Delivery Model

Assumptions

Everything the model believes, stated before the math. If you do not buy one of these, do not buy the output.

1. Delivery is a time-to-event process on quarterly intervals; cancellation is a competing risk with its own empirical hazard.
2. Projects in the same class share a baseline hazard, estimated non-parametrically from resolved outcomes (Kaplan-Meier).
3. A sponsor's history moves their projects' hazard through a single multiplier, shrunk toward the sector base rate when the sponsor's sample is thin (Resolution Tracking Model).
4. Dependencies gate delivery as a series system: the delivery mass in a quarter is scaled by the joint probability that every gating dependency has completed by then (Dependency Model).
5. Delivered MW convolves the COD distribution with the empirical capacity-attainment ratio (delivered / promised MW) from outcomes.
6. Where class outcome history is thin (fewer than 10 resolved projects), the model does not pretend to know the baseline: it runs on a labeled wide prior and the distribution reads wide.

Derivation

The baseline delivery hazard per project class is the Kaplan-Meier hazard over resolved outcomes. With d_t deliveries and n_t projects still at risk in quarter t:

The project-level hazard multiplies the baseline by the sponsor multiplier m_s (shrunk per Resolution Tracking), capped at 1:

Delivery and cancellation are competing risks. The discrete mass of delivery in quarter t survives both hazards up to t and then fires the delivery hazard:

Each quarter's delivery mass is then gated by the dependency joint completion profile G(t) - the probability every evidence-bound dependency has completed by t (a series system; correlated members share one multiplier, never a product of independents):

P10 / P50 / P90 read off the CDF. Expected delivered MW multiplies the CDF by promised MW and the mean attainment ratio from outcomes. The delay distribution re-bases the COD mass against the promised COD; cancellation probability is the total cancel mass over the horizon.

Thin-history fallback: below 10 resolved class outcomes the baseline is replaced by a wide prior hazard (6% per quarter delivery, 1.5% cancellation), the output is flagged widePrior, confidence drops to LOW, and the notes say why.

Identification strategy

Why the estimate supports the claimed meaning - and where the model refuses to claim more than the data carries.

• The baseline is identified from resolved outcomes only - projects that actually delivered or died. In-flight projects contribute nothing, so the hazard cannot be contaminated by projects that merely look healthy today.
• The sponsor multiplier is identified from the sponsor's own resolved record, shrunk toward the sector base rate at weight n/(n+K): a sponsor with three resolved projects is half-shrunk. Thin sponsors cannot manufacture a good multiplier from a small sample.
• The dependency gate is identified from evidence-bound edges only. An assumed dependency is labeled INFERRED and the gate is the series joint of what the record actually binds - the model never gates on a dependency nobody documented.
• The output is always the full distribution. A single-date answer would claim identification the data does not support; the P10-P90 spread is the honest statement of what the class history can pin down.

Inputs and outputs

Calibration and gate evidence

Validation design

• Rolling-origin backtest against outcomes: every resolved project is predicted from its announcement-date evidence and scored - Brier and log score on resolution, interval coverage on COD.
• The reliability diagram must sit near the diagonal on resolved history before any customer sees a narrow distribution.

Evidence on record

• Backtest results are not yet published in the sealed source. The scoring harness and the wide-prior behavior are coded and gated; the score ledger accrues as predictions resolve.

Failure modes

The ways this model declines, degrades or goes UNKNOWN - and what it prints when it does.

• Project not in the graph: every output UNKNOWN, confidence LOW.
• Thin class history (n < 10): wide prior, widePrior flag set, confidence LOW, note printed - the model refuses to look precise on thin data.
• No promised COD on record: delay distribution, expected delay and P(delivered by promised COD) are UNKNOWN.
• No promised MW on record: delivered-MW path is UNKNOWN.
• No evidence-bound dependency graph: delivery is ungated and the notes say the answer is upside-biased.

Sensitivity

• The sponsor multiplier moves the whole hazard path proportionally; a sponsor at 2x base-rate hazard roughly doubles early-quarter delivery mass while history says so.
• The dependency gate is the binding constraint on late quarters: an edge with a 10-quarter expected duration suppresses COD mass until its completion profile rises.
• The wide prior (6% quarterly) is the dominant sensitivity on thin classes: the answer is wide because the prior is wide, and the page of record says so.