Concept

One-way sensitivity

analytical

Overview

A one-way (or one-at-a-time) sensitivity analysis varies a single input across its plausible range while holding every other input fixed, and records how much the output moves. It is the basic method for measuring a parameter’s leverage on the result — repeated input by input, it is how a model’s drivers are found and ranked.

Body

The procedure. For one input: choose a low and a high value spanning its credible range, recompute the output at each while all other inputs stay at their base-case values, and record the resulting output swing (high-case output − low-case output). That swing is the input’s leverage on the output. Repeat for each input of interest. Because only one input moves at a time, each swing is unambiguously attributable to that single parameter.

Choosing the range is the analysis. The swing depends entirely on the low/high range chosen, so that choice carries the judgment. A defensible range comes from the input’s own uncertainty — a market price’s historical band, a proxy’s error band, a comparable’s observed spread — not a blanket ±10% applied to everything. A uniform percentage flatters well-known inputs and understates volatile ones, which corrupts the ranking; the point of the method is to let genuinely uncertain inputs show genuinely large swings.

What it produces. A per-parameter output range — a low value, a high value, and the swing between them. Collected across parameters and sorted by swing magnitude, these become a tornado chart, and the parameters with the largest swings are the model’s drivers. The natural axes are the inputs with both wide ranges and real leverage: an input price, a discount rate, a capacity factor, a key conversion.

Why one-at-a-time, at this level. Moving one input per run is the deterministic, Excel-grade form of sensitivity analysis: change one cell, read the new output, log the swing — clean attribution and no special tooling. It is distinct from moving several inputs together as a coherent scenario, and from probabilistic methods (sampling all inputs at once) that sit outside the maturity anchor.

Limits & typical error

Holding everything else fixed misses interactions. One-at-a-time cannot capture combined effects: two inputs that each move the answer modestly can move it sharply together, or cancel. The method is blind to any effect that only appears when inputs move jointly.
Varying correlated inputs independently is physically inconsistent. When two inputs are linked — an intermittent plant’s capacity factor and its realized power price, a conversion and the recycle flow it sets — flexing one while pinning the other models a state that cannot occur, so the isolated swing misstates the real exposure.
The result is only as honest as the chosen range. A swing computed over an arbitrary, too-narrow, or too-wide range mis-measures leverage, and a uniform ±X% across unlike inputs mis-ranks them. The ranking is an artifact of the ranges as much as of the model.
Two endpoints can hide a nonlinear response. Sampling only the low and high values misses curvature or non-monotonic behavior between them; a parameter flat at its extremes but steep in the middle (or the reverse) is misrepresented by a single high-minus-low swing.
It traces spokes, not the whole space. Each one-way sweep is a line through the base case along one axis; the genuine best or worst case — several inputs adverse at once — lies off every individual spoke and is typically more extreme than any single one-way result. That combined case is the province of a scenario, not of any one-way run.
Every swing is centered on the base case. When the model is nonlinear, the swings — and therefore the ranking — depend on the base point they are measured around; a different base case can reorder the drivers.

Mini-example

A one-way sweep of the electricity price on green ammonia’s levelized cost. Holding everything else at the running-example baseline (~10 MWh/t, capacity factor ~0.90, capital and fixed opex fixed), the cost is ~$800/t at the base price of ~$40/MWh. Sweeping the price across a plausible ~$30–60/MWh band — drawn from market history, not a flat ±10% — recomputes only the electricity term:

$30/MWh →  electricity ~$300/t  →  levelized ~$705/t
$40/MWh →  electricity ~$400/t  →  levelized ~$800/t   (base)
$60/MWh →  electricity ~$600/t  →  levelized ~$1,005/t

The swing is ~$300/t over the band — a single, clean number for the power price’s leverage, with every other input untouched.

Separately, to show what one-at-a-time misses: one-way sweeps of capacity factor and of power price each move the cost on their own, but the true downside — an intermittent plant running at a low capacity factor in a high-price year — is worse than either single sweep, because that adverse combination sits off both spokes. Capturing it needs the two inputs moved together as a scenario, which one-way analysis cannot represent.