Response Surface Analysis of the Experimental Data from a Cubic Central Composite Design in the Presence of the Lack of Fit of the Second-Order Polynomial Regression Model

2020 ◽  
Vol 22 (1) ◽  
pp. 121-129
Author(s):  
Insoo Rheem ◽  
Sungsue Rheem
Keyword(s):  
Experimental Data ◽  
Regression Model ◽  
Central Composite Design ◽  
Response Surface ◽  
Surface Analysis ◽  
Polynomial Regression ◽  
Lack Of Fit ◽  
Order Polynomial ◽  
Central Composite ◽  
Polynomial Regression Model

Optimization of Separation Process of Waste Polyester-Cotton Fiber by Using Response Surface Analysis

2012 ◽  
Vol 535-537 ◽  
pp. 1564-1568
Author(s):  
Huang Huang ◽  
Yong Ling Yu ◽  
Wei Kong
Keyword(s):  
Hydrochloric Acid ◽  
Response Surface ◽  
Surface Analysis ◽  
Polynomial Regression ◽  
Response Surface Analysis ◽  
Hydrolysis Method ◽  
Blend Fiber ◽  
Acid Reaction ◽  
Solid Liquid ◽  
Central Composite

In this study, the response surface methodology was used to optimize parameters of the diluted hydrochloric acid hydrolysis method, which was adopted to separate the polyester-cotton blend fiber. The four parameters reaction time, mass fraction of hydrochloric acid, reaction temperature and solid-liquid ratio were determined by the single factor experiment as they are significant for the process of separation. By introducing the experiment of four factors on three levels designed by Box-Benhnken central composite method, a quadric polynomial regression model for the fiber weight loss rate was established. And the response surface graphs were plotted to illustrate the optimizing process. The response surface analysis determined that the optimized value of the four parameters were 98 minutes, 10.7%, 96.5 °C and 4.3 g/100ml respectively. Under these conditions, polyester-cotton blend fiber was completely separated.

scholarly journals OPTIMASI RESPON PADA PERCOBAAN FAKTORIAL DENGAN MENGGUNAKAN METODE PERMUKAAN RESPON

2019 ◽  
Vol 4 (2) ◽  
pp. 51
Author(s):  
Falin Tristanti Ayu ◽  
Izzati Rahmi HG ◽  
Yudiantri Asdi
Keyword(s):  
Response Surface Methodology ◽  
Central Composite Design ◽  
Factorial Design ◽  
Response Surface ◽  
Lack Of Fit ◽  
Central Composite

Metode Permukaan Respon atau Response Surface Methodology adalah gabungan dari teknik matematika dan statistika yang digunakan dalam pemodelan dan analisis dimana respon yang diamati dipengaruhi oleh sejumlah variabel. Metode permukaan respon digunakan untuk mencari taraf-taraf peubah bebas yang dapat mengoptimalkan respon. Dengan metode ini dapat diketahui model empirik yang menyatakan hubungan antara variabel-variabel independen dengan variabel respon, serta dapat diketahui nilai variabel-variabel independen yang menyebabkan nilai variabel respon menjadi optimal. Eksperimen dengan metode permukaan respon dilakukan dalam dua tahap yaitu eksperimen tahap I dan eksperimen tahap II. Desain eksperimen yang digunakan pada eksperimen tahap I adalah desain faktorial dua level sedangkan desain eksperimen yang digunakan pada eksperimen tahap II adalah Central Composite Design (CCD). Tahapan dalam metode permukaan respon pada intinya yaitu mencari fungsi aproksimasi yang menyatakan hubungan antara variabel independen dengan variabel respon, mengestimasi parameter-parameter dari fungsi aproksimasi yang diperoleh dengan metode kuadrat terkecil dan selanjutnya dilakukan analisis pengepasan permukaan. Karakteristik permukaan respon digunakan untuk menentukan apakah jenis titik stasionernya maksimum, minimum atau titik pelana. Prosedur pengujian yang dilakukan dalam metode permukaan respon diantaranya uji kesesuaian model regresi (lack of fit), uji parameter regresi secara serentak dan pengujian asumsi residual.Kata Kunci: Desain eksperimen, Metode Permukaan Respon (Response Surface Methodology), Two Level Factorial Design, Central Composite Design (CCD)

