scholarly journals Optimization of Split-Plot Design in the Context of Mixture Process Variable Settings

2021 ◽  
pp. 1-36
Author(s):  
Samson W. Wanyonyi ◽  
Ayubu A. Okango ◽  
Julius K. Koech ◽  
Betty C. Korir
Keyword(s):  
Factorial Design ◽  
Process Variable ◽  
Optimality Criteria ◽  
Mixture Design ◽  
Parameter Estimates ◽  
Process Variables ◽  
Split Plot ◽  
Set Up ◽  
Plot Structure ◽  
Plot Design

In the presence of process variables, a mixture design has become well-known in statistical modeling due to its utility in modeling the blending surface, which empirically predicts any mixture's response and serves as the foundation for optimizing the expected response blends of different components.  In the most common practical situation involving a mixture-process variable, restricted randomization occurs frequently. This problem is solved when the split-plot layout arrangement is used within the constraints. This study's primary goal was to find the best split-plot design (SPD) for the settings mixture-process variables. The SPD was made up of a simplex centroid design (SCD) of four mixture blends and a factorial design with a central composite design (CCD) of the process variable and compared six different context split-plot structure arrangement.  We used JMP software version 15 to create D-optimal split-plot designs. The study compared the constructed designs' relative efficiency using A-, D-, I-, and G- optimality criteria. Furthermore, a graphical technique (fraction of design space plot) was used to display, explain, and evaluate experimental designs' performance in terms of precision of the six designs' variance prediction properties. We discovered that arranging subplots with more SCD points than pure mixture design points within SPD with two high process variables is more helpful and provides more precise parameter estimates. We recommend using SPDs in experiments involving mixture process settings developments to measure the mixture components' interaction effects and the processing conditions. Also, the investigation should be set up at each of the points of a factorial design.

scholarly journals Exploration of D-, A-, I- and G- Optimality Criteria in Mixture Modeling

2021 ◽  
pp. 15-28
Author(s):  
Samson W. Wanyonyi ◽  
Ayubu A. Okango ◽  
Julius K. Koech
Keyword(s):  
Optimal Design ◽  
Literature Review ◽  
Optimality Criterion ◽  
Process Variable ◽  
Optimality Criteria ◽  
Mixture Modeling ◽  
Process Variables ◽  
Combination Model ◽  
Design Optimality ◽  
Plot Design

A design optimality criterion, such as D-, A-, I-, and G- optimality criteria, is often used to analyze, evaluate and compare different designs options in mixture modeling test. A mixture test is an experiment where the descriptive variable and response rely only on the mixture's relative ratio in the mix but not its composition. The study geared toward exploring D-, A-, I-, and G- optimality criteria and their efficiency in determining an optimal split-plot design in mixture modeling within the presences of process variables. We evaluated and discussed in detail D-, A-, I-, and G- optimality criteria based on literature review. We also explored and examine why I- and D-optimal criteria are often involved within the formulation of an optimal design in the context of mixture process variable settings. We recommend that optimality criterion must always be used when assessing the various styles of designs so as to search out a desirable design that matches a combination model.

A Case Study Involving Mixture–Process Variable Experiments within a Split-Plot Structure

2012 ◽  
Vol 24 (1) ◽  
pp. 80-93
Author(s):  
Tae-Yeon Cho ◽  
Douglas C. Montgomery ◽  
Connie M. Borror
Keyword(s):  
Process Variable ◽  
Split Plot ◽  
Plot Structure

scholarly journals Lab-Scale Fiber Spinning Experimental Design Cost Comparison

2010 ◽  
Vol 5 (1) ◽  
pp. 155892501000500 ◽  
Author(s):  
Jeffrey C. Moreland ◽  
Julia L. Sharp ◽  
Philip J. Brown
Keyword(s):  
Factorial Design ◽  
Response Surface ◽  
Second Order ◽  
Fiber Spinning ◽  
Raw Material ◽  
Time Cost ◽  
Response Surface Design ◽  
Surface Design ◽  
Split Plot ◽  
Plot Design

