• Journal of Korean Society for Quality Management
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• v.39 no.3
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• pp.400-411
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• 2011

Process variables are factors in an experiment that are not mixture components but could affect the blending properties of the mixture ingredients. For example, the effectiveness of an etching solution which is measured as an etch rate is not only a function of the proportions of the three acids that are combined to form the mixture, but also depends on the temperature of the solution and the agitation rate. Efficient designs for the mixture components-process variables experiments depend on the mixture components-process variables model which is called a combined model. We often use the product model between the canonical polynomial model for the mixture and process variables model as a combined model. In this paper we propose three starting models for the mixture components-process variables experiments. One of the starting model we are considering is the model which includes product terms up to cubic order interactions between mixture effects and the linear & pure quadratic effect of the process variables from the product model. In this paper, we propose a method for finding robust designs and practical designs with respect to D-, G-, and I-optimality for the various starting combined models and then, we find practically efficient and robust designs for estimating the regression coefficients for those models. We find the prediction capability of those recommended designs in the case of three components and three process variables to be good by checking FDS(Fraction of Design Space) plots.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.3
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• pp.349-354
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• 2007

A mixture experiment is a special type of the response surface experiment in which the factors are the components of a mixture, and the response variable is a function of the proportions of each component. When a new mixture product is developed, there are a large number of components, and the first objective of the experiment is to identify the ones that are most important by doing a screening experiment. We propose a method of screening mixture components using the correlation coefficients when t-tests cannot identify significant components.

• Journal of Korean Society for Quality Management
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• v.40 no.3
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• pp.347-358
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• 2012

Purpose: Given the mixture components - process variables experimental data, we propose the strategy to find the proper combined model. Methods: Process variables are factors in an experiment that are not mixture components but could affect the blending properties of the mixture ingredients. For example, the effectiveness of an etching solution which is measured as an etch rate is not only a function of the proportions of the three acids that are combined to form the mixture, but also depends on the temperature of the solution and the agitation rate. Efficient designs for the mixture components - process variables experiments depend on the mixture components - process variables model which is called a combined model. We often use the product model between the canonical polynomial model for the mixture and process variables model as a combined model. Results: First we choose the reasonable starting models among the class of admissible product models and practical combined models suggested by Lim(2011) based on the model selection criteria and then, search for candidate models which are subset models of the starting model by the sequential variables selection method or all possible regressions procedure. Conclusion: Good candidate models are screened by the evaluation of model selection criteria and checking the residual plots for the validity of the model assumption. The strategy to find the proper combined model is illustrated with examples in this paper.

• Proceedings of the Korean Society for Quality Management Conference
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• 2009.10a
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• pp.15-22
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• 2009

Quality variations in mixture products such as medicine, food, engineering chemicals, and alloy materials can be caused by their own sub-components. For instance, discharging characteristics of a lithium-ion rechargeable battery depend upon the mixture ratio of ethylene, dimethyle, and ethyle-methyle, all of which consists an electrolyte solution in the battery. Thus it is important to determine tolerances of mixture components in maintaining the product quality at a desired level. This paper proposes a simple but efficient approach to a mixture tolerancing method with multi-response variables. We use a response surface method for empirical modelling between mixture components. An illustrative example of the proposed method is given.

• Journal of the Korean Statistical Society
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• v.9 no.2
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• pp.145-172
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• 1980

Draper and Lawrence (1965a) have given mixture designs for three factors when all the mixture components can vary on the entire factor space so that the region of interest is an equilateral triangle in two dimensions. In this paper their work is extended to the cases when the region of interest is an echelon, parallelogram, pentagon or hexagon, because of the restirctions imposed on some or all of the mixture components. The principles used in the choice of appropriate designs are those originally introduced by Box and Draper(1959). It is assumed that a response surface equation of first order is fitted, but there is a possibility of bias error due to presence of second order terms in the true model. Minimum bias designs for several cases of restricted regions of interest are illustrated.

• The Journal of the Acoustical Society of Korea
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• v.22 no.8
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• pp.711-716
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• 2003

This paper proposes the method to select the number of optimal mixtures in each state in Continuous Density HMM (Hidden Markov Models), Previously, researchers used the same number of mixture components in each state of HMM regardless spectral characteristic of speaker, To model each speaker as accurately as possible, we propose to use a different number of mixture components for each state, Selection of mixture components considered the probability value of mixture by each state that affects much parameter estimation of continuous density HMM, Also, we use PCA (principal component analysis) to reduce the correlation and obtain the system' stability when it is reduced the number of mixture components, We experiment it when the proposed method used average 10% small mixture components than the conventional HMM, When experiment result is only applied selection of mixture components, the proposed method could get the similar performance, When we used principal component analysis, the feature vector of the 16 order could get the performance decrease of average 0,35% and the 25 order performance improvement of average 0.65%.

