Design of Experiments (DOE)

This branch of applied statistics deals with planning, conducting, analyzing and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters.

A strategically planned and executed experiment may provide a great deal of information about the effect on a response variable due to one or more factors. Many experiments involve holding certain factors constant and altering the levels of another variable. This One–Factor–at–a–Time (or OFAT) approach to process knowledge is, however, inefficient when compared with changing factor levels simultaneously.

Many of the current statistical approaches to designed experiments originate from the work of R. A. Fisher in the early part of the 20th century. Fisher demonstrated how taking the time to seriously consider the design and execution of an experiment before trying it helped avoid frequently encountered problems in analysis. Key concepts in creating a designed experiment include blocking, randomization and replication.

A well–performed experiment may provide answers to questions such as:

  • What are the key factors in a process?
  • At what settings would the process deliver acceptable performance?
  • What are the key, main and interaction effects in the process?
  • What settings would bring about less variation in the output?

A repetitive approach to gaining knowledge is encouraged, typically involving these consecutive steps:

  1. A screening design which narrows the field of variables under assessment.
  2. A “full factorial” design which studies the response of every combination of factors and factor levels, and an attempt to zone in on a region of values where the process is close to optimization.
  3. A response surface design to model the response.

Blocking: When randomizing a factor is impossible or too costly, blocking lets you restrict randomization by carrying out all of the trials with one setting of the factor and then all the trials with the other setting.

Randomization: Refers to t he order in which the trials of an experiment are performed. A randomized sequence helps eliminate effects of unknown or uncontrolled variables.

Replication: Repetition of a complete experimental treatment, including the setup.

Contributed by Keith M. Bower, www.KeithBower.com.

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