Many statistical experimental designs are too costly or require too much raw material to be feasible for lab-scale fiber spinning experiments. In this study a four-factor response surface design is presented to study the fiber spinning process in detail at the lab scale. The time, cost, and amount of raw material required to execute the proposed design are compared to the typical completely randomized 24 factorial design used in fiber spinning experiments and also to a standard four-factor response surface design. Sample fiber data as well as analysis from a typical statistical software package is provided to further demonstrate the differences between each design. By designating some treatment factors in the design as hard-to-change, split-plotting is used to reduce the time, cost, and amount of raw material required to complete the experiment. The proposed split-plot design is faster and less expensive than a typical factorial design and has the advantage of fitting a more complex second-order model to the system. When compared to a standard response surface design, the proposed split-plot design provides the same second-order modeling capabilities but reduces the cost of the experiment by 53%, the total time by 36%, and the amount of polymer required by 24%. Thus, a split-plot response surface design based on hard-to-change factors is recommended in lab-scale spinning.

scholarly journals A Split Plot Design for an Optimal Mixture Process Variable Design of a Baking Experiment

2019 ◽  
Vol 1417 ◽  
pp. 012018
Author(s):  
Mika Alvionita Sitinjak ◽  
Utami Dyah Syafitri ◽  
Erfiani
Keyword(s):  
Process Variable ◽  
Split Plot ◽  
Plot Design

scholarly journals Genotype and environmental interaction effect on heterosis expression in maize

Genetika ◽  
2004 ◽  
Vol 36 (2) ◽  
pp. 171-180 ◽  
Author(s):  
Branka Kresovic ◽  
Zivorad Videnovic ◽  
Miodrag Tolimir
Keyword(s):  
Interaction Effect ◽  
Environmental Interaction ◽  
Maize Hybrids ◽  
Rainfed Conditions ◽  
Split Plot ◽  
Set Up ◽  
Curvilinear Regression ◽  
Plot Design

The three-year studies on effects of irrigation and sowing densities were carried out on chernozem at Zemun Polje in the period 1998-2000. The four-replicate trial was set up according to the split-plot design. Six ZP maize hybrids (ZP 360, ZP 539, ZP 580, ZP 633, ZP 677. and ZP 704) were sown in seven densities (40,816, 50,125, 59,523, 69,686, 79,365, 89,286 and 98,522 plants ha-1) under both, irrigation and rainfed conditions. Obtained results indicate that yields of hybrids under irrigation conditions were lower at sowing densities up to 50.000 plants ha-1 (40,816 and 50,125). The hybrid ZP 539 had similar yields (13.44-13.93 t ha-1) at densities ranging from 60,000 to 100,000 plants ha-1. The highest yields of hybrids ZP 360 and ZO 580 were achieved with the densities of 80,000, 90,000 and 100,000 plants ha-1. The hybrid ZP 633 had the highest yields at the densities of 60,000-90,000 plants ha-1, while the highest yields of the hybrids ZP 677 and ZP 704 were achieved with densities of 60,000-100,000 plants ha-1. The curvilinear regression was determined by the analysis of dependence of achieved yields of maize hybrids on sowing densities. The following maximum yields could be expected under irrigation conditions: ZP 360 - 14.19 t ha-1 with the sowing density of 93,500 plants ha-1; ZP 539 - 14.03 t ha-1 with the sowing density of 78,500 plants ha-1; ZP 580 - 14.41 t ha-1 with the sowing density of 95,700 plants ha-1; ZP 633 - 13.64 t ha-1 with the sowing density of 80,000 plants ha-1: ZP 677 - 13.31 t ha-1 with the sowing density of 92,250 plants ha-1 and ZP 704 - 14.33 t ha-1 with the sowing density of 84,111 plants ha-1.

scholarly journals Nitrogén, réz és molibdén kölcsönhatások repcére (Brassica napus L.)

