Dependency Model

Assumptions

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

1. A dependency is only real when evidence binds it. An assumed dependency is labeled INFERRED and never silently upgraded.
2. The graph is a series system: every gating edge must complete for the project to deliver on time.
3. Edges carry completion-probability profiles built from an evidence state (complete / in progress / not started / unknown) and a versioned empirical base rate per dependency type.
4. Dependencies inside a correlation group (same utility, same supplier, same node) fail together: their joint contribution is one shared multiplier, never the product of independent probabilities.
5. Base-rate priors are policy-versioned placeholders until outcome history re-estimates them; until then the bands are wide and labeled.

Derivation

Each edge gets a per-quarter completion profile. An in-flight edge completes at its type's base quarterly rate q_type; a not-started edge burns its first quarter at half rate. A printed expected-completion date (evidence-bound) concentrates mass to at least 45% in the quarter it falls due. The cumulative profile is:

The joint completion profile is the series product over independent edges, with each correlation group contributing a single factor - the geometric mean of its members, not their product:

The critical dependency is the edge on the longest evidence-adjusted duration chain; slack is the float between an edge's earliest achievable completion and the date its successor needs it. Sensitivity is one-at-a-time toggling: each edge is forced complete in turn and the change in P(deliver on time) is ranked as a tornado.

Current versioned priors (per dependency type, quarterly base completion / expected remaining quarters): transmission upgrade 0.08 / 10; interconnection agreement 0.10 / 8; transformer delivery 0.10 / 8; equipment delivery 0.12 / 6; permit 0.18 / 4; water 0.18 / 4; fiber 0.22 / 3; construction 0.12 / 6; financing 0.22 / 3; generation supply 0.10 / 8; other 0.15 / 5.

Identification strategy

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

• The series form is the identification statement: the project delivers only when every gating edge completes, so the joint is a product (with grouped edges sharing one factor), never an average. Averaging would manufacture on-time probability the graph does not contain.
• Correlation groups are identified from the record (shared utility, supplier, node), and the shared-multiplier rule is what keeps one utility delay from being priced as several independent risks - or, worse, several independent chances of rescue.
• Expected-completion dates only bind when they are evidence-bound on the record; a marketing date in prose does not move the profile.

Inputs and outputs

Calibration and gate evidence

Validation design

• Edge base rates are re-estimated from outcomes as history accrues; until then the bands are wide and labeled.
• Correlation groups are validated on resolved multi-project failures - one utility delay hitting several projects at once.

Evidence on record

• Re-estimation has not yet run in the sealed source; the priors are the versioned placeholders above, explicitly labeled as policy pending outcome history.

Failure modes

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

• No evidence-bound edges: the Delivery gate is absent and downstream models are told the answer is ungated (upside-biased).
• Unknown edge status: treated as not-started (the conservative reading), never as complete.
• Missing expected-completion date: the edge runs on its type base rate only - no mass is concentrated around an unstated date.
• Dependency type outside the versioned table: falls to the 'other' prior (0.15 / 5) rather than a guess.

Sensitivity

• The joint profile is most sensitive to the slowest edges: one 10-quarter transmission upgrade dominates the gate until its profile rises.
• Correlation grouping can move the joint materially on grouped books: three grouped edges at 0.5 contribute 0.5 (geometric mean), not 0.125 (independent product) - the rule raises joint probability where risks move together and removes false diversification.
• Base-rate priors are the largest open sensitivity: they are policy placeholders, and the page of record says so until outcomes re-estimate them.