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