2017 ◽  
Vol 66 (2) ◽  
pp. 349-360
Author(s):  
Imre Kádár
Keyword(s):  
Soil Analysis ◽  
N Fertilization ◽  
List Type ◽  
Brassica Napus L ◽  
Calcium Ammonium Nitrate ◽  
Cu Content ◽  
Plant Parts ◽  
Split Plot ◽  
Set Up ◽  
Plot Design

Interactions between the elements N, Cu and Mo were studied on rape in 2000 in a field experiment set up on chernozem loam soil with lime deposits. The ploughed layer of the soil contained 3% humus, around 5% CaCO3 and around 20% clay. Soil analysis showed that the area was well supplied with Ca, Mg, K and Mn, had satisfactory Cu content, but was only poorly or moderately supplied with P and Zn. The groundwater depth was 13–15 m and the area was prone to drought. The experiment was originally set up in a split-plot design with 4N × 3Cu = 12 treatments in three replications, giving a total of 36 plots. The N rates, applied as calcium ammonium nitrate, were 0, 100, 200 and 300 kg ha−1 and the Cu rates, in the form of CuSO4, were 0, 50 and 100 kg ha−1. In the 5th year of the experiment the 15 m long plots were halved and the two half-plots were separated by a 1 m path. The experiment thus became a strip-split-plot design, consisting of 4N×3Cu×2Mo = 24 treatments in three replications, giving a total of 72 plots. The 48 kg ha−1 Mo was applied in the form of (NH4)6Mo7O24·4H2O. The generative phases of flowering and ripening were characterized by drought and depression. The main results were as follows: As a result of N fertilization, the seed yield fell from 2 t ha−1 to 0.8 t ha−1. However, the stem yield increased from 5 t ha−1 to 8 t ha−1 due to the more favourable N effects in the vegetative phase. As a result, the harvest index increased from 4.6 to 13.0.Most of the element contents became concentrated and enriched in the plant parts. The concentrations of Na, Fe, Mn and Zn increased with the N supply, whereas that of Ba decreased in the straw at harvest. Both N and Cu addition stimulated the incorporation of Cu in the straw. The phenomenon of N×Mo synergy was observed. N and Mo became enriched in the stem in both the N and Mo treatments. This N×Mo interaction was also manifested in the seed.Higher contents of N, P, Mg, Zn, Cu, Mo, Se and Co were recorded in the seed at harvest, exceeding the concentrations in the straw. A total of 206 kg N, 172 kg Ca, 142 kg K, 78 kg S, 39 kg P and 32 kg Mg was incorporated into the aboveground biomass of rapeseed, i.e. 10.4 t ha−1 air-dry matter. In the case of combine harvesting, if the by-products are ploughed into the soil, the quantity of nutrients leaving the field falls to a fraction.Under the conditions of this experiment, 40 kg N, 5 kg Ca (7 kg CaO), 14 kg K (17 kg K2O), 10 kg S, 12 kg P (27 kg P2O5) and 5 kg Mg (8 kg MgO) was required for the production of 1 t rapeseed. These data could serve as a guideline for the extension service in establishing the nutritional needs of winter rapeseed.

scholarly journals Nitrogén, réz és molibdén kölcsönhatások lucerna kultúrában (Medicago sativa L.)

2017 ◽  
Vol 66 (2) ◽  
pp. 375-390
Author(s):  
Imre Kádár
Keyword(s):  
Nutrient Content ◽  
List Type ◽  
Calcium Ammonium Nitrate ◽  
Cu Content ◽  
Wide Range ◽  
Split Plot ◽  
Loam Soil ◽  
Mo Content ◽  
Set Up ◽  
Plot Design

