Full Factorial and Fractional Factorial Experiments at Three Levels

2021 ◽  
pp. 265-314
Keyword(s):  
Fractional Factorial ◽  
Factorial Experiments ◽  
Full Factorial

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.

Optimal Design Procedure for Two-Level Fractional Factorial Experiments Given Partial Prior Information about Parameters

1978 ◽  
Vol 22 (1) ◽  
pp. 598-598
Author(s):  
Steven M. Sidik ◽  
Arthur G. Holms
Keyword(s):  
Optimal Design ◽  
Prior Knowledge ◽  
Prior Information ◽  
Design Procedure ◽  
Fractional Factorial ◽  
Factorial Experiment ◽  
Factorial Experiments ◽  
Full Factorial Experiment ◽  
Main Effects ◽  
Full Factorial

In many cases in practice an experimenter has some prior knowledge of indefinite validity concerning the main effects and interactions which would be estimable from a two-level full factorial experiment. Such information should be incorporated into the design of the experiment.

Sensitivity Analysis of a 2.5kW Proton Exchange Membrane Fuel Cell Stack by Statistical Method

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
N. Rajalakshmi ◽  
G. Velayutham ◽  
K. S. Dhathathreyan
Keyword(s):  
Sensitivity Analysis ◽  
Fuel Cell ◽  
Proton Exchange Membrane ◽  
Proton Exchange ◽  
Fractional Factorial ◽  
Factorial Experiments ◽  
Fuel Cell Stack ◽  
Fuel Cell Performance ◽  
Exchange Membrane ◽  
Full Factorial

This paper describes the application of statistical analysis to a 2.5kW proton exchange membrane fuel cell stack operation, by experimental design methodology, whereby robust design conditions were identified for the operation of fuel cell stacks. The function is defined as the relationship between the fuel cell power and the operating pressure and stoichiometry of the reactants. Four types of control factors, namely, the pressures of the fuel and oxidant and the flow rates of the fuel and oxidant, are considered to select the optimized conditions for fuel cell operation. All the four factors have two levels, leading a full factorial design requiring 24 experiments leading to 16 experiments and fractional factorial experiments, 24−1, leading to 8 experiments. The experimental data collected were analyzed by statistical sensitivity analysis by checking the effect of one variable parameter on the other. The mixed interaction between the factors was also considered along with main interaction to explain the model developed using the design of experiments. The robust design condition for maximum fuel cell performance was found to be air flow rate, and the interaction between the air pressure and flow rate compared to all other factors and their interactions. These fractional factorial experiments, presently applied to fuel cell systems, can be extended to other ranges and factors with various levels, with a goal to minimize the variation caused by various factors that influence the fuel cell performance but with less number of trials compared to full factorial experiments.

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.

scholarly journals 3D Printing for Energy-Saving: Evidence from Hydraulic Manifolds Design

Energies ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2462 ◽  
Author(s):  
Jun-hui Zhang ◽  
Gan Liu ◽  
Ruqi Ding ◽  
Kun Zhang ◽  
Min Pan ◽  
...  
Keyword(s):  
High Pressure ◽  
Pressure Drop ◽  
Numerical Methods ◽  
3D Printing ◽  
Pressure Loss ◽  
Smooth Transition ◽  
Factorial Experiments ◽  
Space Requirement ◽  
Geometrical Features ◽  
Full Factorial

With the compact circuit layout and small size, hydraulic manifolds sometimes cause high pressure loss. The purpose of this paper is to investigate the pressure loss under different circumstances with various geometry features and present solutions to reduce pressure loss. The pressure loss performance is evaluated by both experimental and numerical methods. Verified by the experiments, the numerical simulations are qualified to depict the correct trend of the pressure drop. After the basic analysis of traditional passages, three novel forms are proposed, which are very hard to be manufactured by a common method. Furthermore, the geometrical features are selected optimally by means of full factorial experiments to balance the pressure loss and space requirement. Moreover, taking advantage of 3D printing, it is possible to build the passages in novel forms which are beyond the capacity of conventional manufacturing. Results show that the pressure loss can be reduced considerably by adopting a smooth transition, where the reduction can reach up to 50%.

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