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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

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Lecture 1

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  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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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!)

  8. 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

  9. 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

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