Lecture 1

1 / 9

# Lecture 1 - PowerPoint PPT Presentation

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Lecture 1' - lunea-mayo

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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