Pricing the cost of an independence assumption on HS2, across schedule and cost, and a low-cost correction available to any project
Coupled schedule and cost Bayesian networks on HS2: the priced independence gap, with structural, distributional and component-breach tests
PEER REVIEWED PAPER
By Nikhil Dhand
Delhi, India
Abstract
This paper presents a low-cost diagnostic for the quantitative risk modelling of megaprojects and prices, on High Speed 2 (HS2), what the most common modelling shortcut costs. In 2013 the programme’s quantitative risk model treated its threats as broadly independent, a choice stated explicitly in clause 4.2.3 of its Cost and Risk Status Report (Department for Transport and HS2 Ltd, 2013). On a megaproject the principal threats are not independent: adverse ground conditions raise the likelihood of tunnelling delay; tunnelling delay extends the programme; an extended programme carries a standing-army cost; and that cost propagates to inflation and the supply chain. Risk accumulates in one direction, in a way an independence assumption cannot represent.
I reconstruct HS2’s Phase 1 risk as two coupled Bayesian networks. The first is a ten-system schedule model whose output is the programme slip in days. The second is a twelve-system cost model in which one node, Schedule Delay Cost, is derived from that slip; so that schedule risk enters the cost answer through an explicit, documented mechanism rather than by assertion. Each network is run through several configurations, holding the engine and the random seed (4209) fixed, and varying only how much dependence the model is permitted to represent.
On schedule, switching the dependencies on, and changing nothing else, raises the P90 programme slip from 3,671 days (about 10.1 years) to 4,535 days (about 12.4 years); roughly 864 days, or 2.4 years, of schedule exposure attributable to model structure alone. The dependency-aware slip falls inside the official reset of a 2036–2043 opening, a slip of ten to seventeen years (HS2 Ltd and Department for Transport, 2026).
On cost, the same switch raises the P90 from £67.4bn to £88.6bn: approximately £21.3bn of cost exposure attributable to structure alone, before any new information about the project is introduced. A bootstrap of the raw output places the sampling error on that figure at about £0.1bn. The dependency-aware cost chain reaches the floor of the official reset range of £87.7bn to £102.7bn from the coupled register alone. Updating the chain on evidence, with each document admitted only at the cut-off on or after its date, carries it to the band and past it: the public record alone reaches £91.8bn, inside the band, and the system-level magnitudes a sponsor already holds reach £105.4bn, about £2.7bn above its ceiling, with schedule counterparts of 4,671 and 6,187 days. The structure sets the level; disclosure carries the rest, and the distance between the two updated lenses measures the disclosure gap directly. Decomposing each gap, using a chain run with the noisy-OR combination rule disabled, shows that the conditional structure, the bare fact that the risks are connected, carries most of it: 74 per cent of the cost gap and 59 per cent of the schedule gap, with the noisy-OR rule supplying the remainder.
The result is hardened against the obvious objections. A topology test (eight runs across reversed, common-cause, sparse and dense variants of each graph) leaves the independence gap intact in every case (£17.6bn to £21.7bn on cost; 833 to 895 days on schedule). A distributional-shape test (lognormal magnitudes in place of three-point ranges) moves the P90 by under one per cent. And a component-breach test, run on the per-node output, shows the dependence lifting both the expected number of simultaneous breaches of the independent ceilings (from 0.60 to 0.96 among the six cost drivers) and (the property an independence assumption most conceals) its variance (from 0.54 to 0.80), the statistical signature of co-movement.
The implication for a sponsor is direct. The same registers, run twice, would have revealed most of these gaps at the outset, at the cost of one additional simulation each. Every headline figure is recomputed from the raw output by a separate check, and the structural-robustness sweep, the distributional test and the component-breach test are reported in full.
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How to cite this paper: Dhand, N. (2026). The Register Has No Memory; PM World Journal, Vol. XV, Issue VIII, August. Available online at https://pmworldjournal.com/wp-content/uploads/2026/08/pmwj167-Aug2026-Dhand-The-Register-Has-No-Memory.pdf
About the Author
Nikhil Dhand
Delhi, India
Nikhil Dhand, PMP is a Senior Project Controls Consultant with 11 years of cross-sector experience delivering projects for UK, US, and Indian clients across solar EPC, highways, urban infrastructure, and complex project delivery. He is the creator of Probabilistic Chain Analysis™ (PCA) and RiskPulse V12™ — a Bayesian Monte Carlo risk engine calibrated using data from 16,000+ infrastructure projects across 8 sectors.
Author of Risk Runs the Project (forthcoming, Amazon KDP).
ORCID: 0009-0000-6526-8399 | Zenodo: 10.5281/zenodo.19436269
Contact: nikhildhand.research@gmail.com |
