scholarly journals FRACTIONAL FACTORIALS IN A CASE STUDY NUTRITION EXPERIMENT WITH BANANA TREES

2019 ◽  
Vol 37 (3) ◽  
pp. 335
Author(s):  
Paulo César Moraes RIBEIRO ◽  
Matheus Pena CAMPOS ◽  
Leila Aparecida Salles PIO ◽  
Júlio Sílvio de Sousa BUENO FILHO
Keyword(s):  
Reference Population ◽  
Fractional Factorial ◽  
Optimized Design ◽  
Fractional Factorials ◽  
Planning Strategy ◽  
Banana Tree ◽  
Average Variance ◽  
Potential Factors ◽  
Quadratic Effects ◽  
Full Factorial

In this paper we study combining designs concatenating levels from a full factorial for some factors with screening alternatives for the others. This was done to deal with a practical situation in plant nutrition experiments. The original problem was a study design for 14 potential factors in banana tree nutrition, and researchers imagined four full factorials were needed to test their hypothesis, being two from the 33 and two of the 34 series. As this would demand at least 216 experimental units and facing limited resources we seek for a different planning strategy. The idea was to combine in the same experiment four  instances of DSD (Denitive Screening Designs) for 10 three-level factors, each in a different block, with a fraction of the full factorial of the 34 series. A central point treatment, with average level for all factors, was present in all blocks. Interchange algorithms were used to concatenate the factor levels. Resulting optimized design was compared to the designs sampled following the same principle. Design comparison criterion was the expected average variance of the estimates for factors (Ar optimality). Optimization  reduced 4.02% of the average values of the criterion in a reference population of sampled designs. It was possible to show that the variance for linear and quadratic effects in the full factorial were higher than in the optimized plan. As an example, the analysis of an actual eld trial is presented. Authors recommend the use of fractional factorial strategy including DSD designs in agronomic trials, specially in the screening phase.

Generation of Two-Level Cost Optimal Fractional Factorials

1978 ◽  
Vol 22 (1) ◽  
pp. 599-599
Author(s):  
Joseph J. Pignatiello
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Minimum Cost ◽  
Fractional Factorial ◽  
Factorial Experiment ◽  
Mathematical Programming Problem ◽  
Fractional Factorials ◽  
Number Of Factors ◽  
Main Effects ◽  
Full Factorial

It is assumed that, in a 2k factorial experiment, there are different costs per observation at each of the factor combinations. When the number of factors, k, increases, the total number of observations in the full factorial increases rapidly as does the expense of observing all observations in the full factorial. If the experimenter can assume certain classes of higher-order interactions are negligible, then advantage may be taken by observing measurements from an orthogonal fractional factorial. For any “1/2p” fraction of the full factorial, a 2k-p experiment, there are 2p feasible orthogonal fractions that could be selected at random. This paper develops an algorithm for generating the minimum cost such fraction in an efficient way. The problem is formulated as a mathematical programming problem subject to a resolution III constraint (main effects unconfounded). Computational experience is presented.

Exploring the Role of Interaction Effects in Visual Conjoint Analysis

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Brian Sylcott ◽  
Jeremy J. Michalek ◽  
Jonathan Cagan
Keyword(s):  
Conjoint Analysis ◽  
Consumer Preferences ◽  
Consumer Preference ◽  
Interaction Effects ◽  
Fractional Factorial ◽  
Main Effects ◽  
Full Factorial ◽  
Biased Estimates ◽  
Data Requirements

In conjoint analysis, interaction effects characterize how preference for the level of one product attribute is dependent on the level of another attribute. When interaction effects are negligible, a main effects fractional factorial experimental design can be used to reduce data requirements and survey cost. This is particularly important when the presence of many parameters or levels makes full factorial designs intractable. However, if interaction effects are relevant, main effects design can create biased estimates and lead to erroneous conclusions. This work investigates consumer preference interactions in the nontraditional context of visual choice-based conjoint analysis, where the conjoint attributes are parameters that define a product's shape. Although many conjoint studies assume interaction effects to be negligible, they may play a larger role for shape parameters. The role of interaction effects is explored in two visual conjoint case studies. The results suggest that interactions can be either negligible or dominant in visual conjoint, depending on consumer preferences. Generally, we suggest using randomized designs to avoid any bias resulting from the presence of interaction effects.