The influence of the regression model and final speed criteria on the reliability of lactate threshold determined by the Dmax method in endurance-trained runners

2016 ◽  
Vol 41 (10) ◽  
pp. 1039-1044 ◽  
Author(s):  
Júlio César Camargo Alves ◽  
Cecília Segabinazi Peserico ◽  
Geraldo Angelo Nogueira ◽  
Fabiana Andrade Machado
Keyword(s):  
Regression Model ◽  
Regression Models ◽  
Lactate Threshold ◽  
Polynomial Regression ◽  
Third Order ◽  
The Third ◽  
Constant Regression ◽  
Order Polynomial ◽  
Final Speed ◽  
Polynomial Regression Model

Few studies verified the reliability of the lactate threshold determined by Dmax method (LTDmax) in runners and it remains unclear the effect of the regression model and the final speed on the reliability of LTDmax. This study aimed to examine the test–retest reliability of the speed at LTDmax in runners, considering the effects of the regression models (exponential-plus-constant vs third-order polynomial) and final speed criteria (complete vs proportional). Seventeen male, recreational runners performed 2 identical incremental exercise tests, with increments of 1 km·h–1 each for 3 min on treadmill to determine peak treadmill speed (Vpeak) and lactate threshold. Earlobe capillary blood samples were collected during rest between the stages. The Vpeak was defined as the speed of the last complete stage (complete final speed criterion) and as the speed of the last complete stage added to the fraction of the incomplete stage (proportional final speed criterion). Lactate threshold was determined from exponential-plus-constant and from third-order polynomial regression models with both complete and proportional final speed criteria and from fixed blood lactate level of 3.5 mmol·L−1 (LT3.5mM). The LTDmax obtained from the exponential-plus-constant regression model presented higher reliability (coefficient of variation (CV) ≤ 3.7%) than the LTDmax calculated from the third-order polynomial regression model (CV ≤ 5.8%) and LT3.5mM (CV = 5.4%). The proportional final speed criterion is more appropriate when using the exponential-plus-constant regression model, but less appropriate when using the third-order polynomial regression model. In conclusion, exponential-plus-constant using the proportional final speed criterion is preferred over LT3.5mM and over third-order polynomial regression model to determine a reliable LTDmax.

Systematic Dimensional Calibration Process for 3D Printed Parts in Selective Laser Sintering (SLS)

2015 ◽  
Author(s):  
Sangho Ha ◽  
Hweeyoung Han ◽  
Daeil Kwon ◽  
Namhun Kim ◽  
Hyeonnam Kim ◽  
...  
Keyword(s):  
Regression Model ◽  
Polynomial Regression ◽  
Selective Laser Sintering ◽  
Laser Sintering ◽  
Engineering Properties ◽  
Calibration Process ◽  
Order Polynomial ◽  
3D Printed ◽  
Deformation Patterns ◽  
Polynomial Regression Model

The selective laser sintering (SLS) processes, known for enhancing engineering properties and durability of products, are widely used in auto part development processes. The dimensional displacements of the 3D printed parts, however, hinder utilizing the technology directly to enhance their development process. In general, the SLS process causes curved shapes (convex) due to thermal deformation (thermal expansion and thermal contraction) in the powder sintering and cooling processes, which accompanies multi-phase changes of the raw materials (polymer powders). In this research, we aim to present a systematic dimensional calibration process by investigating and analyzing the dimensional deformation patterns of 3D printed samples in SLS platform (using 3D Systems’ sPro60 SD). Firstly, the test samples with complex features are produced to check the reference dimensional deviation of the SLS process. Secondly, the deformation patterns are measured and analyzed as a form of a 2nd order polynomial regression model in the global Cartesian coordinates of the platform. Lastly, the dimensional calibration methods to minimize the process errors are presented by the pre-processing of the original CAD file (.stl) with inverse transformation of the features using the 2nd order polynomial regression model. At the end of the paper, we will propose an algorithm that predicts the deformation and calibrates point-based 3D CAD STL files of samples in order to mitigate the dimensional deformation, along with test samples for illustrative purposes.

