Coatings Adhesion DOE: Fraction, Blocks, and Confirmation
A coatings plant wants to increase adhesion strength (higher is better) and reduce variability. Five factors are considered: binder percentage (A), cure temperature (B), line speed (C), additive level (D), and humidity (E). Each has two levels; the team can afford 20 experimental runs including replicates. The quality engineer proposes a full 2^5 = 32-run factorial, but the plant manager rejects it because of production downtime. A statistician suggests a 16-run fraction with generator E = ABCD plus four center points. The team also wants to know whether the effect of line speed depends on cure temperature, because operators believe there is an interaction. Historical data are unreliable because humidity was not recorded. The response is measured as peel strength in N/25 mm with a gauge R&R of 12%. The team must choose a design, account for humidity as a noise factor, and plan confirmation. No factor is hard to change, but runs must be completed in two blocks because of raw-material lots.
1. Evaluate the proposed 16-run design plus center points. What is its resolution, what is aliased, and is it adequate for the team's objectives?
Read the worked answer
The proposed design is a 2^(5-1) fractional factorial with defining relation I = ABCDE, which is resolution V. Main effects are clear of two-factor interactions, and every two-factor interaction is aliased with a three-factor interaction (for example, AB is aliased with CDE). Under the usual assumption that three-factor and higher interactions are negligible, the design estimates all five main effects and all ten two-factor interactions, including line speed x cure temperature. That is adequate for the stated objective. The four center points test curvature and lack of fit, provided the factors are quantitative and the center is actually run. The design is not adequate if the team believes three-factor interactions are large, or if it needs to estimate pure quadratic effects separately; then augmentation is needed. The 16-run fraction plus four centers is a reasonable use of 20 runs and is preferable to a 32-run full factorial that the plant will not support.
2. How should humidity and raw-material lots be handled?
Read the worked answer
Treat raw-material lot as a block. Split the 16 factorial runs into two blocks of 8, confounding the block effect with a high-order interaction, never with a main effect or a key two-factor interaction. Run the four center points across the blocks or in a separate block so curvature is not confounded with lot. Randomize run order within each block. Humidity is a noise factor: record it for every run and either include it as a covariate in the regression or, if it can be controlled, block on low/high humidity. Because humidity was not recorded historically, the team cannot treat historical data as a baseline. If humidity varies widely during the experiment, check whether it interacts with binder or cure temperature; if it does, the optimum may be humidity-dependent. Document lot and humidity in the data table; otherwise the analysis will repeat the historical mistake of an unmeasured confounder.
3. What follow-up and confirmation strategy would you recommend after the 20 runs?
Read the worked answer
Analyze with a half-normal or Pareto plot of effects, then a regression model including block and humidity. Check residuals, lack of fit, and whether the center points indicate curvature. If curvature is significant, augment with axial runs or move to a response-surface design rather than guessing the optimum. Select settings that are robust to humidity and raw-material lot, not just the highest predicted mean. Because gauge R&R is 12%, treat effects close to the measurement variation cautiously. Run 3-5 confirmation runs at the predicted optimum and at a worst-case humidity/lot combination; compare the mean and spread to the prediction interval. If confirmation fails, re-examine the model and aliasing assumptions. Update the control plan with the chosen settings, lot verification, and humidity monitoring. The confirmation runs are the difference between an experimental result and a validated process change.