B.3:6 - Worked cases

B.3:6.1 - Fully calculated case: two necessary independent conditions

Target claim: “The protection function succeeds on a demand.” Assurance use: a bounded reliability argument for a named design decision.

The domain model says that both independently tested conditions must succeed: sensor detection and actuator response. Each has estimated probability 0.9 under the same stated demand class and qualification window. Under the declared independence assumption, the joint probability is:

0.9 × 0.9 = 0.81

Using min(0.9, 0.9) = 0.9 would overstate this conjunction. If the conditions are dependent, even the product is not justified; the result must use the applicable conditional model or remain unresolved. The B.3 result therefore cites the two domain results, the series dependency structure, independence basis, product calculation, 0.81 conclusion, limitations, and the observation that reopens the independence assumption.

What changes in practice: the design decision is evaluated against 0.81, not a falsely “conservative” 0.9. No universal B.3 reliability formula is created.

B.3:6.2 - Routed-away case: dashboard status

Starting sentence: “The dashboard approves launch.”

The dashboard is a publication face. Suppose it displays GateDecision GD-17, which records that a named gate passed for release candidate R. The repaired sentence is: “The dashboard shows GateDecision GD-17 for release candidate R; the decision, not the display, records that the gate passed.”

Use A.21 and the release or permission pattern that consumes the gate decision. No assurance claim is present, so B.3 stops. If the dashboard does not resolve an exact gate decision, it is only a cue and launch approval remains unresolved.

B.3:6.3 - Episteme credibility with a compact result

Target claim: “Model edition M predicts response Y within the declared operating region.” Assurance use: whether an engineer may use that prediction as one input to a reversible design comparison.

The engineer cites the exact model claim, its empirical-validation result, A.2.4 first-use classification and the direct support relation actually used, the A.10 provenance path, the operating region, and the expiry condition. No combination of unlike characteristics is needed. The compact disposition is supported-for-use, limited to the reversible comparison; release, safety, and operation are expressly not carried. No dated assessment Work or reusable record is added because the use does not depend on who performed the already cited validation.

B.3:6.4 - Order-sensitive Method case

An assurance argument relies on a manufacturing sequence whose result changes when two steps are reversed. Recover the B.1.5 composition, order and join conditions and any actual A.15.1 Work the argument consumes. Those direct results may answer the assurance question. Use A.22 only if a separately selected organization contributes another needed premise; then identify its constituents, obtaining relations, applied constraints and use frame. The assurance result cites only the results and structure it actually relies on.