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

• 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

• 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

• 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

• 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

• 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

• 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

• 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!)

• 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

• 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