One Factorata Time OFAT Vs' Designed Experiments

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One Factor-at-a Time (OFAT) Vs. Designed
Experiments
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Tradition vs. Modern

• Historically Engineers and Scientists perform
  OFAT Experiments Vary only one variable (factor)
  at a time while holding others constant
• Statistical DOE is modern approach with many
  benefits. In combination with Statistical
  Process Control (SPC) it is required by ISO9000
  for quality control

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Advantages of DOE over OFAT

• Requires less resources (experiments, time,
  material, etc.) for the amount of information
  obtained
• Estimates of the effect of each factor are higher
  in precision (less variability)
• The interaction between factors can be estimated
  systematically- hit and miss experiments
  usually do not estimate interaction.

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Advantages of DOE over OFAT

• Experimental information is in a larger region of
  the factor space
• Improves prediction of the response in the factor
  space by reducing variability
• Makes process optimization more efficient because
  optimal solution is searched for over the entire
  factor space

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Example 1 Two factors in Three runs

• Engineer plans to compare T and P for a Standard
  gas anneal process on silicon wafers, and a New
  gas anneal process using three experimental runs
• 1) Standard P and standard T
• 2) Standard P and new T
• 3) New P and new T

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Initial (OFAT) Plan

• Use one lot of 48 wafers
• 16 wafers will be used for each of the three
  experimental runs (48 / 3 16)

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OFAT Method
Starting from standard T,P one factor at a time
is changed to obtain the other two runs.
factor space
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OFAT Method

• Standard T is compared to new T using 16 16
  32 wafers at the standard P
• Standard P is compared to new PT using 16 16
  32 wafers at the standard T
• The interaction between T and P (difference
  between effect of T on the response at the
  standard P and effect of T at the new P) cannot
  be estimated- no info at at new P with standard
  P)

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Alternative 22 Statistical Design
-Larger factor space (better model) and
interaction effects captured
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Comparison of methods

• OFAT gives 16 comparisons of the temperature
  effects of going from the standard to the new
  pressure but DOE gives 12 12 24
• Each method includes replicates. Replicates give
  less uncertainty, better estimation of error

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Recap Comparison of methods

• Variance for estimates of effect of factors in
  DOE is 50 less than OFAT
• Greater factor space is covered
• Interaction can be estimated with DOE but not
  with OFAT

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Other Designs
Central Composite excellent for estimating
curvature and modeling- is rotatable if 4
replicates at center point
Optional center point allows us to estimate
curvature
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Contour plot (model) of central composite
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Further Study. . .

• Use these example and others in handout for more
  explanation
• Examine tutorials and help menu topics in Design
  Expert to learn more about designs and how to use
  software
• Check out Stat-Ease web sight for FAQs, ideas
  for simple experiments, etc.
• Ask me for help when you need it