Seven math factors at two or three levels each, evaluated across three location archetypes — 54 deployment cells in 18 inner-array runs. Response: revenue per terminal per day. Optimization criterion: larger-the-better S/N. The full factorial would have required 4,374 runs.
Each run is a specific combination of factor levels deployed across the three noise archetypes.
| Run | Config | N1 Urban | N2 Suburban | N3 Rural | Mean | σ | S/N |
|---|---|---|---|---|---|---|---|
| #01 | 1111111 | $127.7 | $97.1 | $66.3 | $97.1 | 25.06 | 38.81 |
| #02 | 1122222 | $165.4 | $132.6 | $100.7 | $132.9 | 26.38 | 41.94 |
| #03 | 1133333 | $148.6 | $116.3 | $90.3 | $118.4 | 23.84 | 40.93 |
| #04 | 1211223 | $150.6 | $112.8 | $83.7 | $115.7 | 27.40 | 40.53 |
| #05 | 1222331 | $163.0 | $130.2 | $99.5 | $130.9 | 25.92 | 41.81 |
| #06 | 1233112 | $153.0 | $118.9 | $87.7 | $119.9 | 26.66 | 40.91 |
| #07 | 1312132 | $151.4 | $126.5 | $91.3 | $123.1 | 24.67 | 41.23 |
| #08 | 1323213 | $162.0 | $125.9 | $106.4 | $131.4 | 23.03 | 41.99 |
| #09 | 1331321 | $152.9 | $120.7 | $94.4 | $122.7 | 23.95 | 41.27 |
| #10 | 2113322 | $161.1 | $126.9 | $103.0 | $130.3 | 23.84 | 41.87 |
| #11 | 2121133 | $146.3 | $115.4 | $84.8 | $115.5 | 25.13 | 40.60 |
| #12 | 2132211 | $148.0 | $114.6 | $100.6 | $121.1 | 19.87 | 41.34 |
| #13 | 2212313 | $157.9 | $136.4 | $97.7 | $130.7 | 24.91 | 41.79 |
| #14 | 2223121 | $155.2 | $131.3 | $92.6 | $126.4 | 25.79 | 41.43 |
| #15 | 2231232 | $158.5 | $124.5 | $101.3 | $128.1 | 23.46 | 41.72 |
| #16 | 2313231 | $159.5 | $126.1 | $98.2 | $127.9 | 25.08 | 41.63 |
| #17 ★ | 2321312 | $173.0 | $142.9 | $105.0 | $140.3 | 27.80 | 42.39 |
| #18 | 2332123 | $160.9 | $125.3 | $97.0 | $127.7 | 26.16 | 41.58 |
Steeper slope = larger effect. The recommended level for each factor is the peak.
The additive prediction is validated against a field deployment across all three noise archetypes.
Seven factors at three levels (one at two) define a parameter space of 2 × 3⁶ = 1,458 combinations. A full factorial across three noise archetypes is 4,374 deployments — infeasible. The L18 array preserves orthogonal estimation of main effects in 18 inner runs, trading the ability to resolve two-factor interactions for an order-of-magnitude reduction in field cost.
Larger-the-better S/N integrates the mean and variance of each run into a single criterion, biasing the search toward configurations that are robust — high mean and low variance — rather than configurations that peak in a single condition.
Resolution III caveat: main effects are confounded with two-factor interactions. If the confirmation deviates materially, the remedy is a larger array (L27/L36) or a targeted two-factor follow-up.