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Statistics

Concepts

Experiment

  • Each experiment run is a test.
  • An experiment is a series of runs in which changes are made to the input variables of a process or system.
  • An experiment objective is to determine the influence that misc factors have on the output response of the system.
  • The general approach to planning and conducting an experiment is called the strategy of experimentation.
    • Best-Guess Approach
    • One-Factor-at-a-Time (OFAT)
      • The OFAT method consists of selecting a starting point or baseline set of levels for each factor, and then successively varying each factor over its range with the other factors held constant at the baseline level.
      • The major disadvantage of the OFAT strategy is that it fails to consider any possible interaction between the factors.
    • Factorial Experiment
      • The correct approach to dealing with several factors is to conduct a factorial experiment.
      • This is an experimental strategy in which factors are varied together, instead of one at a time.
      • Each factor (combination) can be replicated in an experiment design.
      • Fractional Factorial Experiment: a variation of the basic factorial de# which only a subset of the runs is used.
  • Experiment Design
    • The three basic principles of experimental design are randomization, replication, and blocking. Sometimes we add the factorial principle to these three.
      • Randomization refers to the allocation of the experimental material and the order of individual runs of the experiment to be determined randomly.
      • Replication refers to an independent repeat run of each factor combination.
      • Blocking is a design technique to improve the precision with which comparisons among the factors of interest are made.
        • Often blocking is used to reduce or eliminate the variability transmitted from nuisance factors.
        • A block is a set of relatively homogeneous experimental conditions.
        • Each level of the nuisance factor becomes a block.
        • Then the experimenter divides the observations from the statistical de#to groups that are run in each block.

Design of Experiments

  1. Recognition of and statement of the problem
    • Factor screening or characterization
    • Optimization
    • Confirmation
    • Discovery
    • Robustness
  2. Selection of the response variable
  3. Choice of factors, levels, and range
  4. Choice of experimental design
  5. Performing the experiment
  6. Statistical analysis of the data
  7. Conclusions and recommendations

TBD

  • Random Variables
    • Discrete
    • Continuous
  • Regression Analysis
    • Linear Regression Models
    • Non-Linear Regression Models
  • Survival Analysis
    • Non-Parametric Models
    • Parametric Models