Lecture 1 zCourse Outline zToday: Sections zNext Day: Quick Review of Sections and 1.9 with examples zPlease read these sections. You are responsible for all material in these sections…even those not discussed in class zReview of Regression and Analysis of Variance (ANOVA)…next Saturday at 12:00 in Frieze B166

Experiment zExperimentation is commonly used in industrial and scientific endeavors to understand a system or process zIn an experiment, the experimenter adjusts the settings of input variables (factors) to observe the impact on the system zBetter understanding of how the factors impact the system allows the experimenter predict future values or optimize the process

Why Experimentation zDoctor may believe treatment A is better than treatment B…Engineer believes rust treatment A is more effective than rust treatment B zApparent differences could be due to: yRandom Variation yPhysical differences in experimental units zScientific evidence is required

What is an Experiment Design? zSuppose you are going to conduct an experiment with 8 factors zSuppose each factor has only to possible settings zHow many possible treatments are there? zSuppose you have enough resources for 32 trials. Which treatments are you going to perform? zDesign: specifies the treatments, replication, randomization, and conduct of the experiment

Some Definitions zFactor: variable whose influence upon a response variable is being studied in the experiment zFactor Level: numerical values or settings for a factor zTreatment or level combination: set of values for all factors in a trial zExperimental unit: object, to which a treatment is applied zTrial: application of a treatment to an experimental unit zReplicates: repetitions of a trial zRandomization: using a chance mechanism to assign treatments to experimental units

Types of Experiments zTreatment 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) zVariable Screening: Have a large number of factors, but only a few are important. Experiment should identify the important few. (we will focus on these!) zResponse Surface Exploration: After important factors have been identified, their impact on the system is explored

Types of Experiments zSystem Optimization: Often interested in determining the optimum conditions (e.g., Experimenters often wish to maximize the yield of a process or minimize defects) zSystem 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 zState the objective of the study zChoose the response variable…should correspond to the purpose of the study xNominal the best xlarger the better or smaller the better zChoose factors and levels xAre factors qualitative or quantitative? zChoose experiment design (purpose of this course) zPerform the experiment (use a planning matrix to determine the set of treatments and the order to be run…use true level settings) zAnalyze data (design should be selected to meet objective and so analysis is efficient and easy) zDraw conclusions

Fundamental Principles zReplication: each treatment is applied to experimental units that are representative of the population of interest yreplication allows for estimation of the experimental error yincreasing number of replicates decreases variance of treatment effects and increases the power to detect significant differences zRandomization: use of a chance mechanism (e.g., random number generator) to assign treatments to experimental units or to the sequence of experiments yprovides protection against unknown lurking variables zBlocking: run groups of treatments on homogenous units (block) to reduce variability of effect estimates and have more fair comparisons