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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