Plan variables and sample size for an experiment.
A full factorial design has levels raised to the power of variables conditions, which is why designs grow explosively: two variables at three levels is nine conditions, but four variables is eighty-one. Multiplying by replicates gives the run count and the bench hours that follow. Error degrees of freedom — runs minus conditions — is the statistical payoff of replication and must stay comfortably above zero for any variance-based test.
Design size
Conditions = levels ^ variables; total runs = conditions x replicates
Statistical capacity
Error degrees of freedom = total runs - conditions
Use a fractional factorial or a screening design. These test main effects and low-order interactions at a fraction of the runs, accepting that high-order interactions become confounded.
Three is the practical minimum for estimating variability, and five to ten is common where effect sizes are small. A formal power calculation from an expected effect size is better than a rule of thumb.