Spectrum

Spectrum shows the full duration distribution of your plan from start to terminal node: a histogram running from “best case” on the left to “worst case” on the right, with your expected delivery date sitting in the middle.

What it tells you

A single deadline date is misleading. A plan that finishes between 6 weeks and 7 weeks is a very different plan from one that finishes between 5 weeks and 12 weeks, even if both have the same expected date.

Spectrum shows you the shape. A narrow histogram means low risk: every realisation of the plan finishes close to the expected date. A wide histogram means a long tail: most runs finish on time, but a meaningful fraction slip badly. Two peaks (a bimodal distribution) typically signals a high-impact gated branch: the plan ends earlier if a particular outcome goes one way, much later if it goes the other.

How it’s computed

Spectrum runs a forward monte-carlo pass through the dependency graph. Each task draws a duration from its lognormal distribution, the DAG topology determines what serialises and what parallelises, and the terminal node’s arrival time is recorded for each draw. After enough draws the histogram of arrival times approaches the true plan duration distribution.

Topolog runs monte-carlo by default rather than reaching for a closed-form approximation. Closed-form methods are faster but break down on the plan shapes that matter most — resource contention, gated branches, deliverable handoffs — and we’d rather give you an accurate histogram every time than a fast one that’s sometimes wrong. The histogram, the bands, and the per-sentinel colouring all come from the same monte-carlo pass.

Reading the colours

The histogram is coloured by which sentinel each monte-carlo run terminates on. A plan with success / partial / failure sentinels shows three coloured stacks: how much of the probability mass lands in each end-state, and at what date. If 30% of your monte-carlo runs end on failure at week 8, you’ll see a red lump at the right of the histogram.

What to do with it

• Quote ranges, not single dates. The spectrum’s 10th and 90th percentile are the “no earlier than” and “latest realistic” numbers you should be giving stakeholders.
• Tighten the worst CV. The widest histograms come from one or two tasks with very high CV (uncertainty) on the critical path. Decompose those tasks; the daughter tasks usually estimate more confidently and the spectrum tightens.
• Cut a bimodal’s left peak off. A bimodal distribution where the left peak comes from a low- probability happy-path gate is usually false optimism. Re-estimate the gate’s prior toward the centre and the headline number moves to where it should always have been.

Related

• Critical path - which chain of tasks shapes the spectrum’s right tail.
• The scheduler - how the spectrum’s expected-date and 2σ bounds anchor the projected done-by date for each plan.