Concept

Numbering up / down

Overview

Numbering up (or down) is meeting a required capacity with several identical units in parallel instead of one larger or smaller unit. It’s the alternative to size-scaling a single item: where the six-tenths rule stretches one unit, numbering replicates a standard one — the route taken when a single item would be too large to build, or when modular replication is how the equipment actually comes.

Body

Two ways to reach a capacity. Scale one unit larger (priced with the six-tenths rule), or place N identical units in parallel (numbering up). Numbering down is the same in reverse. The choice is one bespoke large item vs. a count of standard ones.

When to number instead of scale. Scale a single unit while the size step stays modest; number up or down once the size difference exceeds roughly 2–3×. Beyond that the single-unit scaling is extrapolated too far — and past a class’s largest standard size (see sizing scalars) a single larger unit may not exist, forcing replication anyway.

The cost trade-off.

• Scaling one unit captures economy of scale: with exponent n < 1, cost per unit of capacity falls as the unit grows.
• Numbering up forgoes it: N units cost on the order of N × one unit — roughly linear in the count — so replicating to reach a large capacity costs more than one large unit would, where feasible.

What numbering up buys: standard (cheaper, faster, lower-risk) fabrication, modularity, easier turndown and higher availability (units taken offline individually — a lever on the capacity factor), and manufacturing learning across identical units.

Where it sits. Numbering up substitutes for the six-tenths step for that item: its contribution to capex is N × a single standard unit’s cost (shared infrastructure handled separately). The decision is per-item — some items scale, others are numbered up.

Limits & typical error

• Applying the six-tenths discount across a count overstates the scale economy — N parallel units priced as one unit scaled N× borrows a sublinear discount that modular replication doesn’t deliver; numbered-up cost is ~linear.
• Modeling numbered-up capacity as one large unit understates cost the other way — assuming a single large unit exists when none can be built claims an unavailable economy of scale.
• The ~2–3× switch point is a heuristic — where scaling gives way to numbering depends on the class maximum and on fabrication and transport limits; it flags roughly where to reconsider, not an exact break.
• “Identical units” is an idealization — shared spares, common utilities, one control system, or unequal sizes break the clean N×: some cost grows slower than N (shared infrastructure), some faster (more tie-ins).
• Count is discrete — capacity is met by a whole number of units, rounded up, leaving slack a continuous model hides — larger in fractional terms when few units are involved.

Mini-example

The hydrogen front end of a large green ammonia plant is numbered up, not scaled. A single electrolyzer module is on the order of a few to ~10 MW; a several-hundred-MW requirement is met by tens of identical modules in parallel, because a single electrolyzer that size doesn’t exist. Its capex contribution is roughly module cost × count — linear, no six-tenths discount — and the modularity buys standard manufacturing and the ability to take stacks offline without stopping the plant.

Contrast the synthesis loop in the same plant: the 8 MW syngas compressor is a single standard machine scaled from a 5 MW reference (the six-tenths worked case), because 8 MW is well within the compressor class’s single-unit range. One plant, both regimes.

Edge case: pricing that electrolyzer fleet as a single 200 MW unit scaled with the six-tenths rule would apply an economy of scale modular stacks don’t provide — understating cost by treating linear replication as sublinear growth.

See also

• Six-tenths rule
• Equipment sizing
• Sizing scalars (by equipment class)
• Capex
• Capacity factor