• Korean Journal of Remote Sensing
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• v.26 no.6
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• pp.681-691
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• 2010

LiDAR waveform decomposition plays an important role in LiDAR data processing since the resulting decomposed components are assumed to represent reflection surfaces within waveform footprints and the decomposition results ultimately affect the interpretation of LiDAR waveform data. Decomposing the waveform into a mixture of Gaussians involves two related problems; 1) determining the number of Gaussian components in the waveform, and 2) estimating the parameters of each Gaussian component of the mixture. Previous studies estimated the number of components in the mixture before the parameter optimization step, and it tended to suggest a larger number of components than is required due to the inherent noise embedded in the waveform data. In order to tackle these issues, a new LiDAR waveform decomposition algorithm based on the sequential approach has been proposed in this study and applied to the ICESat waveform data. Experimental results indicated that the proposed algorithm utilized a smaller number of components to decompose waveforms, while resulting IMP value is higher than the GLA14 products.

• Computers and Concrete
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• v.19 no.5
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• pp.555-566
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• 2017

Recently some efforts have been performed to combine the advantages of light-weight and self-compacting concrete in one package called Light-Weight Self-Compacting Concrete (LWSCC). Accurate prediction of hardened properties from fresh state characteristics is vital in design of concrete structures. Considering the lack of references in mixture design of LWSCC, investigating the proper mixture components and their effects on mechanical properties of LWSCC can lead to a reliable basis for its application in construction industry. This study utilizes wide range of existing data of LWSCC mixtures to study the individual and combined effects of the components on the compressive strength. From sensitivity of compressive strength to the proportions and interaction of the components, two equations are proposed to estimate the LWSCC compressive strength. Predicted values of the equations are in good agreement with the experimental data. Application of lightweight aggregate to reduce the density of LWSCC may bring some mixing problems like segregation. Reaching a higher strength by lowered density is a challenging problem that is investigated as well. The results show that, the compressive strength can be improved by increasing the of mixture density of LWSCC, especially in the range of density under $2000Kg/m^3$.

• Journal of Korean Society for Quality Management
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• v.48 no.2
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• pp.269-282
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• 2020

Purpose: The practical design for experiments with mixtures of q components is consisted in the four types of design points, vertex, center of edge, axial, and center points in a (q-1)-dimensional simplex space. We propose a sequential method for the successful construction of the design space in Quality by Design (QbD) by allowing the different number of replicates at the four types of design points in the practical design when the quadratic canonical polynomial model is assumed. Methods: To compare the mixture designs efficiency, fraction of design space (FDS) plot is used. We search for the practical mixture designs whose the minimal half-width of the tolerance interval per a standard deviation, which is denoted as d₂, is less than 4.5 at 0.8 fraction of the design space. They are found by adding the different number of replicates at the four types of the design points in the practical design. Results: The practical efficient mixture designs for the number of components between three and five are listed. The sequential method to establish a design space is illustrated with the two examples based on the simulated data. Conclusion: The designs with the center of edge points replications are more efficient than those with the vertex points replication. We propose the sample size of at least 23 for three components, 28 for four components, and 33 for the five components based on the list of efficient mixture designs.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.194-202
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• 2019

Reliability analysis of the components frequently starts with the data that manufacturer provides. If enough failure data are collected from the field operations, the reliability should be recomputed and updated on the basis of the field failure data. However, when the failure time record for a component contains only a few observations, all statistical methodologies are limited. In this case, where the failure records for multiple number of identical components are available, a valid alternative is combining all the data from each component into one data set with enough sample size and utilizing the useful information in the censored data. The ROK Navy has been operating multiple Patrol Killer Guided missiles (PKGs) for several years. The Korea Multi-Function Control Console (KMFCC) is one of key components in PKG combat system. The maintenance record for the KMFCC contains less than ten failure observations and a censored datum. This paper proposes a Bayesian approach with a Dirichlet mixture model to estimate failure time density for KMFCC. Trends test for each component record indicated that null hypothesis, that failure occurrence is renewal process, is not rejected. Since the KMFCCs have been functioning under different operating environment, the failure time distribution may be a composition of a number of unknown distributions, i.e. a mixture distribution, rather than a single distribution. The Dirichlet mixture model was coded as probabilistic programming in Python using PyMC3. Then Markov Chain Monte Carlo (MCMC) sampling technique employed in PyMC3 probabilistically estimated the parameters' posterior distribution through the Dirichlet mixture model. The simulation results revealed that the mixture models provide superior fits to the combined data set over single models.