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

• The Korean Journal of Applied Statistics
• /
• v.25 no.1
• /
• pp.215-223
• /
• 2012

Response surface methodology(RSM) is a very useful statistical techniques for improving and optimizing the product process. By this reason, RSM has been utilized extensively in the industrial world, particularly in the circumstances where several product variables potentially influence some quality characteristic of the product. In order to estimate the optimal condition of product variables, an experiment is being conducted defining appropriate experimental region. However, this experimental region can vary with the experimental circumstances and choice of a researcher. Response surface designs can be classified, according to the shape of the experimental region, into spherical and cuboidal. In the spherical case, the design is either rotatable or very near-rotatable. The central composite design(CCD)s widely used in RSM is an example of 5-level and spherical design. The cuboidal CCDs(CCDs with ${\alpha}=1$) is appropriate when an experimental region is cuboidal but this design dose not satisfy the rotatability as it is not spherical. Practically, a 3-level spherical design is often required in the industrial world where various level of experiments are not available. Box-Behnken design(BBD)s are a most popular 3-level spherical designs for fitting second-order response surfaces and satisfy the rotatability but the experimental region does not vary with the number of variables. The new experimental design with expanded experimental region can be considered if the predicting response at the extremes are interested. This paper proposes a new 3-level spherical RSM which are constructed to expand the experimental region together with number of product variables.

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.173-176
• /
• 2004

In this study, the multidisciplinary aerodynamic-structural optimal design is carried out for the supersonic fighter wing. Through the aeroelastic analyses of the various candidate wings, the aerodynamic and structural performances are calculated such as the lift coefficient, the drag coefficient and the deformation of the wing. In general, the supersonic fighter is maneuvered under the various flight conditions and those conditions must be considered all together during the design process. The multi-point design, therefore, is deemed essential. For this purpose, supersonic dash, long cruise range and high angle of attack maneuver are selected as representative design points. Based on the calculated performances of the candidate wings, the response surfaces for the objectives and constraints are generated and the supersonic fighter wing is designed for better aerodynamic performances and less weights than the baseline. At each design point, the single-point design is performed to obtain better performances. Finally, the multi-point design is performed to improve the aerodynamic and structural performances for all design points. The optimization results of the multi-point design are compared with those of the single-point designs and analyzed in detail.

• Journal of Soil and Groundwater Environment
• /
• v.15 no.1
• /
• pp.9-18
• /
• 2010

In this study, Solid-phase micro-extraction (SPME) with Gas Chromatograph using Flame Ionization Detector (GC/FID) was studied as a possible alternative to liquid-liquid extraction for the analysis of Methyl tert-butyl ether (MTBE) and Tertiary-butyl ether (TBA) in water and an optimization condition of trace analysis of MTBE and TBA using the design of experiment (DOE) was described. The aim of our research was to apply experimental design methodology in the optimization condition of trace analysis of fuel oxygenated compounds in soil-phase microextraction with GC/FID. The reactions of SPME were mathematically described as a function of parameters of Temp ($X_1$), Volume ($X_2$), Time ($X_3$) and Salt ($X_4$) being modeled by the use of the partial factorial designs, which was used for fitting 2nd order response surface models and was alternative to central composite designs. The model predicted agreed with the experimentally observed result ($Y_1$(MTBE, $R^2$ = 0.96, $Y_2$ (TBA, $R^2$ = 0.98)). The estimated ridge of the expected maximum responses and optimal conditions for MTBE and TBA were 278.13 and (Temp ($X_1$) = $48.40^{\circ}C$, Volume ($X_2$) = 73.04 mL, Time ($X_3$) = 11.51 min and Salt ($X_4$) = 12,50 mg/L), and 127.89 and (Temp ($X_1$) = $52.12^{\circ}C$, Volume ($X_2$) = 88.88mL, Time ($X_3$) = 65.40 min and Salt ($X_4$) = 12,50 mg/L), respectively.

