Forecasting needs explicit uncertainty

A deterministic schedule answers what follows from entered durations and dependencies. A scenario asks what follows if a declared set of assumptions changes. A probability statement requires a model of uncertainty and a basis for its distributions and dependence. These are different claims. A report should identify which one it makes. Calling an optimistic scenario likely does not turn it into a probabilistic forecast. Calling a calculated mean expected does not validate the underlying estimates as empirical distributions.

The Delivery atlas transforms each entered estimate range using its stated PERT method. The canonical method is PERT mean = (optimistic + 4 × most likely + pessimistic) / 6. Variance = ((pessimistic − optimistic) / 6)^2. The resulting task mean and variance are conditional on the fictional inputs. The app then uses the mean durations for the dependency calculation. These transformations are reproducible, but reproducibility is not calibration. The paper supplies no field project-duration sample from which to estimate the inputs or verify the approximation against field outcomes.

For the reference study, the selected path variance is 1.11 squared weeks and the selected-path standard deviation is 1.05 weeks. Against a target of 20.00 weeks, the engine’s selected-path normal deadline approximation is 82.9%. This percentage is explicitly not the probability of the whole project finishing on time. It excludes competing-path uncertainty and path switching, assumes the relevant independence conditions and relies on the entered estimates. It should be labelled with those limits wherever it is used.

Illustrative. The earlier-target study changes only the target to 18.00 weeks. The network duration remains 19.00 weeks while the selected-path approximation becomes 17.1%. The contrast shows that a deadline changes the question asked of the distribution approximation, not the work itself. It offers no evidence that management can improve completion confidence by selecting a different desired date. The target is an input to interpretation, not an acceleration mechanism.

Illustrative. Scenario envelopes also require careful language. The reference network’s all-optimistic duration is 13.00 weeks and its all-pessimistic duration is 25.00 weeks. These are whole-network recalculations using the respective task assumptions. They are not confidence bounds and do not establish the maximum possible delay. An omitted approval refusal or redesign condition can sit outside both. The envelope is useful when the reader understands the cases it represents and the mechanisms it excludes.

A project finishes only when all required terminal obligations are complete. A selected-path approximation describes a narrower event. Another branch can become slower even when it is not critical under the entered means. In the tied-branches study, the engine counts 2 critical paths yet reports the selected-path approximation 82.9%. The equality of that reading to the reference is not evidence of equal whole-project confidence. It reflects the selected path and variance used by the limited method.

Dependence can change uncertainty materially. Tasks can share weather, resources, design decisions or supplier exposures. Treating their duration variation as independent may understate or otherwise misrepresent aggregate uncertainty. The app contains no correlation inputs and performs no stochastic network simulation. A real completion-confidence analysis should use an appropriate model and evidence for dependence, competing paths and conditional events. This paper does not invent a correlation coefficient or claim that a single adjustment can repair all such omissions.

Path switching matters even without tied means. The duration-switch study changes which branch governs the deterministic finish. Under uncertainty, such switching can occur across possible outcomes as well. A probability method confined to one selected path cannot fully represent that behaviour. This is why a displayed percentage should not be promoted into an external warranty or a complete risk estimate. The network result can still be useful for screening sensitivities, provided its scope remains attached to the claim.

The deterministic-path study sets each range to its most-likely duration and matches the target to the resulting finish. The engine then reports 100.0% for the conditional deadline event. This is a zero-variance boundary rule, not proof of certain real-world delivery. The inputs explicitly remove duration variation, and the model still excludes resources, calendars, omitted work and acceptance failure. A deterministic numerical boundary should be explained as such to avoid a misleading certainty claim.

Illustrative. The path-enumeration study has 64 critical paths while the display limit is 50. Counting and listing serve different purposes. The bounded list protects usability, while the total count discloses that more paths exist than are displayed. A reviewer should not infer completeness from the visible list alone. This fictional equal-branch network is a computational boundary case, not an empirical description of a project. Its purpose is to verify the distinction and its reporting.

A fictional sponsor compares a single-branch programme with a programme that has several competing branches. Both show the same mean-duration finish. The sponsor asks whether their chance of meeting a target is therefore the same. The manager explains that mean-duration equality does not establish distributional equality. The number and dependence of competing routes can affect completion. The small app's selected-path reading cannot settle that broader question.

The team identifies the claim the decision requires. For a bounded internal sequence discussion, the deterministic comparison may be adequate. For a consequential delivery promise, the authority may need a full-network uncertainty model with supported distributions and dependence. The manager should not invent a correction factor based solely on the number of paths. Such a factor would add another unsupported model. The correct next step is an appropriate method and evidence, or a narrower commitment.

The report therefore retains the conditional mean dates and labels the selected-path approximation precisely. It states that the publication supplies no whole-project probability. This qualification is meaningful even when the displayed percentages happen to match. Numerical similarity does not prove equivalence of the events being measured. The case illustrates a communication and method-selection issue rather than a new frozen probability calculation. Its transferable lesson is to define the event before comparing confidence claims.

The required uncertainty analysis follows the consequence of reliance. A local sequencing discussion may need a deterministic comparison with clear limits. A resource reservation may need scenarios around readiness and availability. A public delivery promise or major investment may require a more complete uncertainty model and domain evidence. The small app is not defective because it does not answer every question. It becomes misleading when its narrow output is used for a broader claim without the additional analysis the decision requires.

The fictional uncertainty register is completed by representation type. SUPPLY-VARIATION retains a duration range under a fixed equipment scope. CONFIGURATION-CHOICE records mutually exclusive equipment concepts and therefore needs alternative work definitions. TEST-DISPOSITION records a possible rejection and an unresolved correction obligation. INSPECTION-COVERAGE records uncertainty about executable capacity. The manager refuses to absorb all four into a longer supply duration: that edit would place the consequence on the wrong activity and imply that elapsed waiting settles configuration, quality and capacity. The register states a separate next instrument for each entry, without adding a probability or a new numerical case to the frozen studies.

A sensitivity should change a declared assumption and preserve the comparison basis. The frozen studies isolate topology, supply estimates, an inserted gate, tied branches and the deadline. This helps a reader identify the cause of an output change. Real alternatives may change several assumptions together; those can be useful scenarios, but their interpretation should acknowledge the combined changes. A difference between broad scenarios is not automatically attributable to one named intervention.

The uncertainty communication test compares two fictional requests made from the same network. The planner wants to prioritise attention between branches; the operator wants a dependable shutdown promise. For the first request, the selected-path reading can identify a conditional sensitivity alongside competing routes. For the second, the manager records that dependence, resource availability and acceptance outcomes are not represented, so the printed reading cannot answer the requested event. The packet keeps the computation available and changes the claim presented to each audience. Its contribution is an event-to-method test: a number is informative when the event it calculates matches the decision question, not merely when its label contains the word probability.

A completed method-routing note makes the remaining work finite. Branch attention goes to the existing forward and backward dates. The shutdown commitment goes to an assessment of the whole release system, with distributions and dependence justified if a probability is required. Configuration choice goes to a scope decision before any timing model is strengthened. A missing inspection booking goes to resource confirmation rather than a more elaborate duration distribution. This ordering prevents expensive uncertainty analysis from compensating for an unresolved categorical prerequisite. It also identifies when further numerical analysis adds little: if a decisive operating condition already holds the proposed commitment, resolve that condition before refining a percentage that cannot release it.