DOE analysis walkthrough

Learning objectives

• Code a 2^3 factorial experiment and compute main effects and interactions.
• Fit a coded regression and inspect residuals in a free spreadsheet.
• Choose a safe operating setting and confirm it.

Core idea

Design of Experiments estimates factor effects and interactions from planned, randomized combinations more efficiently than one-factor-at-a-time trials.

Spreadsheet lab

• Code low = −1, high = +1 for temperature, pressure, dwell.
• Interaction columns = product of factor codes (e.g. AB, ABC).
• Effect_A = mean(Y at A=+1) − mean(Y at A=−1); repeat for each column.
• Fit coded regression with =LINEST(Y, X_matrix, TRUE, TRUE).
• Predict at chosen setting; run a confirmation run.

Garment-factory example

Fusing bond strength on a 2^3 design (temp, pressure, dwell) shows dominant temperature effect (+8 N), temp×dwell interaction (+3 N) and no pressure effect within the tested range. Confirmation run at high temperature and mid dwell reproduces the gain.

Method

1. Verify randomization and replication.
2. Compute main effects and interactions.
3. Inspect residuals vs run order.
4. Confirm the chosen setting before rolling out.

Common mistakes

• Optimising outside the tested range.
• Ignoring interactions because only main effects were plotted.
• Skipping the confirmation run.