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Lecture 1

- Course Outline
- Today: Sections 1.1-1.3
- Next Day: Quick Review of Sections 1.4-1.7 and 1.9 with examples
- Please read these sections. You are responsible for all material in these sections…even those not discussed in class
- Review of Regression and Analysis of Variance (ANOVA)…next Saturday at 12:00 in Frieze B166

Experiment

- Experimentation is commonly used in industrial and scientific endeavors to understand a system or process
- In an experiment, the experimenter adjusts the settings of input variables (factors) to observe the impact on the system
- Better understanding of how the factors impact the system allows the experimenter predict future values or optimize the process

Why Experimentation

- Doctor may believe treatment A is better than treatment B…Engineer believes rust treatment A is more effective than rust treatment B
- Apparent differences could be due to:
- Random Variation
- Physical differences in experimental units
- Scientific evidence is required

What is an Experiment Design?

- Suppose you are going to conduct an experiment with 8 factors
- Suppose each factor has only to possible settings
- How many possible treatments are there?
- Suppose you have enough resources for 32 trials. Which treatments are you going to perform?
- Design: specifies the treatments, replication, randomization, and conduct of the experiment

Some Definitions

- Factor: variable whose influence upon a response variable is being studied in the experiment
- Factor Level: numerical values or settings for a factor
- Treatment or level combination: set of values for all factors in a trial
- Experimental unit: object, to which a treatment is applied
- Trial: application of a treatment to an experimental unit
- Replicates: repetitions of a trial
- Randomization: using a chance mechanism to assign treatments to experimental units

Types of Experiments

- Treatment Comparisons: Purpose is to compare several treatments of a factor (have 3 diets and would like to see if they are different in terms of effectiveness)
- Variable Screening: Have a large number of factors, but only a few are important. Experiment should identify the important few. (we will focus on these!)
- Response Surface Exploration: After important factors have been identified, their impact on the system is explored

Types of Experiments

- System Optimization: Often interested in determining the optimum conditions (e.g., Experimenters often wish to maximize the yield of a process or minimize defects)
- System Robustness: Often wish to optimize a system and also reduce the impact of uncontrollable (noise) factors. (e.g., would like a fridge to cool to a set temperature…but the fridge must work in Florida, Alaska and Michigan!)

Systematic Approach to Experimentation

- State the objective of the study
- Choose the response variable…should correspond to the purpose of the study
- Nominal the best
- larger the better or smaller the better
- Choose factors and levels
- Are factors qualitative or quantitative?
- Choose experiment design (purpose of this course)
- Perform the experiment (use a planning matrix to determine the set of treatments and the order to be run…use true level settings)
- Analyze data (design should be selected to meet objective and so analysis is efficient and easy)
- Draw conclusions

Fundamental Principles

- Replication: each treatment is applied to experimental units that are representative of the population of interest
- replication allows for estimation of the experimental error
- increasing number of replicates decreases variance of treatment effects and increases the power to detect significant differences
- Randomization: use of a chance mechanism (e.g., random number generator) to assign treatments to experimental units or to the sequence of experiments
- provides protection against unknown lurking variables
- Blocking: run groups of treatments on homogenous units (block) to reduce variability of effect estimates and have more fair comparisons

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