Anti-aging Control an Analysis of Public Perspectives (노화 제어를 위한 전통 편의식 개발 가능성에 대한 연구)

  • Bok, Hye-Ja;Choi, Soo-Keun
    • Journal of the East Asian Society of Dietary Life
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    • v.18 no.3
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    • pp.322-330
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    • 2008
  • This study was performed to the possibility of developing anti-aging convenient food that is to Koreans' taste. Editor: this abstract appears to describe a study of public opinion and not related to the development of anti-aging convenient foods. In total, The 150 adults, living in Seoul (Korea), participated in this study in the capacity of subjects. Editor: You really have to mention the age-range of the subjects, as senility is an old age disease. In particular, you talk about the intention of subjects (discussed below) to buy anti-aging food products. This would be directly related to their age, as I assume that older people would be more concerned about senility that relatively younger subjects. They were randomly assigned to 25 groups. In result initial descriptive analysis revealed that, 82 percent of subjects awoke to were aware of senility, and the while 26.7 percent were seriously thought of it concerned. Furthermore, The 58.7 percent said that believed food has the possibility has a role in of controlling senility, and the while 64.0 percent said stated that senility may be controlled by eating constitutional foods. Further comparative analysis of In the case of the group of which members subjects have been who were trying to control senility revealed that their, the reliance on food general and constitutional food was significantly higher than those who have not tried to do so did nothing. The From the 61.3 percent have been of subject who were trying to control senility, from among them, the 74.0 percent and the 22.7 percent were relied on physical taking exercises and anti-aging foods, respectively. Likewise, it was ascertained When asked whether subjects intend to purchase anti-aging convenient food if it was is developed. The 67.3 percent and the 72.7 percent indicated their intentionded to purchase the normal product and constitutional products, respectively. Resultantly, anti-aging convenient food was in demand to some extent. Given that anti-aging products are in high demand, In such a case, senile severity (p<0.05), anti-aging possibility in constitutional foods (p<0.001) and anti-aging action (p<0.001) are regarded as variables in the purchase of the normal products. In the case of relation to constitutional products, anti-aging possibility in constitutional food (p<0.001) and anti-aging action (p<0.001) were regarded as variables.

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Extraction of Primary Factors Influencing Dam Operation Using Factor Analysis (요인분석 통계기법을 이용한 댐 운영에 대한 영향 요인 추출)

  • Kang, Min-Goo;Jung, Chan-Yong;Lee, Gwang-Man
    • Journal of Korea Water Resources Association
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    • v.40 no.10
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    • pp.769-781
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    • 2007
  • Factor analysis has been usually employed in reducing quantity of data and summarizing information on a system or phenomenon. In this analysis methodology, variables are grouped into several factors by consideration of statistic characteristics, and the results are used for dropping variables which have lower weight than others. In this study, factor analysis was applied for extracting primary factors influencing multi-dam system operation in the Han River basin, where there are two multi-purpose dams such as Soyanggang Dam and Chungju Dam, and water has been supplied by integrating two dams in water use season. In order to fulfill factor analysis, first the variables related to two dams operation were gathered and divided into five groups (Soyanggang Dam: inflow, hydropower product, storage management, storage, and operation results of the past; Chungju Dam: inflow, hydropower product, water demand, storage, and operation results of the past). And then, considering statistic properties, in the gathered variables, some variables were chosen and grouped into five factors; hydrological condition, dam operation of the past, dam operation at normal season, water demand, and downstream dam operation. In order to check the appropriateness and applicability of factors, a multiple regression equation was newly constructed using factors as description variables, and those factors were compared with terms of objective function used in operation water resources optimally in a river basin. Reviewing the results through two check processes, it was revealed that the suggested approach provided satisfactory results. And, it was expected for extracted primary factors to be useful for making dam operation schedule considering the future situation and previous results.

Time-series Mapping and Uncertainty Modeling of Environmental Variables: A Case Study of PM10 Concentration Mapping (시계열 환경변수 분포도 작성 및 불확실성 모델링: 미세먼지(PM10) 농도 분포도 작성 사례연구)

  • Park, No-Wook
    • Journal of the Korean earth science society
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    • v.32 no.3
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    • pp.249-264
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    • 2011
  • A multi-Gaussian kriging approach extended to space-time domain is presented for uncertainty modeling as well as time-series mapping of environmental variables. Within a multi-Gaussian framework, normal score transformed environmental variables are first decomposed into deterministic trend and stochastic residual components. After local temporal trend models are constructed, the parameters of the models are estimated and interpolated in space. Space-time correlation structures of stationary residual components are quantified using a product-sum space-time variogram model. The ccdf is modeled at all grid locations using this space-time variogram model and space-time kriging. Finally, e-type estimates and conditional variances are computed from the ccdf models for spatial mapping and uncertainty analysis, respectively. The proposed approach is illustrated through a case of time-series Particulate Matter 10 ($PM_{10}$) concentration mapping in Incheon Metropolitan city using monthly $PM_{10}$ concentrations at 13 stations for 3 years. It is shown that the proposed approach would generate reliable time-series $PM_{10}$ concentration maps with less mean bias and better prediction capability, compared to conventional spatial-only ordinary kriging. It is also demonstrated that the conditional variances and the probability exceeding a certain thresholding value would be useful information sources for interpretation.