Screening Six Molding Factors in Eight Runs with a Hard-to-Change Tool Insert
An injection-molding team must reduce warp on a glass-filled nylon housing. Warp is measured in mm, lower is better; the current mean is 0.42 mm against a specification maximum of 0.30 mm. Six factors are candidates: melt temperature (A), mold temperature (B), injection speed (C), packing pressure (D), cooling time (E), and gate geometry (F). Factor F is a tool insert that requires a 6-hour teardown to change. Only eight molding runs are affordable in the trial window, and each run takes four hours. The team proposes a 2^(6-3) fractional factorial in eight runs, all factors at two levels, and plans to declare the largest effects as root causes and implement them immediately. One team member wants to add center points to test for curvature. The plant statistician is on leave. The customer requires evidence that improvements are not due to noise before a PPAP resubmission in six weeks.
1. Assess the proposed design. What is its resolution, what can legitimately be concluded, and what is the main risk?
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Six factors in eight runs is a 2^(6-3) design, which is resolution III: main effects are clear of each other but each main effect is aliased with one or more two-factor interactions, and two-factor interactions are aliased with each other. With a good generator choice the aliasing structure is known, but it cannot be resolved without additional runs.
The legitimate conclusion is limited: 'these main effects are large in this design; one or more of them, or an aliased interaction, is worth pursuing.' Declaring root causes and implementing immediately is not supported, because the largest observed effect could be a two-factor interaction disguised as a main effect. For example, an apparent melt-temperature effect might actually be a mold-temperature × injection-speed interaction.
The second major risk is the hard-to-change factor F. If all eight runs are randomized freely, the design will demand multiple insert changes and the team will likely run F in blocks or keep it fixed, which silently converts the experiment into a split-plot. Then whole-plot effects (F and anything confounded with it) are tested against the wrong error term and can appear significant when they are not. Also, with eight runs and no replication there is no pure-error estimate; significance testing depends on higher-order interactions being negligible, which is an assumption, not evidence.
2. How should the hard-to-change factor F be handled, and what design would you recommend within the constraints?
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Treat the randomization restriction explicitly rather than ignoring it. F should be a whole-plot factor: change the insert as few times as possible and run the sub-plot combinations (A–E) within each insert condition. If F must be studied, use at least two whole plots per F level so whole-plot error can be estimated, which means four insert changes.
Given the six-week and eight-run constraints, the better recommendation is usually to fix F at the current geometry for the screening study, run a 2^(5-1) resolution V design in 16 runs, or if only eight runs exist, a resolution III design in A–E and study F separately in a focused two-level comparison. Sixteen runs give main effects clear of two-factor interactions, which is the minimum needed to support the 'root cause' claim the team wants to make.
A modern alternative is a definitive screening design: it can estimate main effects and allow for some two-factor interactions with fewer runs, and it accommodates three-level factors. If the team insists on eight runs, the deliverable must be framed as a screening hypothesis, followed by a confirmation run or a foldover before implementation. Foldover of the resolution III design yields resolution IV, separating main effects from two-factor interactions at 16 runs.
Practical plan: run the 16-run design with F as a whole plot, randomize sub-plot order within each whole plot, and include at least three center points for curvature and pure error.
3. What do center points add in this situation, and what can they not tell you?
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Center points add three things. First, they provide a test for overall curvature: if the average response at the center differs significantly from the average of the factorial runs, a first-order model is inadequate and the optimum or a nonlinear region is nearby. Second, they provide a replicate-based estimate of pure error, which the eight-run design otherwise lacks. Third, they give a check on experimental execution, since center runs should agree within measurement and process noise.
They cannot identify which factor is responsible for curvature. The curvature contrast pools the quadratic effects of all factors, so a significant result says 'some factor is nonlinear' without saying which one. Resolving that requires axial runs or a response-surface design, such as a central composite or Box-Behnken design, after the screening stage.
With a hard-to-change factor, center points also require care. A center point at which F is at its mid-level may not be physically possible if F is a categorical insert geometry, and center runs must be assigned within whole plots to contribute correctly to the error structure. If center points are added to a resolution III design, they do not fix the aliasing of main effects with two-factor interactions, so they should not be used as a substitute for a higher-resolution design or a confirmation run. Finally, center points should be planned before running, not appended after the factorial runs are complete, so that run order and setup conditions remain comparable.