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

• 한국생물공학회:학술대회논문집
• /
• 2005.04a
• /
• pp.68-72
• /
• 2005

Leuconostoc citreum is one of the representative strains of Leuconostoc spp. that show fast growth rates in fermented vegetables. Sequential experimental designs including the Plackett-Burman design, fractional factorial design, steepest ascent analysis, central composite design and response surface methodology were introduced tooptimize and improve the medium for Leuconostoc citreum. Fifteen medium ingredients were examined and glucose (20 g/l), yeast extract (12.5 g/l), sodium acetate trihydrate (6.12 g/l), potassium phosphate (42.55 g/l) and dibasic ammonium citrate (4.12 g/l)were chosen as the best components to give a critical and positive effect for cell-growth. The biomass was increased to 2.79 g/l (169%), compared to the 1.65 g/l in MRS medium.

• Biotechnology and Bioprocess Engineering:BBE
• /
• v.9 no.4
• /
• pp.278-284
• /
• 2004

Leuconostoc citreum is one of the representative strains of Leuconostoc spp. that show fast growth rates in fermented vegetables. Sequential experimental designs including the Plackett-Burman design, fractional factorial design, steepest ascent analysis, central composite design and response surface methodology were introduced to optimize and improve the medium for L. citreum. Fifteen medium ingredients were examined and glucose ($20 g/\ell$), yeast extract ($12.5g/\ell$), sodium acetate trihydrate ($6.12g/\ell$), potassium phosphate ($42.55g/\ell$), and dibasic ammonium citrate ($4.12g/\ell$), were chosen as the best components to give a critical and positive effect for cell-growth. The biomass was increased to ($2.79g/\ell$), (169%), compared to the $1.65g/\ell$ in MRS medium.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.16 no.3
• /
• pp.1630-1638
• /
• 2015

The finite element analysis has become an essential process to investigate the structural performance in many industry fields. In addition, the computer's performance is improving rapidly, but in large design problems, there is a limit to apply the optimal design techniques. For this, it is general to introduce a metamodel based optimization technique. The method to generate an approximate model can be classified into curve fitting and interpolation, and each representative one is response surface model and kriging interpolation method. This study proposes an ensemble model made of RSM and kriging to solve a structural design problem. The suggested method is applied to the designs of two bar and automobile outer tie rod.

• International Journal of Precision Engineering and Manufacturing
• /
• v.5 no.4
• /
• pp.61-68
• /
• 2004

Necessity to address engineering system uncertainties in design processes has long been acknowledged. To obtain quality of product, a safety factor is traditionally used by many design engineers due to its easy of use and comprehension. However, the safety factor approach often yields either conservative or unreliable designs, since it ignores the type of probability distribution and the mechanism of uncertainty propagation from the input to the output. For a consistent reliability-based design, two fundamental issues must be investigated thoroughly. First, the design-decision process that clearly identifies a mechanism of uncertainty propagation under system uncertainties needs to be developed, which must be an efficient and accurate process. To identify the mechanism more effectively, an adaptive probability analysis is proposed by adaptively setting probability levels through a posteriori error estimation. The second is to develop the design process that not only yields a high quality design but also a cost-effective optimum design from manufacturing point of view. As a result, a response surface methodology is specially developed for RBDO, thus enhancing numerical challenges of efficiency and complicatedness. Side crashworthiness application is used to demonstrate the integrated design process for product and manufacturing process design.

• Journal of Korean Society for Quality Management
• /
• v.30 no.4
• /
• pp.58-67
• /
• 2002

Since the inception of off-line quality control, it has drawn a particular attention from research community and it has been implemented in a wide variety of industries mainly due to its extensive applicability to numerous real situations. Emphasizing design issues rather than control issues related to manufacturing processes, off-line quality control has been recognized as a cost-effective approach to quality improvement. It mainly consists of three design stages: system design, parameter design, and tolerance design which are implemented in a sequential manner. Utilizing experimental designs and optimization techniques, off-line quality control is aimed at achieving product performance insensitive to external noises by reducing process variability. In spite of its conceptual soundness and practical significance, however, off-line quality control has also been criticized to a great extent due to its heuristic nature of investigation. In addition, it has also been pointed out that the process optimization procedures are inefficient. To enhance the current practice of off-line quality control, this study proposes an integrated optimization model by utilizing a well-established statistical tool, so called response surface methodology (RSM), and a tolerance - cost relationship.