scholarly journals An empirical study of Taiwan’s food security index

2009 ◽  
Vol 13 (7) ◽  
pp. 1056-1063 ◽  
Author(s):  
Chih-Yang Yeh ◽  
Pei-San Liao ◽  
Chieh-Yu Liu ◽  
Jeng-Fu Liu ◽  
Hsing-Yi Chang
Keyword(s):  
Regression Model ◽  
Polynomial Regression ◽  
Energy Requirement ◽  
Second Order ◽  
Activity Level ◽  
Dietary Energy ◽  
Order Polynomial ◽  
The Status ◽  
Level Of Economic Development ◽  
Polynomial Regression Model

AbstractObjectiveThe FAO has developed an approach for estimating the prevalence of undernourishment. Based on the FAO method Taiwan has a prevalence of undernourishment of 3·98 %, which is higher than that of some developing countries. As this is not a true reflection of the status of undernourishment in our nation, the purpose of the present study was to modify the FAO methodology for Taiwan.DesignTwo factors were considered in the modified version. As the minimum dietary energy requirement was the main factor contributing to the inflated prevalence in Taiwan, we adjusted for a lighter physical activity level, based on the average BMI of the Taiwanese population, and calculated a new minimum dietary energy requirement. We then fitted a second-order polynomial regression model for prediction of per capita dietary energy supply.ResultsThe adjusted minimum dietary energy requirement was reduced to 7648 kJ/d or 7765 kJ/d compared with the original value of 8054 kJ/d. This resulted in a decrease of the prevalence of undernourishment in Taiwan to 2·5 % or 3·0 %, which is much closer to that of other countries with the same level of economic development. The second-order polynomial regression model efficiently reduced the variation in dietary energy consumption and resulted in an undernourishment prevalence of less than 2·5 %.ConclusionsThis new adapted method is more appropriate for Taiwan. It is recommended that each country evaluates the appropriateness of the FAO approach for its population.

Response surface central composite design optimization of soluos dumpsite leachate treatment using agricultural biowaste

2021 ◽  
Vol 1 (2) ◽  
pp. 026-034
Author(s):  
Lukumon Salami ◽  
Lukman Bakare
Keyword(s):  
Regression Model ◽  
Central Composite Design ◽  
Design Optimization ◽  
Response Surface ◽  
Contact Time ◽  
Second Order ◽  
Coefficient Of Determination ◽  
Leachate Treatment ◽  
Percentage Removal ◽  
Central Composite

Process optimization plays a very important role in the process industries as it helps to miximise desire output by minimizing the cost of process variables. The aim of this work is to carry out response surface central composite design optimization of Soluos dumpsite leachate treatment using agricultural biowaste. Leachate collected from Soluos dumpsite in Lagos was treated using adsorbent prepared from Muas sapientum peels by studying the effects of adsorbent dosage and contact time on the percentage removal of total dissolved solids (TDS) with the aid of design expert software version 10.0.3. The developed second order regression model was adopted in comparison with the linear and two factor interaction ( ) model based on its coefficient of determination (R2) value and its adequacy by analysis of variance (ANOVA). 80.34 percentage removal of TDS was achieved under experimental process at contact time of 120 mins and dosage of 1 g/100mL while 81.134 percentage removal of TDS was obtained under simulation process at contact time of 63.469 mins and dosage of 0.994 g/100 mL. the values obtained under simulation condition were adopted as the optimum conditions. The developed second order regression model predicted the experimental data up to 98.10 percent confidence level hence it is a true representation of the treatment process and can be used to navigate the design space and optimization process of treatment of Soluos dumpsite leachate.

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