The Mechanisms by Which Adaptive One-factor-at-a-time Experimentation Leads to Improvement

2005 ◽  
Vol 128 (5) ◽  
pp. 1050-1060 ◽  
Author(s):  
Daniel D. Frey ◽  
Rajesh Jugulum
Keyword(s):  
Case Studies ◽  
Random Error ◽  
High Probability ◽  
Fractional Factorial ◽  
Engineering Systems ◽  
Factorial Experiments ◽  
Physical Experiments ◽  
Simulation Results ◽  
Main Effects ◽  
Full Factorial

This paper examines mechanisms underlying the phenomenon that, under some conditions, adaptive one-factor-at-a-time experiments outperform fractional factorial experiments in improving the performance of mechanical engineering systems. Five case studies are presented, each based on data from previously published full factorial physical experiments at two levels. Computer simulations of adaptive one-factor-at-a-time and fractional factorial experiments were carried out with varying degrees of pseudo-random error. For each of the five case studies, the average outcomes are plotted for both approaches as a function of the strength of the pseudo-random error. The main effects and interactions of the experimental factors in each system are presented and analyzed to illustrate how the observed simulation results arise. The case studies show that, for certain arrangements of main effects and interactions, adaptive one-factor-at-a-time experiments exploit interactions with high probability despite the fact that these designs lack the resolution to estimate interactions. Generalizing from the case studies, four mechanisms are described and the conditions are stipulated under which these mechanisms act.

Characterization of a Solid Oxide Fuel Cell Gas Turbine Hybrid System Based on a Factorial Design of Experiments Using Hardware Simulation

2011 ◽  
Author(s):  
Bernardo Restrepo ◽  
Larry E. Banta ◽  
David Tucker
Keyword(s):  
Fuel Cell ◽  
Design Of Experiments ◽  
Solid Oxide Fuel Cell ◽  
Factorial Design ◽  
Gas Turbine ◽  
Fractional Factorial Design ◽  
Solid Oxide ◽  
Fractional Factorial ◽  
Oxide Fuel ◽  
Full Factorial

A full factorial experimental design and a replicated fractional factorial design were carried out using the Hybrid Performance (HyPer) project facility installed at the National Energy Technology Laboratory (NETL), U.S. Department of Energy to simulate gasifer/fuel cell/turbine hybrid power systems. The HyPer facility uses hardware in the loop (HIL) technology that couples a modified recuperated gas turbine cycle with hardware driven by a solid oxide fuel cell model. A 34 full factorial design (FFD) was selected to study the effects of four factors: cold-air, hot-air, bleed-air bypass valves, and the electric load on different parameters such as cathode and turbine inlet temperatures, pressure and mass flow. The results obtained, compared with former results where the experiments were made using one-factor-at-a-time (OFAT), show that no strong interactions between the factors are present in the different parameters of the system. This work also presents a fractional factorial design (ffd) 34-2 in order to analyze replication of the experiments. In addition, a new envelope is described based on the results of the design of experiments (DoE), compared with OFAT experiments, and analyzed in an off-design integrated fuel cell/gas turbine framework. This paper describes the methodology, strategy, and results of these experiments that bring new knowledge concerning the operating state space for this kind of power generation system.

Application of the Taguchi method to the design of a robot sensor

Robotica ◽  
1995 ◽  
Vol 13 (6) ◽  
pp. 607-617 ◽  
Author(s):  
H. Rowlands ◽  
D. T. Pham
Keyword(s):  
Experimental Design ◽  
Taguchi Method ◽  
Factorial Design ◽  
Optimum Design ◽  
Fractional Factorial ◽  
Experimental Techniques ◽  
Factorial Designs ◽  
Design Technique ◽  
Systematic Method ◽  
Full Factorial

SummaryThis paper considers the use of the Taguchi method as a means to identify the optimum design of a robot sensor. The sensor is modelled by a complex set of equations which makes optimisation using traditional calculusbased methods difficult. The Taguchi method is employed as a systematic method to understand the performance of the sensor whilst using a limited number of model evaluations. The Taguchi method is based on the experimental design technique and the results of using a full factorial design, 1/2 and 1/4 fractional factorial designs are compared. The advantage of using the Taguchi method over traditional experimental techniques is also discussed.

scholarly journals Neural Network Assisted Experimental Designs for Food Research

2000 ◽  
Vol 5 (2) ◽  
pp. 97
Author(s):  
H.S. Ramaswamy ◽  
C. Chen ◽  
S. Sreekanth ◽  
S.S. Sablani ◽  
S.O. Prasher
Keyword(s):  
Input Data ◽  
Fractional Factorial ◽  
Experimental Designs ◽  
Original Form ◽  
Food Research ◽  
Ann Models ◽  
Mathematical Equations ◽  
The Mean ◽  
Relative Errors ◽  
Full Factorial

The ability of artificial neural networks (ANN) in predicting full factorial data from the fractional data corresponding to some of the commonly used experimental designs is explored in this paper. Factorial and fractional factorial designs such as L8, L9, L18, and Box and Behnken schemes were considered both in their original form and with some variations (L8+6, L15 and L9+1). Full factorial (3 factors x 5 levels) and fractional data were generated employing sixteen different mathematical equations (four in each category: linear, with and without interactions, and non-linear, with and without interactions). Different ANN models were trained and the best model was chosen for each equation based on their ability to predict the fractional data. The best experimental design was then chosen based on their ability to simulate the full- factorial data for each equation. In several cases, the mean relative errors with the L18 design (which had more input data than other models) were even higher than with other smaller fractional design. In general, the ANN assisted Lm, Box and Behnken, L15 and L18 designs were found to predict the full factorial data reasonably well with errors less than 5 %. The L8+6 model performed well with several experimental datasets reported in the literature.  

