Hard-to-Change Factor in a Molding DOE
A medical-device molder wants to reduce warp in a polycarbonate housing. Four factors are identified: melt temperature (A), packing pressure (B), cooling time (C), and gate insert design (D). A and B are easy to change; C is moderately easy; D requires a 4-hour tool change and only two insert designs are available. The team has budget for 16 experimental runs plus three center points, and production will allow only two tool changes during the trial. The quality engineer proposes a full 2^4 factorial with three center points and complete randomization. The Black Belt is concerned about cost and time. The response is warp measured in micrometers at three locations per part; the team will measure five parts per run. Historical warp is 120-260 micrometers with a target below 150 micrometers. The team wants to estimate main effects and all two-factor interactions. A previous fractional factorial had resolution III and produced conflicting conclusions.
1. Evaluate the proposed full factorial with complete randomization. What design would you recommend?
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Evaluation: A full 2^4 factorial with complete randomization is statistically clean but operationally impossible. D requires a 4-hour tool change; 16 runs fully randomized would mean up to 16 insert changes, while production allows only two. The 19-run plan also ignores the hard-to-change structure. Alternative: Use a split-plot design with D as the whole-plot factor and A, B, C as subplot factors. Run one block at D1 and one at D2, randomizing the eight A by B by C combinations within each block; add center points within each whole plot. This uses 16 runs plus centers and two tool changes. Caveat: With only one whole plot per D level, the D main effect is confounded with whole-plot error. If the team needs a formal test on D, negotiate two whole plots per level, which means four tool changes, or treat D as a demonstration factor to be confirmed. Reasoning: Design structure must follow randomization constraints; a textbook full factorial that cannot be randomized is not a valid plan.
2. Explain the confounding and resolution implications of the alternative design. How should the data be analyzed?
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Resolution and confounding: The proposed split-plot is not a fractional factorial; it is a full 2^3 in A, B, and C within each D level, so all A by B, A by C, B by C and D by A, D by B, D by C interactions are estimable in principle. D main effect uses whole-plot error; subplot effects use the smaller subplot error. Analysis implications: Use a mixed model with whole-plot and subplot terms, not a single pooled ANOVA. Do not compare the D main effect to the subplot error. If the team instead chooses a 2^(4-1) resolution IV design to save runs, main effects are clear of two-factor interactions, but two-factor interactions are confounded with each other; follow up with a foldover or confirmation. Reasoning: The previous resolution III study failed because main effects were aliased with two-factor interactions. The new design must be analyzed at the correct error stratum.
3. Given only two tool changes, how should the runs be randomized and blocked, and what confirmation is needed?
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Randomization with two tool changes: Do not randomize D. Set D1, then randomize the eight A by B by C combinations within that whole plot; change to D2 and randomize the eight combinations again. Randomize run order within each block and record any drift. Place center points at the start and end of each whole plot, or at least one per whole plot, to check curvature and stability. Blocking: Treat tool change as a block; include block in the model. Interpretation: Because D is confounded with block and time, any D effect is inseparable from a time or setup effect unless the order is reversed in a follow-up. A confirmatory run with D reversed, or a second replicate, is needed before committing to an insert design. Reasoning: Randomization protects against nuisance factors; where randomization is constrained, blocking and confirmation replace it.