Design of Engineering Experiments Part 6

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Confounding the 2k Factorial Design in Four Blocks

• Example a 25 design, each block holds eight
  runs. Needs four blocks. Select ADE and BCE to be
  confounded. Two defining contrasts
• L1 x1 x4 x5
• L2 x2 x3 x5
• (L1, L2) (0,0), (0,1), (1,0), (1,1)

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Confounding in the 2k Factorial Design

• Four blocks 3 dof
• ADE 1 dof
• BCE 1 dof
• An additional effect must be confounded
  generalized interaction of ADE and BCE
• (ADE)(BCE) ABCD
• dof (blocking) dof (effects confounded)

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Confounding the 2k Factorial Design in 2p Blocks

• p independent effects to be confounded
• Each block contains 2k-p runs
• Blocks may be created by the p defining contrasts
  L1, L2, , Lp
• Number of generalized effects to be confounded
• 2p p - 1

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Partial Confounding

• Estimate of error
• Prior estimate of error
• Assuming certain interactions to be negligible
• Replicating the design
• If an effect is confounded in all replicates
  completely confounded
• If an effect is confounded in some replicates,
  but not all partial confounding

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• Interaction sums of squares only data from the
  replicates in which an interaction is not
  confounded are used

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Example 7-3 A 23 Design with Partial Confounding

• Factors carbonation, pressure, and line speed
• Response fill height
• Each batch of syrup only large enough to test
  four treatment combinations
• Two replicates
• ABC is confounded in replicate I, AB confounded
  in replicate II

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