Interactions between the elements N, Cu and Mo were studied on alfalfa in 1996-1999 in a field experiment set up on chernozem loam soil with lime deposits. The ploughed layer of the soil contained 3% humus, around 5% CaCO3 and around 20% clay. Soil analysis showed that the area was well supplied with Ca, Mg, K and Mn had satisfactory Cu content, but was only poorly or moderately supplied with P and Zn. The groundwater depth was 13–15 m and the area was prone to drought. The experiment was originally set up in a split-plot design with 4N × 3Cu = 12 treatments in three replications, giving a total of 36 plots. The N rates, applied as calcium ammonium nitrate, were 0, 100, 200 and 300 kg·ha−1 and the Cu rates, in the form of CuSO4, were 0, 50 and 100 kg·ha−1. In the 5th year of the experiment the 15 m long plots were halved and the two half-plots were separated by a 1 m path. The experiment thus became a strip-split-plot design, consisting of 4N×3Cu×2Mo = 24 treatments in three replications, giving a total of 72 plots. The 48 kg·ha−1 Mo was applied in the form of (NH4)6Mo7O24·4H2O. The main results were as follows: In this chernozem loam soil the N, Cu, Mo treatments did not affect the yield of alfalfa. During the four years studied (1996–1999), a total of 32 t·ha−1 of hay was harvested, with maximum yields (4–5 t·ha−1) at the first mowing. Considering the years, the 2nd year of alfalfa was the most successful with a yield of 11 t·ha−1.With increasing rates of N, the incorporation of N, NO3-N, Ca, Mg, Na, and sometimes Cu increased, while that of K decreased in the hay. Due to the 10–12-year residual effect of CuSO4 the original Cu content of the hay improved by 30–50%, i.e. 2–4 mg·kg–1.A single dose of 48 kg·ha−1 Mo raised the hay Mo content by an order of magnitude to 18–69 mg·kg–1 even after 5–8 years. The Mo content decreased with age and the number of mowings. Nevertheless, the hay became unsuitable for use as animal feed. Mo fertilization also influenced the incorporation of other elements, demonstrably increasing the uptake of N, Ca and Mg and moderating that of K, NO3-N and Cu.As a specific catalyst for the N-binding microorganisms in the soil, Mo is able to increase the soil N supply and thus the N content of the plants. Mo is also necessary for NO3 reduction, so the quantity of NO3-N is reduced through incorporation into proteins in response to Mo. In the present experiment, N-Mo and N-Cu synergism and Mo-NO3 antagonism were manifested.Due to the influence of the different years, mowings and treatments, the minimum and maximum element contents of the hay varied over a wide range. In 12 mowings over the course of four years a total of 1190 kg N, 787 kg K, 768 kg Ca, 154 kg Mg, 128 kg S, 102 kg P, 12 kg Na, 8 kg Fe, 5 kg Al, 4 kg Sr and 2 kg each of Mn and B was taken up per hectare, together with 416 g Zn, 288 g Ba, 256 g Cu and 96 g Mo per ha. The uptake of Mo was 1131 g·ha−1 on Mo-treated soil.The specific nutrient content of 1 t hay was 37 kg N, 25 kg K, 24 kg Ca, 5 kg Mg and 3 kg P (7 kg P2O5). N abundance was associated with elevated specific nutrient content under the given experimental conditions. On this soil atmospheric N fixation was able to cover the N requirements of alfalfa.

scholarly journals PENGARUH PEMANGKASAN TANAMAN SENGON TERHADAP KERAGAAN TANAMAN SELA DALAM SISTEM AGROFORESTRI SENGON

BUANA SAINS ◽  
2008 ◽  
Vol 8 (2) ◽  
pp. 189
Author(s):  
Abdul Hamid
Keyword(s):  
Agroforestry System ◽  
Growth And Yield ◽  
Paraserianthes Falcataria ◽  
Split Plot ◽  
And Performance ◽  
Set Up ◽  
Tree Performance ◽  
Plot Design

The effects of pruning of Paraserianthes falcataria tree in an agroforestry system on yield of intercrops and tree performance were studied at Perhutani RPH Jatirejo, BKPH Pare, KPJH Kediri. Maize, stick nut, and chili were used as companion crops in between rows of two years old Paraserianthes falcataria tree. A split plot design with four replicates was set up for the experiment. The trees were 25%, 50% and 75% pruned. The measured parameters included growth and yield of the intercrops and performance of the tree. Results of this study showed that regular pruning of the agroforestry tree and planting of intercrops did not hinder growth and performance of the agroforestry tree, especially that was pruned 75%. Pruning of the tree also increase yield of the intercrops

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