Concept

Installation factor / Lang factor

Overview

An installation factor grosses a piece of equipment’s purchased cost up to its installed cost — the foundations, piping, steel, electrical, instrumentation, and labor a delivered machine needs before it can operate. The Lang factor is the coarsest version: a single multiplier on the whole plant’s purchased-equipment cost that reaches total fixed capital in one step.

Body

Why a delivered machine isn’t an installed one. A compressor at the factory gate is a fraction of what it costs running in a plant. The difference is installation content — foundations, structural steel, piping and valves, electrical, instruments and controls, insulation, plus construction labor and indirect field costs. The factor f rolls it into one multiplier:

C_installed = C_purchased × f

Two granularities.

• Per-class installation factors — each class carries its own f (commonly ~2–4), because bulk-and-labor content differs by type; a heavily-piped item installs at a higher multiple than a package unit. Applied item by item, these sum to installed ISBL.
• The Lang factor — a single multiplier on total purchased-equipment cost by plant type (~3.1 solids, ~4.7 fluids, ~3.6 mixed) that jumps straight to total fixed capital, folding in installation, off-sites, and indirects. The fastest, bluntest estimate.

Track the scope each factor spans. A per-class installation factor stops at installed ISBL — OSBL and indirects are layered on separately toward total capex. A Lang factor already contains those layers, landing on total fixed capital. The two aren’t interchangeable; know what a factor already includes before adding anything on top.

Where it sits. Installation factoring follows the purchased cost from sizing and six-tenths scaling, and precedes (or, for the Lang factor, replaces) the roll-up to total capex.

Limits & typical error

• A single factor hides the equipment mix it was calibrated on — one blended factor fits neither a compressor-and-piping-heavy plant nor a package-unit-heavy one exactly.
• Mismatching what the factor already includes is the costliest error — a Lang factor (already bundling OSBL and indirects) plus OSBL again double-counts off-sites; a per-class factor (installed ISBL only) with OSBL forgotten undercounts. Either way moves total capital a large fraction.
• The factor multiplies the equipment-cost error beneath it — like every factored layer, f transmits a systematic base error unchanged; it doesn’t average it out.
• Factors carry a location and labor basis — installation is labor-heavy, so a factor calibrated for one country’s construction labor misstates installed cost elsewhere.
• Solids-vs-fluids and material assumptions are baked in — the fluids factor on a solids plant imports the wrong bulk-and-labor profile, and a factor fitted to standard metallurgy understates a high-alloy build.

Mini-example

Costing the green ammonia synthesis loop’s ISBL. The cost-driving items — the ~$2.7M syngas compressor (the six-tenths worked case) and the reactor — are summed to a purchased-equipment cost, then multiplied by a per-class installation factor of ~3.5 (a round anchor for fluid-processing equipment) to reach installed ISBL. The faster alternative: take the plant’s whole purchased-equipment total × the fluids Lang factor of ~4.7 to land directly on total fixed capital.

Edge case: applying that ~4.7 Lang factor — which already includes off-sites and indirects — and then adding the ~40% OSBL allowance from the battery-limits example would count off-sites twice, inflating total capital by roughly that allowance from a pure scope double-count.

See also

• Capex
• Six-tenths rule
• Battery limits (ISBL / OSBL)
• Total capex (battery-limits → total plant)
• Equipment sizing