QUANT homework

Design of Experiments

Experimental Design

• Systematic process to layout, design, and investigate problems in research and industry

• Starts with a screening process to identify factors (variables) that may have an impact on responses intended to be observed • May consist of a number of iterative experiments to upgrade and revise factors and details

understood regarding the factors • Start by choosing factors that may affect results • Factors that do not change during the experiments are referred to as constants (or controlled)

• Optimization follows the screen process where the focus is on establishing an approach for predicting the response variable from the factors identified during the screening process • Formulate hypothesis of the relation between factors and predicted outcomes of the experiment • Construct a statistical model that represents experiment results

• Testing follows optimization to ensure procedures are sound and to evaluate the robustness relative to fluctuations in factor conditions

Experimental Design

• The experimental design specifies the number and type of experiments as well as the factors and their combinations used for each experiment, and how many times experiments will be run (replicated) and in what order. • What measurements to take (responses) is also specified

• Specify conditions and assumptions under which experiments are run is determined

• What levels (values) of each factor should be examined

• Resources and materials needed for the experiments are stated

• Run a series of simulations , or actual experiments, to refine factor selection and understanding of factor effects

Sections to include in Experimental Design write up • Title

• Hypothesis (questions to be investigated)

• Design type (simple, factorial, partial factorial)

• Factors and Levels of the factors

• Response variable and how it is measured

• Number of replications

• Constraints, assumptions, limitations of the experiment

Some frequent responses that are measured

• Mean

• Standard deviation

• Variance

• Standard error

Type of Experimental Designs

• Simple • Start with a initial benchmark configuration and then vary one factor level of a factor

at a time and then observe performance • The number (n) of experiments to be conducted is

• Where ni is the number of levels for the ith factor. K is the number of factors. For example, in an experiment with 2 factors with 3 and 4 levels respectively

n= 1 + (3-1) + (4-1) = 1 + 2 + 3 = 6 simple experiments are to be conducted

Types of Experimental Designs

• Full factorial design • For each successive experiment or simulation, investigate all possible

combinations of all factor levels

• The number (n) of experiments to be conducted is

• For example, in an experiment with 2 factors with 3 and 4 levels respectively

n= 3x4 = 12 experiments are to be conducted

Type of Experimental Designs

• Fractional Factorial Designs • Uses a subset of factors and factor levels in the experiments

• Experimental groupings

• Conducting a full factorial design investigation may not be warranted or feasible

• Number of experiments to conduct is determined by multiplying together the subset of factor levels of the select factors that will be investigated

Power of a design

• Used to address issues of experimental accuracy • Determine sample size needed to measure the response at a desired level of

accuracy

Experimental Design common errors

• Ignoring causes of experimental error that may impact results

• All important factors, that can impact results, have not been identified

• When varying several factors, have a lack of clarity to what the actual effect is

• Using multiple simple designs as opposed to a factorial design

• Not examining the impact of interactions between factors … if factor level effects are being influenced by the presence of other factor levels