Using Minitab Factorial DOE for Engineering Process Screening

Requirements

Before creating a factorial design in Minitab, define the engineering question you want to answer. Typical requirements include:

• Identify the process factors (inputs) you suspect influence the response (output).
• Choose the number of levels for each factor; for screening, two levels (low/high) are standard.
• Determine the experimental resources available (time, cost, material) to set an upper bound on the number of runs.
• State the desired resolution of the design, which controls how main effects and interactions are aliased.

These inputs guide the selection of a design that is both statistically efficient and practically feasible.

Smallest Suitable Design

For screening many factors with limited runs, a fractional factorial design is the smallest suitable option. In Minitab you can generate a 2k‑p design by specifying:

1. The total number of factors k.
2. The desired resolution (III, IV, or V). Higher resolution reduces confounding of main effects with two‑factor interactions.
3. Optionally, the number of replicates or center points to estimate pure error and check curvature.

Example: five factors (k=5) with a resolution IV design (2^(5‑2)) yields 8 runs. Minitab automatically calculates the alias structure and presents it in the design summary.

Trust/Data Boundaries

Minitab assumes that the worksheet contains clean, numeric data that meet the assumptions underlying ANOVA:

• Factor levels are coded correctly (typically –1 for low, +1 for high).
• Response measurements are independent and approximately normally distributed.
• There are no systematic measurement errors or drift across runs.

If data violate these assumptions, the effect estimates and p‑values may be misleading. Therefore, before analysis you should:

1. Check for outliers using a boxplot or residuals plot.
2. Assess normality with a probability plot of the residuals.
3. Verify that factor columns contain only the two coded levels (or the specified center point value).

Operational Checks

After defining the design, follow these steps to ensure the experiment and analysis are sound:

1. Review the design summary – confirm the number of runs, resolution, and alias structure match your intentions.
2. Run the experiment – randomize the run order if possible to mitigate lurking variables.
3. Analyze the design – use Stat > DOE > Factorial > Analyze Factorial Design. Minitab will produce:
1. An ANOVA table with effect estimates, sums of squares, and p‑values.
2. A Pareto chart of standardized effects.
3. Interaction plots for any significant two‑factor interactions.
4. Residuals plots (normal probability, versus fits, versus order) for diagnostic checking.
4. Verify power – if the design includes replicates or center points, Minitab can compute the power to detect effects of a given size; ensure it meets your project’s sensitivity requirement.

Failure Modes and Conditions That Would Change the Design

Several outcomes indicate that the current design may be inadequate and a redesign is warranted:

• Non‑significant main effects with high residual variance – suggests the experiment lacks power; consider adding replicates or switching to a higher‑resolution fractional factorial.
• Significant curvature detected via center points – indicates possible quadratic effects; a response surface design (central composite or Box‑Behnken) would be more appropriate.
• Aliasing obscures critical interactions – if the alias structure shows that a two‑factor interaction of interest is confounded with another effect, increase the resolution (e.g., move from resolution III to IV) or adopt a full factorial if resources allow.
• Outliers or non‑normal residuals – points to measurement error or uncontrolled variability; improve measurement systems or control experimental conditions before re‑running.
• Unbalanced data due to missing runs – Minitab’s default Type III sums of squares can produce biased estimates; either restore balance by re‑running missing trials or explicitly choose an appropriate sums‑of‑squares method.

When any of these conditions appear, return to the requirements step, adjust the design parameters (number of factors, resolution, replicates, or design type), and regenerate the design in Minitab before proceeding.