Design of Experiments

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Chapter 14

• Design of Experiments

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Introduction

• Concerns experimentation to determine the
  relationship between manipulable factors and a
  response of interest
• Each combination of factors is a design point
• An individual response values with its factor
  settings is a run
• Want to minimize the number of runs while
  maximizing what you learn

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Experiment Designs

• Screening Designs which of many factors have the
  greatest effect on the response. Factors settings
  are usually binary (hi/lo on/off etc.)
• Response Surface Designs which settings of a set
  of continuous factors give the best response
• Factorial Designs look at many combinations of
  factor levels (chosen judiciously)

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Example Acme Pinata Corp

• 9 factors define a glue
• Flour (white/whole wheat)
• Sifted (yes/no)
• Type (water/milk)
• Temp (cool/warm)
• Salt (yes/no)
• Liquid (4/5 teaspoons)
• Clamp (yes/no)
• Sugar (yes/no)
• Coat (thin/thick)
• Response strength of bond between two pieces of
  paper

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Main effects here are counfounded with 2-way
interactions
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Analysis of the data must assume 2-way
interactions are all zero
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SiftedYes ?(TypeW SaltYes) or (TypeM
SaltNo) SiftedNo ?(TypeW SaltNo) or
(TypeM SaltYes)
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Fractional Fractorial Resolution
resolution 3 Main effects are not confounded
with other main effects. They are confounded with
one or more two-way interactions, which must be
assumed to be zero for the main effects to be
meaningful. resolution 4 Main effects are
not confounded with either other main effects or
two-factor interactions. However, two-factor
interactions can be confounded with other
two-factor interactions. resolution 5 There
is no confounding between main effects, between
two-factor interactions, or between main effects
and two-factor interactions.
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Blocking for extraneous factors
e.g. suppose could only do 4 runs per day
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Analysis of the Data
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Screening for Interactions

• Optimizing operation of a nuclear plant
• Five factors
• Feed rate (10/15)
• Catalyst (1/2)
• Stir rate (100/120)
• Temperature (140/180)
• Concentrator (3/6)
• Response is reactor output
• Full Factorial design has 32 runs

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JMP DOE Prepares the Model
Generates the correct Fit Model dialog for the
design
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Interaction Profiles
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Response Surface Designs

• Useful for modeling a curved surface as a
  function of continuous factors
• Curved usually means quadratic
• Need three levels of each factor to fit a
  quadratic
• Standard designs include central composite and
  Box-Behnken

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Central Composite
Box-Behnken
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