scholarly journals Assessment of Fractional Factorial Design for the Selection andScreening of Appropriate Components of a Self-nanoemulsifyingDrug Delivery System Formulation

2019 ◽  
Vol 9 (4) ◽  
pp. 609-618 ◽  
Author(s):  
Ilham Kuncahyo ◽  
Syaiful Choiri ◽  
Achmad Fudholi ◽  
Ronny Martien ◽  
Abdul Rohman
Keyword(s):  
Particle Size ◽  
Factorial Design ◽  
Delivery System ◽  
Tween 80 ◽  
Fractional Factorial ◽  
Drug Bioavailability ◽  
Main Effects ◽  
Full Factorial ◽  
Adequate Design ◽  
Selection Of

Purpose: Recently, a self-nanoemulsifying drug delivery system (SNEDDS) has showngreat improvement in the enhancement of drug bioavailability. The selection of appropriatecompositions in the SNEDDS formulation is the fundamental step towards developing asuccessful formulation. This study sought to evaluate the effectiveness of fractional factorialdesign (FFD) in the selection and screening of a SNEDDS composition. Furthermore, the mostefficient FFD approach would be applied to the selection of SNEDDS components.Methods: The types of oil, surfactant, co-surfactant, and their concentrations were selected asfactors. 26 full factorial design (FD) (64 runs), 26-1 FFD (32 runs), 26-2 FFD (16 runs), and 26-3 FFD(8 runs) were compared to the main effect contributions of each design. Ca-pitavastatin (Ca-PVT)was used as a drug model. Screening parameters, such as transmittance, emulsification time,and drug load, were selected as responses followed by particle size along with zeta potentialfor optimized formulation.Results: The results indicated that the patterns of 26 full FD and 26-1 for both main effects andinteractions were similar. 26-3 FFD lacked adequate precision when used for screening owing tothe limitation of design points. In addition, capryol, Tween 80, and transcutol P were selected tobe developed in a SNEDDS formulation with a particle size of 69.7 ± 5.3 nm along with a zetapotential of 33.4 ± 2.1 mV.Conclusion: Herein, 26-2 FFD was chosen as the most efficient and adequate design for theselection and screening of SNEDDS composition. The optimized formulation fulfilled therequirement of a quality target profile of a nanoemulsion.<br />

An Algorithm for Optimized Design of Maneuvering Experiments

2002 ◽  
Vol 46 (03) ◽  
pp. 214-227 ◽  
Author(s):  
S. Sutulo ◽  
C. Guedes Soares
Keyword(s):  
Significant Loss ◽  
Factor Space ◽  
Optimized Design ◽  
Third Order ◽  
Ship Maneuvering ◽  
Important Conclusion ◽  
Under Construction ◽  
The Given ◽  
Full Factorial ◽  
Coarse Grids

Properties of an adjusted version of Mitchell's algorithm for synthesis of D-optimized experimental designs for response estimation were studied numerically for a third-order polynomial linear regression model widely used in ship maneuvering. Numerical experiments for 2, 3, and 4-factor cases were conducted for different numbers of levels in the classic full-factorial plan used as a set of candidate points. Selection of the runs to be included in the design under construction was made after an exhaustive search. Initial designs were obtained with the pseudo-random or quasi-random generation. A method of assembling an optimized design with the given degree of redundancy is proposed. An important conclusion is that relatively coarse grids can be used for discretizing the factor space that can facilitate substantially the synthesis of the designs without any significant loss of quality.

Using Shape Grammars to Identify Salient Features in Support of Product Family Design

2014 ◽  
Author(s):  
Timothy D. Culbertson ◽  
Timothy W. Simpson
Keyword(s):  
Product Family ◽  
Consumer Preference ◽  
Fractional Factorial ◽  
Factorial Experiment ◽  
Ultrasound Transducers ◽  
Shape Grammars ◽  
Product Family Design ◽  
Baseline Design ◽  
The Impact ◽  
Full Factorial

Product form and aesthetics play a major role in consumer preference and product differentiation. During product family design, it is important to differentiate products in the family yet similarities among some stylistic features may connote a more coherent design strategy. Shape grammars offer a method for producing designs with a coherent style along with the ability to control the variation of the output shapes. In this paper, we investigate the use of shape grammars to support product family design, namely, identification of features that shape the perceptions of similarity within a family. A survey-based approach is implemented wherein the impact of a shape parameter on product style is evaluated by comparing design variants to a baseline design. Respondents are asked to rate the style similarities on a Likert-like scale, and candidate shape parameters are screened for aesthetic significance using a fractional factorial experiment. The approach is demonstrated using a family of medical ultrasound transducers, and our screening is validated using a full factorial experiment with practicing ultrasound transducer designers and engineers.

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