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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

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lecture 1
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
  • 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
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
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
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
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 experiments1
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
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
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